[1] | 1 | // HelicityMatrixElements.cc is a part of the PYTHIA event generator. |
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| 2 | // Copyright (C) 2012 Philip Ilten, Torbjorn Sjostrand. |
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| 3 | // PYTHIA is licenced under the GNU GPL version 2, see COPYING for details. |
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| 4 | // Please respect the MCnet Guidelines, see GUIDELINES for details. |
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| 5 | |
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| 6 | // Function definitions (not found in the header) for physics classes |
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| 7 | // used in tau decays. |
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| 8 | |
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| 9 | #include "HelicityMatrixElements.h" |
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| 10 | |
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| 11 | namespace Pythia8 { |
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| 12 | |
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| 13 | //========================================================================== |
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| 14 | |
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| 15 | // The HelicityMatrixElements class. |
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| 16 | |
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| 17 | //-------------------------------------------------------------------------- |
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| 18 | |
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| 19 | // Initialize the helicity matrix element. |
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| 20 | |
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| 21 | void HelicityMatrixElement::initPointers(ParticleData* particleDataPtrIn, |
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| 22 | Couplings* couplingsPtrIn) { |
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| 23 | |
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| 24 | particleDataPtr = particleDataPtrIn; |
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| 25 | couplingsPtr = couplingsPtrIn; |
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| 26 | for(int i = 0; i <= 5; i++) |
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| 27 | gamma.push_back(GammaMatrix(i)); |
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| 28 | |
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| 29 | } |
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| 30 | |
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| 31 | //-------------------------------------------------------------------------- |
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| 32 | |
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| 33 | // Initialize the channel for the helicity matrix element. |
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| 34 | |
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| 35 | HelicityMatrixElement* HelicityMatrixElement::initChannel( |
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| 36 | vector<HelicityParticle>& p) { |
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| 37 | |
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| 38 | pID.clear(); |
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| 39 | pM.clear(); |
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| 40 | for(int i = 0; i < static_cast<int>(p.size()); i++) { |
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| 41 | pID.push_back(p[i].id()); |
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| 42 | pM.push_back(p[i].m()); |
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| 43 | } |
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| 44 | initConstants(); |
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| 45 | return this; |
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| 46 | |
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| 47 | } |
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| 48 | |
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| 49 | //-------------------------------------------------------------------------- |
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| 50 | |
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| 51 | // Calculate a particle's decay matrix. |
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| 52 | |
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| 53 | void HelicityMatrixElement::calculateD(vector<HelicityParticle>& p) { |
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| 54 | |
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| 55 | // Reset the D matrix to zero. |
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| 56 | for (int i = 0; i < p[0].spinStates(); i++) { |
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| 57 | for (int j = 0; j < p[0].spinStates(); j++) { |
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| 58 | p[0].D[i][j] = 0; |
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| 59 | } |
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| 60 | } |
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| 61 | |
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| 62 | // Initialize the wave functions. |
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| 63 | initWaves(p); |
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| 64 | |
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| 65 | // Create the helicity vectors. |
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| 66 | vector<int> h1(p.size(),0); |
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| 67 | vector<int> h2(p.size(),0); |
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| 68 | |
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| 69 | // Call the recursive sub-method. |
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| 70 | calculateD(p, h1, h2, 0); |
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| 71 | |
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| 72 | // Normalize the decay matrix. |
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| 73 | p[0].normalize(p[0].D); |
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| 74 | |
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| 75 | } |
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| 76 | |
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| 77 | //-------------------------------------------------------------------------- |
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| 78 | |
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| 79 | // Recursive sub-method for calculating a particle's decay matrix. |
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| 80 | |
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| 81 | void HelicityMatrixElement::calculateD(vector<HelicityParticle>& p, |
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| 82 | vector<int>& h1, vector<int>& h2, unsigned int i) { |
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| 83 | |
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| 84 | if (i < p.size()) { |
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| 85 | for (h1[i] = 0; h1[i] < p[i].spinStates(); h1[i]++) { |
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| 86 | for (h2[i] = 0; h2[i] < p[i].spinStates(); h2[i]++) { |
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| 87 | calculateD(p, h1, h2, i+1); |
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| 88 | } |
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| 89 | } |
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| 90 | } |
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| 91 | else { |
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| 92 | p[0].D[h1[0]][h2[0]] += calculateME(h1) * conj(calculateME(h2)) * |
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| 93 | calculateProductD(p, h1, h2); |
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| 94 | } |
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| 95 | |
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| 96 | } |
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| 97 | |
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| 98 | //-------------------------------------------------------------------------- |
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| 99 | |
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| 100 | // Calculate a particle's helicity density matrix. |
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| 101 | |
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| 102 | void HelicityMatrixElement::calculateRho(unsigned int idx, |
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| 103 | vector<HelicityParticle>& p) { |
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| 104 | |
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| 105 | // Reset the rho matrix to zero. |
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| 106 | for (int i = 0; i < p[idx].spinStates(); i++) { |
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| 107 | for (int j = 0; j < p[idx].spinStates(); j++) { |
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| 108 | p[idx].rho[i][j] = 0; |
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| 109 | } |
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| 110 | } |
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| 111 | |
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| 112 | // Initialize the wave functions. |
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| 113 | initWaves(p); |
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| 114 | |
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| 115 | // Create the helicity vectors. |
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| 116 | vector<int> h1(p.size(),0); |
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| 117 | vector<int> h2(p.size(),0); |
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| 118 | |
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| 119 | // Call the recursive sub-method. |
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| 120 | calculateRho(idx, p, h1, h2, 0); |
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| 121 | |
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| 122 | // Normalize the density matrix. |
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| 123 | p[idx].normalize(p[idx].rho); |
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| 124 | |
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| 125 | } |
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| 126 | |
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| 127 | //-------------------------------------------------------------------------- |
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| 128 | |
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| 129 | // Recursive sub-method for calculating a particle's helicity density matrix. |
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| 130 | |
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| 131 | void HelicityMatrixElement::calculateRho(unsigned int idx, |
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| 132 | vector<HelicityParticle>& p, vector<int>& h1, vector<int>& h2, |
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| 133 | unsigned int i) { |
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| 134 | |
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| 135 | if (i < p.size()) { |
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| 136 | for (h1[i] = 0; h1[i] < p[i].spinStates(); h1[i]++) { |
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| 137 | for (h2[i] = 0; h2[i] < p[i].spinStates(); h2[i]++) { |
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| 138 | calculateRho(idx, p, h1, h2, i+1); |
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| 139 | } |
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| 140 | } |
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| 141 | } |
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| 142 | else { |
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| 143 | // Calculate rho from a hard process. |
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| 144 | if (p[1].direction < 0) |
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| 145 | p[idx].rho[h1[idx]][h2[idx]] += p[0].rho[h1[0]][h2[0]] * |
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| 146 | p[1].rho[h1[1]][h2[1]] * calculateME(h1)*conj(calculateME(h2)) * |
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| 147 | calculateProductD(idx, 2, p, h1, h2); |
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| 148 | // Calculate rho from a decay. |
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| 149 | else |
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| 150 | p[idx].rho[h1[idx]][h2[idx]] += p[0].rho[h1[0]][h2[0]] * |
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| 151 | calculateME(h1)*conj(calculateME(h2)) * |
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| 152 | calculateProductD(idx, 1, p, h1, h2); |
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| 153 | return; |
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| 154 | } |
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| 155 | |
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| 156 | } |
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| 157 | |
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| 158 | //-------------------------------------------------------------------------- |
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| 159 | |
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| 160 | // Calculate a decay's weight. |
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| 161 | |
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| 162 | double HelicityMatrixElement::decayWeight(vector<HelicityParticle>& p) { |
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| 163 | |
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| 164 | complex weight = complex(0,0); |
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| 165 | |
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| 166 | // Initialize the wave functions. |
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| 167 | initWaves(p); |
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| 168 | |
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| 169 | // Create the helicity vectors. |
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| 170 | vector<int> h1(p.size(),0); |
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| 171 | vector<int> h2(p.size(),0); |
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| 172 | |
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| 173 | // Call the recursive sub-method. |
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| 174 | decayWeight(p, h1, h2, weight, 0); |
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| 175 | |
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| 176 | return real(weight); |
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| 177 | |
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| 178 | } |
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| 179 | |
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| 180 | //-------------------------------------------------------------------------- |
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| 181 | |
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| 182 | // Recursive sub-method for calculating a decay's weight. |
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| 183 | |
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| 184 | void HelicityMatrixElement::decayWeight(vector<HelicityParticle>& p, |
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| 185 | vector<int>& h1, vector<int>& h2, complex& weight, unsigned int i) { |
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| 186 | |
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| 187 | if (i < p.size()) { |
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| 188 | for (h1[i] = 0; h1[i] < p[i].spinStates(); h1[i]++) { |
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| 189 | for (h2[i] = 0; h2[i] < p[i].spinStates(); h2[i]++) { |
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| 190 | decayWeight(p, h1, h2, weight, i+1); |
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| 191 | } |
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| 192 | } |
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| 193 | } |
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| 194 | else { |
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| 195 | weight += p[0].rho[h1[0]][h2[0]] * calculateME(h1) * |
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| 196 | conj(calculateME(h2)) * calculateProductD(p, h1, h2); |
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| 197 | } |
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| 198 | |
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| 199 | } |
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| 200 | |
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| 201 | //-------------------------------------------------------------------------- |
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| 202 | |
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| 203 | // Calculate the product of the decay matrices (hard process). |
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| 204 | |
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| 205 | complex HelicityMatrixElement::calculateProductD(unsigned int idx, |
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| 206 | unsigned int start, vector<HelicityParticle>& p, |
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| 207 | vector<int>& h1, vector<int>& h2) { |
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| 208 | |
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| 209 | complex answer(1,0); |
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| 210 | for (unsigned int i = start; i < p.size(); i++) { |
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| 211 | if (i != idx) { |
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| 212 | answer *= p[i].D[h1[i]][h2[i]]; |
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| 213 | } |
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| 214 | } |
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| 215 | return answer; |
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| 216 | |
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| 217 | } |
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| 218 | |
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| 219 | //-------------------------------------------------------------------------- |
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| 220 | |
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| 221 | // Calculate the product of the decay matrices (decay process). |
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| 222 | |
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| 223 | complex HelicityMatrixElement::calculateProductD( |
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| 224 | vector<HelicityParticle>& p, vector<int>& h1, vector<int>& h2) { |
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| 225 | |
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| 226 | complex answer(1,0); |
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| 227 | for (unsigned int i = 1; i < p.size(); i++) { |
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| 228 | answer *= p[i].D[h1[i]][h2[i]]; |
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| 229 | } |
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| 230 | return answer; |
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| 231 | |
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| 232 | } |
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| 233 | |
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| 234 | //-------------------------------------------------------------------------- |
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| 235 | |
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| 236 | // Initialize a fermion line. |
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| 237 | |
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| 238 | void HelicityMatrixElement::setFermionLine(int position, |
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| 239 | HelicityParticle& p0, HelicityParticle& p1) { |
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| 240 | |
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| 241 | vector< Wave4 > u0, u1; |
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| 242 | |
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| 243 | // First particle is incoming and particle, or outgoing and anti-particle. |
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| 244 | if (p0.id()*p0.direction < 0) { |
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| 245 | pMap[position] = position; pMap[position+1] = position+1; |
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| 246 | for (int h = 0; h < p0.spinStates(); h++) u0.push_back(p0.wave(h)); |
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| 247 | for (int h = 0; h < p1.spinStates(); h++) u1.push_back(p1.waveBar(h)); |
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| 248 | } |
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| 249 | // First particle is outgoing and particle, or incoming and anti-particle. |
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| 250 | else { |
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| 251 | pMap[position] = position+1; pMap[position+1] = position; |
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| 252 | for (int h = 0; h < p0.spinStates(); h++) u1.push_back(p0.waveBar(h)); |
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| 253 | for (int h = 0; h < p1.spinStates(); h++) u0.push_back(p1.wave(h)); |
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| 254 | } |
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| 255 | u.push_back(u0); u.push_back(u1); |
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| 256 | |
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| 257 | } |
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| 258 | |
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| 259 | //-------------------------------------------------------------------------- |
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| 260 | |
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| 261 | // Return a fixed width Breit-Wigner. |
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| 262 | |
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| 263 | complex HelicityMatrixElement::breitWigner(double s, double M, double G) { |
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| 264 | |
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| 265 | return (-M * M + complex(0, 1) * M * G) / (s - M * M + complex(0, 1) * M * G); |
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| 266 | |
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| 267 | } |
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| 268 | |
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| 269 | //-------------------------------------------------------------------------- |
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| 270 | |
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| 271 | // Return an s-wave BreitWigner. |
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| 272 | |
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| 273 | complex HelicityMatrixElement::sBreitWigner(double m0, double m1, double s, |
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| 274 | double M, double G) { |
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| 275 | |
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| 276 | double gs = sqrtpos((s - pow2(m0+m1)) * (s - pow2(m0-m1))) / (2*sqrtpos(s)); |
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| 277 | double gM = sqrtpos((M*M - pow2(m0+m1)) * (M*M - pow2(m0-m1))) / (2*M); |
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| 278 | return M*M / (M*M - s - complex(0,1)*G*M*M/sqrtpos(s)*(gs/gM)); |
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| 279 | |
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| 280 | } |
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| 281 | |
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| 282 | //-------------------------------------------------------------------------- |
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| 283 | |
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| 284 | // Return a p-wave BreitWigner. |
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| 285 | |
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| 286 | complex HelicityMatrixElement::pBreitWigner(double m0, double m1, double s, |
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| 287 | double M, double G) { |
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| 288 | |
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| 289 | double gs = sqrtpos((s - pow2(m0+m1)) * (s - pow2(m0-m1))) / (2*sqrtpos(s)); |
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| 290 | double gM = sqrtpos((M*M - pow2(m0+m1)) * (M*M - pow2(m0-m1))) / (2*M); |
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| 291 | return M*M / (M*M - s - complex(0,1)*G*M*M/sqrtpos(s)*pow3(gs/gM)); |
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| 292 | |
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| 293 | } |
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| 294 | |
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| 295 | //-------------------------------------------------------------------------- |
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| 296 | |
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| 297 | // Return a d-wave BreitWigner. |
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| 298 | |
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| 299 | complex HelicityMatrixElement::dBreitWigner(double m0, double m1, double s, |
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| 300 | double M, double G) { |
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| 301 | |
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| 302 | double gs = sqrtpos((s - pow2(m0+m1)) * (s - pow2(m0-m1))) / (2*sqrtpos(s)); |
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| 303 | double gM = sqrtpos((M*M - pow2(m0+m1)) * (M*M - pow2(m0-m1))) / (2*M); |
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| 304 | return M*M / (M*M - s - complex(0,1)*G*M*M/sqrtpos(s)*pow5(gs/gM)); |
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| 305 | |
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| 306 | } |
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| 307 | |
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| 308 | //========================================================================== |
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| 309 | |
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| 310 | // Helicity matrix element for two fermions -> W -> two fermions. This matrix |
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| 311 | // element handles s-channel hard processes in addition to t-channel, assuming |
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| 312 | // the first two particles are a fermion line and the second two particles |
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| 313 | // are a fermion line. This matrix element is not scaled with respect to W |
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| 314 | // propagator energy as currently this matrix element is used only for |
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| 315 | // calculating helicity density matrices. |
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| 316 | |
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| 317 | //-------------------------------------------------------------------------- |
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| 318 | |
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| 319 | // Initialize spinors for the helicity matrix element. |
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| 320 | |
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| 321 | void HMETwoFermions2W2TwoFermions::initWaves(vector<HelicityParticle>& p) { |
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| 322 | |
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| 323 | u.clear(); |
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| 324 | pMap.resize(4); |
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| 325 | setFermionLine(0,p[0],p[1]); |
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| 326 | setFermionLine(2,p[2],p[3]); |
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| 327 | |
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| 328 | } |
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| 329 | |
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| 330 | //-------------------------------------------------------------------------- |
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| 331 | |
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| 332 | // Return element for the helicity matrix element. |
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| 333 | |
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| 334 | complex HMETwoFermions2W2TwoFermions::calculateME(vector<int> h) { |
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| 335 | |
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| 336 | complex answer(0,0); |
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| 337 | for (int mu = 0; mu <= 3; mu++) { |
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| 338 | answer += (u[1][h[pMap[1]]] * gamma[mu] * (1 - gamma[5]) |
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| 339 | * u[0][h[pMap[0]]]) * gamma[4](mu,mu) * (u[3][h[pMap[3]]] |
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| 340 | * gamma[mu] * (1 - gamma[5]) * u[2][h[pMap[2]]]); |
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| 341 | } |
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| 342 | return answer; |
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| 343 | |
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| 344 | } |
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| 345 | |
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| 346 | //========================================================================== |
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| 347 | |
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| 348 | // Helicity matrix element for two fermions -> photon -> two fermions. This |
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| 349 | // matrix element can be combined with the Z matrix element to provide full |
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| 350 | // interference effects. |
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| 351 | |
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| 352 | // p0Q: charge of the incoming fermion line |
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| 353 | // p2Q: charge of the outgoing fermion line |
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| 354 | // s: center of mass energy |
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| 355 | |
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| 356 | //-------------------------------------------------------------------------- |
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| 357 | |
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| 358 | // Initialize wave functions for the helicity matrix element. |
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| 359 | |
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| 360 | void HMETwoFermions2Gamma2TwoFermions::initWaves( |
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| 361 | vector<HelicityParticle>& p) { |
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| 362 | |
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| 363 | u.clear(); |
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| 364 | pMap.resize(4); |
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| 365 | setFermionLine(0, p[0], p[1]); |
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| 366 | setFermionLine(2, p[2], p[3]); |
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| 367 | s = max( 1., pow2(p[4].m())); |
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| 368 | p0Q = p[0].charge(); p2Q = p[2].charge(); |
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| 369 | |
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| 370 | } |
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| 371 | |
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| 372 | //-------------------------------------------------------------------------- |
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| 373 | |
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| 374 | // Return element for the helicity matrix element. |
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| 375 | |
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| 376 | |
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| 377 | complex HMETwoFermions2Gamma2TwoFermions::calculateME(vector<int> h) { |
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| 378 | |
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| 379 | complex answer(0,0); |
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| 380 | for (int mu = 0; mu <= 3; mu++) { |
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| 381 | answer += (u[1][h[pMap[1]]] * gamma[mu] * u[0][h[pMap[0]]]) |
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| 382 | * gamma[4](mu,mu) * (u[3][h[pMap[3]]] * gamma[mu] * u[2][h[pMap[2]]]); |
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| 383 | } |
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| 384 | return p0Q*p2Q * answer / s; |
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| 385 | |
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| 386 | } |
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| 387 | |
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| 388 | //========================================================================== |
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| 389 | |
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| 390 | // Helicity matrix element for two fermions -> Z -> two fermions. This matrix |
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| 391 | // element can be combined with the photon matrix element to provide full |
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| 392 | // interference effects. |
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| 393 | |
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| 394 | // Note that there is a double contraction in the Z matrix element, which can |
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| 395 | // be very time consuming. If the two incoming fermions are oriented along |
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| 396 | // the z-axis, their helicities must be opposite for a non-zero matrix element |
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| 397 | // term. Consequently, this check is made to help speed up the matrix element. |
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| 398 | |
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| 399 | // sin2W: sine of the Weinberg angle |
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| 400 | // cos2W: cosine of the Weinberg angle |
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| 401 | // zM: on-shell mass of the Z |
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| 402 | // zG: on-shell width of the Z |
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| 403 | // p0CA: axial coupling of particle 0 to the Z |
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| 404 | // p2CA: axial coupling of particle 2 to the Z |
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| 405 | // p0CV: vector coupling of particle 0 to the Z |
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| 406 | // p2CV: vector coupling of particle 2 to the Z |
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| 407 | // zaxis: true if the incoming fermions are oriented along the z-axis |
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| 408 | |
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| 409 | //-------------------------------------------------------------------------- |
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| 410 | |
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| 411 | // Initialize the constant for the helicity matrix element. |
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| 412 | |
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| 413 | void HMETwoFermions2Z2TwoFermions::initConstants() { |
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| 414 | |
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| 415 | // Set the Weinberg angle. |
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| 416 | sin2W = couplingsPtr->sin2thetaW(); |
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| 417 | cos2W = couplingsPtr->cos2thetaW(); |
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| 418 | // Set the on-shell Z mass and width. |
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| 419 | zG = particleDataPtr->mWidth(23); |
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| 420 | zM = particleDataPtr->m0(23); |
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| 421 | // Set the vector and axial couplings to the fermions. |
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| 422 | p0CA = couplingsPtr->af(abs(pID[0])); |
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| 423 | p2CA = couplingsPtr->af(abs(pID[2])); |
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| 424 | p0CV = couplingsPtr->vf(abs(pID[0])); |
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| 425 | p2CV = couplingsPtr->vf(abs(pID[2])); |
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| 426 | |
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| 427 | } |
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| 428 | |
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| 429 | //-------------------------------------------------------------------------- |
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| 430 | |
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| 431 | // Initialize wave functions for the helicity matrix element. |
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| 432 | |
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| 433 | void HMETwoFermions2Z2TwoFermions::initWaves(vector<HelicityParticle>& p) { |
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| 434 | |
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| 435 | vector< Wave4 > u4; |
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| 436 | u.clear(); |
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| 437 | pMap.resize(4); |
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| 438 | setFermionLine(0, p[0], p[1]); |
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| 439 | setFermionLine(2, p[2], p[3]); |
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| 440 | u4.push_back(Wave4(p[2].p() + p[3].p())); |
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| 441 | u.push_back(u4); |
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| 442 | // Center of mass energy. |
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| 443 | s = max( 1., pow2(p[4].m())); |
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| 444 | // Check if incoming fermions are oriented along z-axis. |
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| 445 | zaxis = (p[0].pAbs() == fabs(p[0].pz())) && |
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| 446 | (p[1].pAbs() == fabs(p[1].pz())); |
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| 447 | |
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| 448 | } |
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| 449 | |
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| 450 | //-------------------------------------------------------------------------- |
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| 451 | |
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| 452 | // Return element for helicity matrix element. |
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| 453 | |
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| 454 | complex HMETwoFermions2Z2TwoFermions::calculateME(vector<int> h) { |
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| 455 | |
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| 456 | complex answer(0,0); |
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| 457 | // Return zero if correct helicity conditions. |
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| 458 | if (h[0] == h[1] && zaxis) return answer; |
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| 459 | for (int mu = 0; mu <= 3; mu++) { |
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| 460 | for (int nu = 0; nu <= 3; nu++) { |
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| 461 | answer += |
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| 462 | (u[1][h[pMap[1]]] * gamma[mu] * (p0CV - p0CA * gamma[5]) * |
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| 463 | u[0][h[pMap[0]]]) * |
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| 464 | (gamma[4](mu,nu) - gamma[4](mu,mu)*u[4][0](mu) * |
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| 465 | gamma[4](nu,nu) * u[4][0](nu) / (zM*zM)) * |
---|
| 466 | (u[3][h[pMap[3]]] * gamma[nu] * (p2CV - p2CA * gamma[5]) * |
---|
| 467 | u[2][h[pMap[2]]]); |
---|
| 468 | } |
---|
| 469 | } |
---|
| 470 | return answer / (16 * pow2(sin2W * cos2W) * |
---|
| 471 | (s - zM*zM + complex(0, s*zG/zM))); |
---|
| 472 | |
---|
| 473 | } |
---|
| 474 | |
---|
| 475 | //========================================================================== |
---|
| 476 | |
---|
| 477 | // Helicity matrix element for two fermions -> photon/Z -> two fermions. Full |
---|
| 478 | // interference is obtained by combining the photon and Z helicity matrix |
---|
| 479 | // elements. |
---|
| 480 | |
---|
| 481 | // In general the initPointers and initChannel methods should not be |
---|
| 482 | // redeclared. |
---|
| 483 | |
---|
| 484 | //-------------------------------------------------------------------------- |
---|
| 485 | |
---|
| 486 | // Initialize the matrix element. |
---|
| 487 | |
---|
| 488 | void HMETwoFermions2GammaZ2TwoFermions::initPointers( |
---|
| 489 | ParticleData* particleDataPtrIn, Couplings* couplingsPtrIn) { |
---|
| 490 | |
---|
| 491 | zHME.initPointers(particleDataPtrIn, couplingsPtrIn); |
---|
| 492 | gHME.initPointers(particleDataPtrIn, couplingsPtrIn); |
---|
| 493 | |
---|
| 494 | } |
---|
| 495 | |
---|
| 496 | //-------------------------------------------------------------------------- |
---|
| 497 | |
---|
| 498 | // Initialize the channel for the helicity matrix element. |
---|
| 499 | |
---|
| 500 | HelicityMatrixElement* HMETwoFermions2GammaZ2TwoFermions::initChannel( |
---|
| 501 | vector<HelicityParticle>& p) { |
---|
| 502 | |
---|
| 503 | zHME.initChannel(p); |
---|
| 504 | zHME.initChannel(p); |
---|
| 505 | return this; |
---|
| 506 | |
---|
| 507 | } |
---|
| 508 | |
---|
| 509 | //-------------------------------------------------------------------------- |
---|
| 510 | |
---|
| 511 | // Initialize wave functions for the helicity matrix element. |
---|
| 512 | |
---|
| 513 | void HMETwoFermions2GammaZ2TwoFermions::initWaves( |
---|
| 514 | vector<HelicityParticle>& p) { |
---|
| 515 | |
---|
| 516 | zHME.initWaves(p); |
---|
| 517 | gHME.initWaves(p); |
---|
| 518 | |
---|
| 519 | } |
---|
| 520 | |
---|
| 521 | //-------------------------------------------------------------------------- |
---|
| 522 | |
---|
| 523 | // Return element for the helicity matrix element. |
---|
| 524 | |
---|
| 525 | complex HMETwoFermions2GammaZ2TwoFermions::calculateME(vector<int> h) { |
---|
| 526 | |
---|
| 527 | return zHME.calculateME(h) + gHME.calculateME(h); |
---|
| 528 | |
---|
| 529 | } |
---|
| 530 | |
---|
| 531 | //========================================================================== |
---|
| 532 | |
---|
| 533 | // Helicity matrix element for Z -> two fermions. |
---|
| 534 | |
---|
| 535 | // Helicity matrix element for Z -> two fermions. This matrix element is used |
---|
| 536 | // when the production of the Z is from an unknown process. |
---|
| 537 | |
---|
| 538 | // p2CA: axial coupling of particle 2 to the Z |
---|
| 539 | // p2CV: vector coupling of particle 2 to the Z |
---|
| 540 | |
---|
| 541 | //-------------------------------------------------------------------------- |
---|
| 542 | |
---|
| 543 | // Initialize the constant for the helicity matrix element. |
---|
| 544 | |
---|
| 545 | void HMEZ2TwoFermions::initConstants() { |
---|
| 546 | |
---|
| 547 | // Set the vector and axial couplings to the fermions. |
---|
| 548 | p2CA = couplingsPtr->af(abs(pID[2])); |
---|
| 549 | p2CV = couplingsPtr->vf(abs(pID[2])); |
---|
| 550 | |
---|
| 551 | } |
---|
| 552 | |
---|
| 553 | //-------------------------------------------------------------------------- |
---|
| 554 | |
---|
| 555 | // Initialize wave functions for the helicity matrix element. |
---|
| 556 | |
---|
| 557 | void HMEZ2TwoFermions::initWaves(vector<HelicityParticle>& p) { |
---|
| 558 | |
---|
| 559 | u.clear(); |
---|
| 560 | pMap.resize(4); |
---|
| 561 | // Initialize Z wave function. |
---|
| 562 | vector< Wave4 > u1; |
---|
| 563 | pMap[1] = 1; |
---|
| 564 | for (int h = 0; h < p[pMap[1]].spinStates(); h++) |
---|
| 565 | u1.push_back(p[pMap[1]].wave(h)); |
---|
| 566 | u.push_back(u1); |
---|
| 567 | // Initialize fermion wave functions. |
---|
| 568 | setFermionLine(2, p[2], p[3]); |
---|
| 569 | |
---|
| 570 | } |
---|
| 571 | |
---|
| 572 | //-------------------------------------------------------------------------- |
---|
| 573 | |
---|
| 574 | // Return element for helicity matrix element. |
---|
| 575 | |
---|
| 576 | complex HMEZ2TwoFermions::calculateME(vector<int> h) { |
---|
| 577 | |
---|
| 578 | complex answer(0,0); |
---|
| 579 | for (int mu = 0; mu <= 3; mu++) { |
---|
| 580 | answer += |
---|
| 581 | u[0][h[pMap[1]]](mu) * (u[2][h[pMap[3]]] * gamma[mu] |
---|
| 582 | * (p2CV - p2CA * gamma[5]) * u[1][h[pMap[2]]]); |
---|
| 583 | } |
---|
| 584 | return answer; |
---|
| 585 | } |
---|
| 586 | |
---|
| 587 | //========================================================================== |
---|
| 588 | |
---|
| 589 | // Helicity matrix element for the decay of a CP even Higgs to two fermions. |
---|
| 590 | // All SM and MSSM Higgses couple to fermions with a vertex factor of |
---|
| 591 | // (pfCV - pfCA * gamma[5]) where pf indicates the type of fermion line. For |
---|
| 592 | // simplicity for the SM and MSSM CP even Higgses pfCV is set to one, and |
---|
| 593 | // pfCA to zero, as this matrix element is used only for calculating helicity |
---|
| 594 | // density matrices. |
---|
| 595 | |
---|
| 596 | // p2CA: in the SM and MSSM this coupling is zero |
---|
| 597 | // p2CV: in the SM and MSSM this coupling is given by: |
---|
| 598 | // i * g_w * m_f / (2 * m_W) |
---|
| 599 | // * -1 for the SM H |
---|
| 600 | // * -sin(alpha) / sin(beta) for H^0 u-type |
---|
| 601 | // * -cos(alpha) / cos(beta) for H^0 d-type |
---|
| 602 | // * -cos(alpha) / sin(beta) for h^0 u-type |
---|
| 603 | // * sin(alpha) / cos(beta) for h^0 d-type |
---|
| 604 | |
---|
| 605 | //-------------------------------------------------------------------------- |
---|
| 606 | |
---|
| 607 | // Initialize wave functions for the helicity matrix element. |
---|
| 608 | |
---|
| 609 | void HMEHiggsEven2TwoFermions::initWaves(vector<HelicityParticle>& p) { |
---|
| 610 | |
---|
| 611 | u.clear(); |
---|
| 612 | pMap.resize(4); |
---|
| 613 | p2CA = 0; p2CV = 1; |
---|
| 614 | setFermionLine(2, p[2], p[3]); |
---|
| 615 | |
---|
| 616 | } |
---|
| 617 | |
---|
| 618 | //-------------------------------------------------------------------------- |
---|
| 619 | |
---|
| 620 | // Return element for the helicity matrix element. |
---|
| 621 | |
---|
| 622 | complex HMEHiggsEven2TwoFermions::calculateME(vector<int> h) { |
---|
| 623 | |
---|
| 624 | return (u[1][h[pMap[3]]] * (p2CV - p2CA * gamma[5]) * u[0][h[pMap[2]]]); |
---|
| 625 | |
---|
| 626 | } |
---|
| 627 | |
---|
| 628 | //========================================================================== |
---|
| 629 | |
---|
| 630 | // Helicity matrix element for the decay of a CP odd Higgs to two fermions. |
---|
| 631 | // See HMEHiggsEven2TwoFermions for more details. For the MSSM CP odd Higgs |
---|
| 632 | // pfCA is set to one and pfCV is set to zero. |
---|
| 633 | |
---|
| 634 | // p2CA: in the MSSM this coupling is given by: |
---|
| 635 | // -g_w * m_f / (2 * m_W) |
---|
| 636 | // * cot(beta) for A^0 u-type |
---|
| 637 | // * tan(beta) for A^0 d-type |
---|
| 638 | // p2CV: in the MSSM this coupling is zero |
---|
| 639 | |
---|
| 640 | //-------------------------------------------------------------------------- |
---|
| 641 | |
---|
| 642 | // Initialize wave functions for the helicity matrix element. |
---|
| 643 | |
---|
| 644 | void HMEHiggsOdd2TwoFermions::initWaves(vector<HelicityParticle>& p) { |
---|
| 645 | |
---|
| 646 | u.clear(); |
---|
| 647 | pMap.resize(4); |
---|
| 648 | p2CA = 1; p2CV = 0; |
---|
| 649 | setFermionLine(2, p[2], p[3]); |
---|
| 650 | |
---|
| 651 | } |
---|
| 652 | |
---|
| 653 | //-------------------------------------------------------------------------- |
---|
| 654 | |
---|
| 655 | // Return element for the helicity matrix element. |
---|
| 656 | |
---|
| 657 | complex HMEHiggsOdd2TwoFermions::calculateME(vector<int> h) { |
---|
| 658 | |
---|
| 659 | return (u[1][h[pMap[3]]] * (p2CV - p2CA * gamma[5]) * u[0][h[pMap[2]]]); |
---|
| 660 | |
---|
| 661 | } |
---|
| 662 | |
---|
| 663 | //========================================================================== |
---|
| 664 | |
---|
| 665 | // Helicity matrix element for the decay of a charged Higgs to two fermions. |
---|
| 666 | // See HMEHiggsEven2TwoFermions for more details. For the MSSM charged Higgs |
---|
| 667 | // pfCA is set to +/- one given an H^+/- and pfCV is set to one. |
---|
| 668 | |
---|
| 669 | // p2CA: in the MSSM this coupling is given by: |
---|
| 670 | // i * g / (sqrt(8) * m_W) * (m_d * tan(beta) + m_u * cot(beta)) |
---|
| 671 | // p2CV: in the MSSM this coupling is given by: |
---|
| 672 | // +/- i * g / (sqrt(8) * m_W) * (m_d * tan(beta) - m_u * cot(beta)) |
---|
| 673 | |
---|
| 674 | //-------------------------------------------------------------------------- |
---|
| 675 | |
---|
| 676 | // Initialize wave functions for the helicity matrix element. |
---|
| 677 | |
---|
| 678 | void HMEHiggsCharged2TwoFermions::initWaves(vector<HelicityParticle>& p) { |
---|
| 679 | |
---|
| 680 | u.clear(); |
---|
| 681 | pMap.resize(4); |
---|
| 682 | p2CV = 1; |
---|
| 683 | if (pID[3] == 15 || pID[3] == -16) p2CA = 1; |
---|
| 684 | else p2CA = -1; |
---|
| 685 | setFermionLine(2, p[2], p[3]); |
---|
| 686 | |
---|
| 687 | } |
---|
| 688 | |
---|
| 689 | //-------------------------------------------------------------------------- |
---|
| 690 | |
---|
| 691 | // Return element for the helicity matrix element. |
---|
| 692 | |
---|
| 693 | complex HMEHiggsCharged2TwoFermions::calculateME(vector<int> h) { |
---|
| 694 | |
---|
| 695 | return (u[1][h[pMap[3]]] * (p2CV - p2CA * gamma[5]) * u[0][h[pMap[2]]]); |
---|
| 696 | |
---|
| 697 | } |
---|
| 698 | |
---|
| 699 | //========================================================================== |
---|
| 700 | |
---|
| 701 | // Helicity matrix element which provides an unpolarized helicity |
---|
| 702 | // density matrix. This matrix element is used for unkown hard processes. |
---|
| 703 | |
---|
| 704 | // Note that calculateRho is redefined for this special case, but that in |
---|
| 705 | // general calculateRho should not be redefined. |
---|
| 706 | |
---|
| 707 | //-------------------------------------------------------------------------- |
---|
| 708 | |
---|
| 709 | // Calculate a particle's helicity density matrix. |
---|
| 710 | |
---|
| 711 | void HMEUnpolarized::calculateRho(unsigned int idx, |
---|
| 712 | vector<HelicityParticle>& p) { |
---|
| 713 | |
---|
| 714 | for (int i = 0; i < p[idx].spinStates(); i++ ) { |
---|
| 715 | for (int j = 1; j < p[idx].spinStates(); j++) { |
---|
| 716 | if (i == j) p[idx].rho[i][j] = 1.0 / |
---|
| 717 | static_cast<double>(p[idx].spinStates()); |
---|
| 718 | else p[idx].rho[i][j] = 0; |
---|
| 719 | } |
---|
| 720 | } |
---|
| 721 | |
---|
| 722 | } |
---|
| 723 | |
---|
| 724 | //========================================================================== |
---|
| 725 | |
---|
| 726 | // Base class for all tau decay matrix elements. This class derives from |
---|
| 727 | // the HelicityMatrixElement class and redefines some of the virtual functions. |
---|
| 728 | |
---|
| 729 | // One new method, initHadronicCurrent is defined which initializes the |
---|
| 730 | // hadronic current in the initWaves method. For each tau decay matrix element |
---|
| 731 | // the hadronic current method must be redefined accordingly, but initWaves |
---|
| 732 | // should not be redefined. |
---|
| 733 | |
---|
| 734 | //-------------------------------------------------------------------------- |
---|
| 735 | |
---|
| 736 | // Initialize wave functions for the helicity matrix element. |
---|
| 737 | void HMETauDecay::initWaves(vector<HelicityParticle>& p) { |
---|
| 738 | |
---|
| 739 | u.clear(); |
---|
| 740 | pMap.resize(p.size()); |
---|
| 741 | setFermionLine(0, p[0], p[1]); |
---|
| 742 | initHadronicCurrent(p); |
---|
| 743 | |
---|
| 744 | } |
---|
| 745 | |
---|
| 746 | //-------------------------------------------------------------------------- |
---|
| 747 | |
---|
| 748 | // Return element for the helicity matrix element. |
---|
| 749 | complex HMETauDecay::calculateME(vector<int> h) { |
---|
| 750 | |
---|
| 751 | complex answer(0,0); |
---|
| 752 | for (int mu = 0; mu <= 3; mu++) { |
---|
| 753 | answer += |
---|
| 754 | (u[1][h[pMap[1]]] * gamma[mu] * (1 - gamma[5]) * u[0][h[pMap[0]]]) |
---|
| 755 | * gamma[4](mu,mu) * u[2][0](mu); |
---|
| 756 | } |
---|
| 757 | return answer; |
---|
| 758 | |
---|
| 759 | } |
---|
| 760 | |
---|
| 761 | //-------------------------------------------------------------------------- |
---|
| 762 | |
---|
| 763 | // Return the maximum decay weight for the helicity matrix element. |
---|
| 764 | |
---|
| 765 | double HMETauDecay::decayWeightMax(vector<HelicityParticle>& p) { |
---|
| 766 | |
---|
| 767 | // Determine the maximum on-diagonal element of rho. |
---|
| 768 | double on = real(p[0].rho[0][0]) > real(p[0].rho[1][1]) ? |
---|
| 769 | real(p[0].rho[0][0]) : real(p[0].rho[1][1]); |
---|
| 770 | // Determine the maximum off-diagonal element of rho. |
---|
| 771 | double off = fabs(real(p[0].rho[0][1])) + fabs(imag(p[0].rho[0][1])); |
---|
| 772 | return DECAYWEIGHTMAX * (on + off); |
---|
| 773 | |
---|
| 774 | } |
---|
| 775 | |
---|
| 776 | //-------------------------------------------------------------------------- |
---|
| 777 | |
---|
| 778 | // Calculate complex resonance weights given a phase and amplitude vector. |
---|
| 779 | |
---|
| 780 | void HMETauDecay::calculateResonanceWeights(vector<double>& phase, |
---|
| 781 | vector<double>& amplitude, vector<complex>& weight) { |
---|
| 782 | |
---|
| 783 | for (unsigned int i = 0; i < phase.size(); i++) |
---|
| 784 | weight.push_back(amplitude[i] * (cos(phase[i]) + |
---|
| 785 | complex(0,1) * sin(phase[i]))); |
---|
| 786 | |
---|
| 787 | } |
---|
| 788 | |
---|
| 789 | //========================================================================== |
---|
| 790 | |
---|
| 791 | // Tau decay matrix element for tau decay into a single scalar meson. |
---|
| 792 | |
---|
| 793 | // The maximum decay weight for this matrix element can be found analytically |
---|
| 794 | // to be 4 * m_tau^2 * (m_tau^2 - m_meson^2). However, because m_tau >> m_meson |
---|
| 795 | // for the relevant tau decay channels, this expression is approximated by |
---|
| 796 | // m_tau^4. |
---|
| 797 | |
---|
| 798 | //-------------------------------------------------------------------------- |
---|
| 799 | |
---|
| 800 | // Initialize constants for the helicity matrix element. |
---|
| 801 | |
---|
| 802 | void HMETau2Meson::initConstants() { |
---|
| 803 | |
---|
| 804 | DECAYWEIGHTMAX = 4*pow4(pM[0]); |
---|
| 805 | |
---|
| 806 | } |
---|
| 807 | |
---|
| 808 | //-------------------------------------------------------------------------- |
---|
| 809 | |
---|
| 810 | // Initialize the hadronic current for the helicity matrix element. |
---|
| 811 | |
---|
| 812 | void HMETau2Meson::initHadronicCurrent(vector<HelicityParticle>& p) { |
---|
| 813 | |
---|
| 814 | vector< Wave4 > u2; |
---|
| 815 | pMap[2] = 2; |
---|
| 816 | u2.push_back(Wave4(p[2].p())); |
---|
| 817 | u.push_back(u2); |
---|
| 818 | |
---|
| 819 | } |
---|
| 820 | |
---|
| 821 | //========================================================================== |
---|
| 822 | |
---|
| 823 | // Tau decay matrix element for tau decay into two leptons. Because there is |
---|
| 824 | // no hadronic current, but rather a leptonic current, the calculateME and |
---|
| 825 | // initWaves methods must be redefined. |
---|
| 826 | |
---|
| 827 | //-------------------------------------------------------------------------- |
---|
| 828 | |
---|
| 829 | // Initialize constants for the helicity matrix element. |
---|
| 830 | |
---|
| 831 | void HMETau2TwoLeptons::initConstants() { |
---|
| 832 | |
---|
| 833 | DECAYWEIGHTMAX = 16*pow4(pM[0]); |
---|
| 834 | |
---|
| 835 | } |
---|
| 836 | |
---|
| 837 | //-------------------------------------------------------------------------- |
---|
| 838 | |
---|
| 839 | // Initialize spinors for the helicity matrix element. |
---|
| 840 | |
---|
| 841 | void HMETau2TwoLeptons::initWaves(vector<HelicityParticle>& p) { |
---|
| 842 | |
---|
| 843 | u.clear(); |
---|
| 844 | pMap.resize(4); |
---|
| 845 | setFermionLine(0,p[0],p[1]); |
---|
| 846 | setFermionLine(2,p[2],p[3]); |
---|
| 847 | |
---|
| 848 | } |
---|
| 849 | |
---|
| 850 | //-------------------------------------------------------------------------- |
---|
| 851 | |
---|
| 852 | // Return element for the helicity matrix element. |
---|
| 853 | |
---|
| 854 | complex HMETau2TwoLeptons::calculateME(vector<int> h) { |
---|
| 855 | |
---|
| 856 | complex answer(0,0); |
---|
| 857 | for (int mu = 0; mu <= 3; mu++) { |
---|
| 858 | answer += (u[1][h[pMap[1]]] * gamma[mu] * (1 - gamma[5]) |
---|
| 859 | * u[0][h[pMap[0]]]) * gamma[4](mu,mu) * (u[3][h[pMap[3]]] |
---|
| 860 | * gamma[mu] * (1 - gamma[5]) * u[2][h[pMap[2]]]); |
---|
| 861 | } |
---|
| 862 | return answer; |
---|
| 863 | |
---|
| 864 | } |
---|
| 865 | |
---|
| 866 | //========================================================================== |
---|
| 867 | |
---|
| 868 | // Tau decay matrix element for tau decay into two mesons through an |
---|
| 869 | // intermediate vector meson. This matrix element is used for pi^0 + pi^- |
---|
| 870 | // decays (rho resonances), K^0 + K^- decays (rho resonances), and eta + K^- |
---|
| 871 | // decays (K^* resonances). Note that for the rho resonances the pi^0 + pi^- |
---|
| 872 | // running width dominates while for the K^* resonances the pi^- + K^0 running |
---|
| 873 | // width dominates. |
---|
| 874 | |
---|
| 875 | // vecM: on-shell masses for the vector resonances |
---|
| 876 | // vecG: on-shell widths for the vector resonances |
---|
| 877 | // vecP: phases used to calculate vector resonance weights |
---|
| 878 | // vecA: amplitudes used to calculate vector resonance weights |
---|
| 879 | // vecW: vector resonance weights |
---|
| 880 | |
---|
| 881 | //-------------------------------------------------------------------------- |
---|
| 882 | |
---|
| 883 | // Initialize constants for the helicity matrix element. |
---|
| 884 | |
---|
| 885 | void HMETau2TwoMesonsViaVector::initConstants() { |
---|
| 886 | |
---|
| 887 | // Clear the vectors from previous decays. |
---|
| 888 | vecM.clear(); vecG.clear(); vecP.clear(); vecA.clear(); vecW.clear(); |
---|
| 889 | |
---|
| 890 | // Decay through K^* resonances (eta + K^- decay). |
---|
| 891 | if (abs(pID[2]) == 221) { |
---|
| 892 | DECAYWEIGHTMAX = 10; |
---|
| 893 | pM[2] = particleDataPtr->m0(211); pM[3] = particleDataPtr->m0(311); |
---|
| 894 | vecM.push_back(0.8921); vecM.push_back(1.700); |
---|
| 895 | vecG.push_back(0.0513); vecG.push_back(0.235); |
---|
| 896 | vecP.push_back(0); vecP.push_back(M_PI); |
---|
| 897 | vecA.push_back(1); vecA.push_back(0.038); |
---|
| 898 | } |
---|
| 899 | |
---|
| 900 | // Decay through rho resonances (pi^0 + pi^- and K^0 + K^- decays). |
---|
| 901 | else { |
---|
| 902 | if (abs(pID[2]) == 111) DECAYWEIGHTMAX = 800; |
---|
| 903 | else if (abs(pID[2]) == 311) DECAYWEIGHTMAX = 6; |
---|
| 904 | pM[2] = particleDataPtr->m0(111); pM[3] = particleDataPtr->m0(211); |
---|
| 905 | vecM.push_back(0.7746); vecM.push_back(1.4080); vecM.push_back(1.700); |
---|
| 906 | vecG.push_back(0.1490); vecG.push_back(0.5020); vecG.push_back(0.235); |
---|
| 907 | vecP.push_back(0); vecP.push_back(M_PI); vecP.push_back(0); |
---|
| 908 | vecA.push_back(1.0); vecA.push_back(0.167); vecA.push_back(0.050); |
---|
| 909 | } |
---|
| 910 | calculateResonanceWeights(vecP, vecA, vecW); |
---|
| 911 | |
---|
| 912 | } |
---|
| 913 | |
---|
| 914 | //-------------------------------------------------------------------------- |
---|
| 915 | |
---|
| 916 | // Initialize the hadronic current for the helicity matrix element. |
---|
| 917 | |
---|
| 918 | void HMETau2TwoMesonsViaVector::initHadronicCurrent( |
---|
| 919 | vector<HelicityParticle>& p) { |
---|
| 920 | |
---|
| 921 | vector< Wave4 > u2; |
---|
| 922 | Wave4 u3(p[3].p() - p[2].p()); |
---|
| 923 | Wave4 u4(p[2].p() + p[3].p()); |
---|
| 924 | double s1 = m2(u3, u4); |
---|
| 925 | double s2 = m2(u4); |
---|
| 926 | complex sumBW = 0; |
---|
| 927 | for (unsigned int i = 0; i < vecW.size(); i++) |
---|
| 928 | sumBW += vecW[i] * pBreitWigner(pM[2], pM[3], s2, vecM[i], vecG[i]); |
---|
| 929 | u2.push_back((u3 - s1 / s2 * u4) * sumBW); |
---|
| 930 | u.push_back(u2); |
---|
| 931 | |
---|
| 932 | } |
---|
| 933 | |
---|
| 934 | //========================================================================== |
---|
| 935 | |
---|
| 936 | // Tau decay matrix element for tau decay into two mesons through both |
---|
| 937 | // intermediate vector and scalar mesons. |
---|
| 938 | |
---|
| 939 | // scaC: scalar coupling constant |
---|
| 940 | // scaM: on-shell masses for the scalar resonances |
---|
| 941 | // scaG: on-shell widths for the scalar resonances |
---|
| 942 | // scaP: phases used to calculate scalar resonance weights |
---|
| 943 | // scaA: amplitudes used to calculate scalar resonance weights |
---|
| 944 | // scaW: scalar resonance weights |
---|
| 945 | // vecC: scalar coupling constant |
---|
| 946 | // vecM: on-shell masses for the vector resonances |
---|
| 947 | // vecG: on-shell widths for the vector resonances |
---|
| 948 | // vecP: phases used to calculate vector resonance weights |
---|
| 949 | // vecA: amplitudes used to calculate vector resonance weights |
---|
| 950 | // vecW: vector resonance weights |
---|
| 951 | |
---|
| 952 | //-------------------------------------------------------------------------- |
---|
| 953 | |
---|
| 954 | // Initialize constants for the helicity matrix element. |
---|
| 955 | |
---|
| 956 | void HMETau2TwoMesonsViaVectorScalar::initConstants() { |
---|
| 957 | |
---|
| 958 | DECAYWEIGHTMAX = 5400; |
---|
| 959 | // Clear the vectors from previous decays. |
---|
| 960 | scaM.clear(); scaG.clear(); scaP.clear(); scaA.clear(); scaW.clear(); |
---|
| 961 | vecM.clear(); vecG.clear(); vecP.clear(); vecA.clear(); vecW.clear(); |
---|
| 962 | // Scalar resonance parameters. |
---|
| 963 | scaC = 0.465; |
---|
| 964 | scaM.push_back(0.878); |
---|
| 965 | scaG.push_back(0.499); |
---|
| 966 | scaP.push_back(0); |
---|
| 967 | scaA.push_back(1); |
---|
| 968 | calculateResonanceWeights(scaP, scaA, scaW); |
---|
| 969 | // Vector resonance parameters. |
---|
| 970 | vecC = 1; |
---|
| 971 | vecM.push_back(0.89547); vecM.push_back(1.414); |
---|
| 972 | vecG.push_back(0.04619); vecG.push_back(0.232); |
---|
| 973 | vecP.push_back(0); vecP.push_back(1.4399); |
---|
| 974 | vecA.push_back(1); vecA.push_back(0.075); |
---|
| 975 | calculateResonanceWeights(vecP, vecA, vecW); |
---|
| 976 | |
---|
| 977 | } |
---|
| 978 | |
---|
| 979 | //-------------------------------------------------------------------------- |
---|
| 980 | |
---|
| 981 | // Initialize the hadronic current for the helicity matrix element. |
---|
| 982 | |
---|
| 983 | void HMETau2TwoMesonsViaVectorScalar::initHadronicCurrent( |
---|
| 984 | vector<HelicityParticle>& p) { |
---|
| 985 | |
---|
| 986 | vector< Wave4 > u2; |
---|
| 987 | Wave4 u3(p[3].p() - p[2].p()); |
---|
| 988 | Wave4 u4(p[2].p() + p[3].p()); |
---|
| 989 | double s1 = m2(u3,u4); |
---|
| 990 | double s2 = m2(u4); |
---|
| 991 | complex scaSumBW = 0; complex scaSumW = 0; |
---|
| 992 | complex vecSumBW = 0; complex vecSumW = 0; complex vecSumBWM = 0; |
---|
| 993 | for (unsigned int i = 0; i < scaW.size(); i++) { |
---|
| 994 | scaSumBW += scaW[i] * sBreitWigner(pM[2], pM[3], s2, scaM[i], scaG[i]); |
---|
| 995 | scaSumW += scaW[i]; |
---|
| 996 | } |
---|
| 997 | for (unsigned int i = 0; i < vecW.size(); i++) { |
---|
| 998 | vecSumBW += vecW[i] * pBreitWigner(pM[2], pM[3], s2, vecM[i], vecG[i]); |
---|
| 999 | vecSumBWM += vecW[i] * pBreitWigner(pM[2], pM[3], s2, vecM[i], vecG[i]) / |
---|
| 1000 | pow2(vecM[i]); |
---|
| 1001 | vecSumW += vecW[i]; |
---|
| 1002 | } |
---|
| 1003 | u2.push_back(vecC * (vecSumBW * u3 - s1 * vecSumBWM * u4) / vecSumW + |
---|
| 1004 | scaC * u4 * scaSumBW / scaSumW); |
---|
| 1005 | u.push_back(u2); |
---|
| 1006 | |
---|
| 1007 | } |
---|
| 1008 | |
---|
| 1009 | //========================================================================== |
---|
| 1010 | |
---|
| 1011 | // Tau decay matrix element for tau decay into three mesons. This matrix |
---|
| 1012 | // element provides a base class for all implemented three meson decays. |
---|
| 1013 | |
---|
| 1014 | // mode: three meson decay mode of the tau |
---|
| 1015 | // initMode(): initialize the decay mode |
---|
| 1016 | // initResonances(): initialize the resonance constants |
---|
| 1017 | // s1, s2, s3, s4: center-of-mass energies |
---|
| 1018 | // q, q2, q3, q4: summed and individual hadronic momentum four-vectors |
---|
| 1019 | // a1BW: stored value of a1BreitWigner for speed |
---|
| 1020 | // a1PhaseSpace(s): phase space factor for the a1 |
---|
| 1021 | // a1BreitWigner(s): Breit-Wigner for the a1 |
---|
| 1022 | // T(m0, m1, s, M, G, W): sum weighted p-wave Breit-Wigners |
---|
| 1023 | // T(s, M, G, W): sum weighted fixed width Breit-Wigners |
---|
| 1024 | // F1(), F2(), F3(), F4(): sub-current form factors |
---|
| 1025 | |
---|
| 1026 | //-------------------------------------------------------------------------- |
---|
| 1027 | |
---|
| 1028 | // Initialize constants for the helicity matrix element. |
---|
| 1029 | |
---|
| 1030 | void HMETau2ThreeMesons::initConstants() { |
---|
| 1031 | |
---|
| 1032 | initMode(); |
---|
| 1033 | initResonances(); |
---|
| 1034 | |
---|
| 1035 | } |
---|
| 1036 | |
---|
| 1037 | //-------------------------------------------------------------------------- |
---|
| 1038 | |
---|
| 1039 | // Initialize the hadronic current for the helicity matrix element. |
---|
| 1040 | |
---|
| 1041 | void HMETau2ThreeMesons::initHadronicCurrent(vector<HelicityParticle>& p) { |
---|
| 1042 | |
---|
| 1043 | vector< Wave4 > u2; |
---|
| 1044 | |
---|
| 1045 | // Initialize the momenta. |
---|
| 1046 | initMomenta(p); |
---|
| 1047 | |
---|
| 1048 | // Calculate the center of mass energies. |
---|
| 1049 | s1 = m2(q); |
---|
| 1050 | s2 = m2(q3 + q4); |
---|
| 1051 | s3 = m2(q2 + q4); |
---|
| 1052 | s4 = m2(q2 + q3); |
---|
| 1053 | |
---|
| 1054 | // Calculate the form factors. |
---|
| 1055 | a1BW = a1BreitWigner(s1); |
---|
| 1056 | complex f1 = F1(); |
---|
| 1057 | complex f2 = F2(); |
---|
| 1058 | complex f3 = F3(); |
---|
| 1059 | complex f4 = F4(); |
---|
| 1060 | |
---|
| 1061 | // Calculate the hadronic current. |
---|
| 1062 | Wave4 u3 = (f3 - f2) * q2 + (f1 - f3) * q3 + (f2 - f1) * q4; |
---|
| 1063 | u3 = u3 - (u3 * gamma[4] * q / s1) * q; |
---|
| 1064 | if (f4 != complex(0, 0)) |
---|
| 1065 | u3 = u3 + complex(0, 1) * f4 * epsilon(q2, q3, q4); |
---|
| 1066 | u2.push_back(u3); |
---|
| 1067 | u.push_back(u2); |
---|
| 1068 | |
---|
| 1069 | } |
---|
| 1070 | |
---|
| 1071 | //-------------------------------------------------------------------------- |
---|
| 1072 | |
---|
| 1073 | // Initialize the tau decay mode. |
---|
| 1074 | |
---|
| 1075 | void HMETau2ThreeMesons::initMode() { |
---|
| 1076 | |
---|
| 1077 | if (abs(pID[2]) == 111 && abs(pID[3]) == 111 && abs(pID[4]) == 211) |
---|
| 1078 | mode = Pi0Pi0Pim; |
---|
| 1079 | else if (abs(pID[2]) == 211 && abs(pID[3]) == 211 && abs(pID[4]) == 211) |
---|
| 1080 | mode = PimPimPip; |
---|
| 1081 | else if (abs(pID[2]) == 111 && abs(pID[3]) == 211 && abs(pID[4]) == 311) |
---|
| 1082 | mode = Pi0PimK0b; |
---|
| 1083 | else if (abs(pID[2]) == 211 && abs(pID[3]) == 211 && abs(pID[4]) == 321) |
---|
| 1084 | mode = PimPipKm; |
---|
| 1085 | else if (abs(pID[2]) == 111 && abs(pID[3]) == 211 && abs(pID[4]) == 221) |
---|
| 1086 | mode = Pi0PimEta; |
---|
| 1087 | else if (abs(pID[2]) == 211 && abs(pID[3]) == 321 && abs(pID[4]) == 321) |
---|
| 1088 | mode = PimKmKp; |
---|
| 1089 | else if (abs(pID[2]) == 111 && abs(pID[3]) == 311 && abs(pID[4]) == 321) |
---|
| 1090 | mode = Pi0K0Km; |
---|
| 1091 | else if (abs(pID[2]) == 130 && abs(pID[3]) == 211 && abs(pID[4]) == 310) |
---|
| 1092 | mode = KlPimKs; |
---|
| 1093 | else if (abs(pID[2]) == 111 && abs(pID[3]) == 111 && abs(pID[4]) == 321) |
---|
| 1094 | mode = Pi0Pi0Km; |
---|
| 1095 | else if (abs(pID[2]) == 130 && abs(pID[3]) == 130 && abs(pID[4]) == 211) |
---|
| 1096 | mode = KlKlPim; |
---|
| 1097 | else if (abs(pID[2]) == 211 && abs(pID[3]) == 310 && abs(pID[4]) == 310) |
---|
| 1098 | mode = PimKsKs; |
---|
| 1099 | else if (abs(pID[2]) == 211 && abs(pID[3]) == 311 && abs(pID[4]) == 311) |
---|
| 1100 | mode = PimK0bK0; |
---|
| 1101 | else |
---|
| 1102 | mode = Uknown; |
---|
| 1103 | } |
---|
| 1104 | |
---|
| 1105 | //-------------------------------------------------------------------------- |
---|
| 1106 | |
---|
| 1107 | // Initialize the momenta for the helicity matrix element. |
---|
| 1108 | |
---|
| 1109 | void HMETau2ThreeMesons::initMomenta(vector<HelicityParticle>& p) { |
---|
| 1110 | |
---|
| 1111 | q = Wave4(p[2].p() + p[3].p() + p[4].p()); |
---|
| 1112 | // pi-, pi-, pi+ decay and pi0, pi0, pi- decay. |
---|
| 1113 | if (mode == PimPimPip || mode == Pi0Pi0Pim) { |
---|
| 1114 | q2 = Wave4(p[2].p()); q3 = Wave4(p[3].p()); q4 = Wave4(p[4].p()); |
---|
| 1115 | // K-, pi-, K+ decay. |
---|
| 1116 | } else if (mode == PimKmKp) { |
---|
| 1117 | q2 = Wave4(p[3].p()); q3 = Wave4(p[2].p()); q4 = Wave4(p[4].p()); |
---|
| 1118 | // K0, pi-, Kbar0 decay. |
---|
| 1119 | } else if (mode == PimK0bK0) { |
---|
| 1120 | q2 = Wave4(p[3].p()); q3 = Wave4(p[2].p()); q4 = Wave4(p[4].p()); |
---|
| 1121 | // K_S0, pi-, K_S0 decay. |
---|
| 1122 | } else if (mode == PimKsKs) { |
---|
| 1123 | q2 = Wave4(p[3].p()); q3 = Wave4(p[2].p()); q4 = Wave4(p[4].p()); |
---|
| 1124 | // K_L0, pi-, K_L0 decay. |
---|
| 1125 | } else if (mode == KlKlPim) { |
---|
| 1126 | q2 = Wave4(p[2].p()); q3 = Wave4(p[4].p()); q4 = Wave4(p[3].p()); |
---|
| 1127 | // K_S0, pi-, K_L0 decay. |
---|
| 1128 | } else if (mode == KlPimKs) { |
---|
| 1129 | q2 = Wave4(p[4].p()); q3 = Wave4(p[3].p()); q4 = Wave4(p[2].p()); |
---|
| 1130 | } // K-, pi0, K0 decay. |
---|
| 1131 | else if (mode == Pi0K0Km) { |
---|
| 1132 | q2 = Wave4(p[4].p()); q3 = Wave4(p[2].p()); q4 = Wave4(p[3].p()); |
---|
| 1133 | } // pi0, pi0, K- decay. |
---|
| 1134 | else if (mode == Pi0Pi0Km) { |
---|
| 1135 | q2 = Wave4(p[2].p()); q3 = Wave4(p[3].p()); q4 = Wave4(p[4].p()); |
---|
| 1136 | } // K-, pi-, pi+ decay. |
---|
| 1137 | else if (mode == PimPipKm) { |
---|
| 1138 | q2 = Wave4(p[4].p()); q3 = Wave4(p[2].p()); q4 = Wave4(p[3].p()); |
---|
| 1139 | } // pi-, Kbar0, pi0 decay. |
---|
| 1140 | else if (mode == Pi0PimK0b) { |
---|
| 1141 | q2 = Wave4(p[3].p()); q3 = Wave4(p[4].p()); q4 = Wave4(p[2].p()); |
---|
| 1142 | } // pi-, pi0, eta decay. |
---|
| 1143 | else if (mode == Pi0PimEta) { |
---|
| 1144 | q2 = Wave4(p[3].p()); q3 = Wave4(p[2].p()); q4 = Wave4(p[4].p()); |
---|
| 1145 | } |
---|
| 1146 | |
---|
| 1147 | } |
---|
| 1148 | |
---|
| 1149 | //-------------------------------------------------------------------------- |
---|
| 1150 | |
---|
| 1151 | // Return the phase space factor for the a1. Implements equation 3.16 of Z. |
---|
| 1152 | // Phys. C48 (1990) 445-452. |
---|
| 1153 | |
---|
| 1154 | double HMETau2ThreeMesons::a1PhaseSpace(double s) { |
---|
| 1155 | |
---|
| 1156 | double piM = 0.13957; // Mass of the charged pion. |
---|
| 1157 | double rhoM = 0.773; // Mass of the rho. |
---|
| 1158 | if (s < pow2(3 * piM)) |
---|
| 1159 | return 0; |
---|
| 1160 | else if (s < pow2(rhoM + piM)) { |
---|
| 1161 | double sum = (s - 9 * piM * piM); |
---|
| 1162 | return 4.1 * sum * sum * sum * (1 - 3.3 * sum + 5.8 * sum * sum); |
---|
| 1163 | } |
---|
| 1164 | else |
---|
| 1165 | return s * (1.623 + 10.38 / s - 9.32 / (s * s) + 0.65 / (s * s * s)); |
---|
| 1166 | |
---|
| 1167 | } |
---|
| 1168 | |
---|
| 1169 | //-------------------------------------------------------------------------- |
---|
| 1170 | |
---|
| 1171 | // Return the Breit-Wigner for the a1. Implements equation 3.18 of Z. Phys. C48 |
---|
| 1172 | // (1990) 445-452. |
---|
| 1173 | |
---|
| 1174 | complex HMETau2ThreeMesons::a1BreitWigner(double s) { |
---|
| 1175 | |
---|
| 1176 | |
---|
| 1177 | double a1M = 1.251; // Mass of the a1. |
---|
| 1178 | double a1G = 0.475; // Width of the a1. |
---|
| 1179 | return a1M * a1M / (a1M * a1M - s - complex(0,1) * a1M * a1G |
---|
| 1180 | * a1PhaseSpace(s) / a1PhaseSpace(a1M * a1M)); |
---|
| 1181 | |
---|
| 1182 | } |
---|
| 1183 | |
---|
| 1184 | //-------------------------------------------------------------------------- |
---|
| 1185 | |
---|
| 1186 | // Return summed weighted running p Breit-Wigner resonances. |
---|
| 1187 | |
---|
| 1188 | complex HMETau2ThreeMesons::T(double m0, double m1, double s, vector<double> &M, |
---|
| 1189 | vector<double> &G, vector<double> &W) { |
---|
| 1190 | |
---|
| 1191 | complex num(0, 0); |
---|
| 1192 | double den(0); |
---|
| 1193 | for (unsigned int i = 0; i < M.size(); i++) { |
---|
| 1194 | num += W[i] * pBreitWigner(m0, m1, s, M[i], G[i]); |
---|
| 1195 | den += W[i]; |
---|
| 1196 | } |
---|
| 1197 | return num / den; |
---|
| 1198 | |
---|
| 1199 | } |
---|
| 1200 | |
---|
| 1201 | //-------------------------------------------------------------------------- |
---|
| 1202 | |
---|
| 1203 | // Return summed weighted fixed width Breit-Wigner resonances. |
---|
| 1204 | |
---|
| 1205 | complex HMETau2ThreeMesons::T(double s, vector<double> &M, |
---|
| 1206 | vector<double> &G, vector<double> &W) { |
---|
| 1207 | |
---|
| 1208 | complex num(0, 0); |
---|
| 1209 | double den(0); |
---|
| 1210 | for (unsigned int i = 0; i < M.size(); i++) { |
---|
| 1211 | num += W[i] * breitWigner(s, M[i], G[i]); |
---|
| 1212 | den += W[i]; |
---|
| 1213 | } |
---|
| 1214 | return num / den; |
---|
| 1215 | |
---|
| 1216 | } |
---|
| 1217 | |
---|
| 1218 | //========================================================================== |
---|
| 1219 | |
---|
| 1220 | // Tau decay matrix element for tau decay into three pions. This matrix element |
---|
| 1221 | // is taken from the Herwig++ implementation based on the CLEO fits. |
---|
| 1222 | |
---|
| 1223 | // rhoM: on-shell masses for the rho resonances |
---|
| 1224 | // rhoG: on-shell widths for the rho resonances |
---|
| 1225 | // rhoPp: p-wave phase for the rho coupling to the a1 |
---|
| 1226 | // rhoAp: p-wave amplitude for the rho coupling to the a1 |
---|
| 1227 | // rhoPd: d-wave phase for the rho coupling to the a1 |
---|
| 1228 | // rhoAd: d-wave amplitude for the rho coupling to the a1 |
---|
| 1229 | // f0M: f0 on-shell mass |
---|
| 1230 | // f0G: f0 on-shell width |
---|
| 1231 | // f0P: phase for the coupling of the f0 to the a1 |
---|
| 1232 | // f0A: amplitude for the coupling of the f0 to the a1 |
---|
| 1233 | // f2M: f2 on-shell mass |
---|
| 1234 | // f2G: f2 on-shell width |
---|
| 1235 | // f2P: phase for the coupling of the f2 to the a1 |
---|
| 1236 | // f2P: amplitude for the coupling of the f2 to the a1 |
---|
| 1237 | // sigM: sigma on-shell mass |
---|
| 1238 | // sigG: sigma on-shell width |
---|
| 1239 | // sigP: phase for the coupling of the sigma to the a1 |
---|
| 1240 | // sigA: amplitude for the coupling of the sigma to the a1 |
---|
| 1241 | |
---|
| 1242 | //-------------------------------------------------------------------------- |
---|
| 1243 | |
---|
| 1244 | // Initialize resonance constants for the helicity matrix element. |
---|
| 1245 | |
---|
| 1246 | void HMETau2ThreePions::initResonances() { |
---|
| 1247 | |
---|
| 1248 | // Three charged pion decay. |
---|
| 1249 | if (mode == PimPimPip) DECAYWEIGHTMAX = 6000; |
---|
| 1250 | |
---|
| 1251 | // Two neutral and one charged pion decay. |
---|
| 1252 | else DECAYWEIGHTMAX = 3000; |
---|
| 1253 | |
---|
| 1254 | // Clear the vectors from previous decays. |
---|
| 1255 | rhoM.clear(); rhoG.clear(); |
---|
| 1256 | rhoPp.clear(); rhoAp.clear(); rhoWp.clear(); |
---|
| 1257 | rhoPd.clear(); rhoAd.clear(); rhoWd.clear(); |
---|
| 1258 | |
---|
| 1259 | // Rho parameters. |
---|
| 1260 | rhoM.push_back(.7743); rhoM.push_back(1.370); rhoM.push_back(1.720); |
---|
| 1261 | rhoG.push_back(.1491); rhoG.push_back(.386); rhoG.push_back(.250); |
---|
| 1262 | rhoPp.push_back(0); rhoPp.push_back(3.11018); rhoPp.push_back(0); |
---|
| 1263 | rhoAp.push_back(1); rhoAp.push_back(0.12); rhoAp.push_back(0); |
---|
| 1264 | rhoPd.push_back(-0.471239); rhoPd.push_back(1.66504); rhoPd.push_back(0); |
---|
| 1265 | rhoAd.push_back(3.7e-07); rhoAd.push_back(8.7e-07); rhoAd.push_back(0); |
---|
| 1266 | |
---|
| 1267 | // Scalar and tensor parameters. |
---|
| 1268 | f0M = 1.186; f2M = 1.275; sigM = 0.860; |
---|
| 1269 | f0G = 0.350; f2G = 0.185; sigG = 0.880; |
---|
| 1270 | f0P = -1.69646; f2P = 1.75929; sigP = 0.722566; |
---|
| 1271 | f0A = 0.77; f2A = 7.1e-07; sigA = 2.1; |
---|
| 1272 | |
---|
| 1273 | // Calculate the weights from the phases and amplitudes. |
---|
| 1274 | calculateResonanceWeights(rhoPp, rhoAp, rhoWp); |
---|
| 1275 | calculateResonanceWeights(rhoPd, rhoAd, rhoWd); |
---|
| 1276 | f0W = f0A * (cos(f0P) + complex(0,1) * sin(f0P)); |
---|
| 1277 | f2W = f2A * (cos(f2P) + complex(0,1) * sin(f2P)); |
---|
| 1278 | sigW = sigA * (cos(sigP) + complex(0,1) * sin(sigP)); |
---|
| 1279 | |
---|
| 1280 | } |
---|
| 1281 | |
---|
| 1282 | //-------------------------------------------------------------------------- |
---|
| 1283 | |
---|
| 1284 | // Return the first form factor. |
---|
| 1285 | |
---|
| 1286 | complex HMETau2ThreePions::F1() { |
---|
| 1287 | |
---|
| 1288 | complex answer(0,0); |
---|
| 1289 | |
---|
| 1290 | // Three charged pion decay. |
---|
| 1291 | if (mode == PimPimPip) { |
---|
| 1292 | for (unsigned int i = 0; i < rhoM.size(); i++) { |
---|
| 1293 | answer += - rhoWp[i] * pBreitWigner(pM[3], pM[4], s2, rhoM[i], rhoG[i]) |
---|
| 1294 | - rhoWd[i] / 3.0 * pBreitWigner(pM[2], pM[4], s3, rhoM[i], rhoG[i]) |
---|
| 1295 | * (s2 - s4); |
---|
| 1296 | } |
---|
| 1297 | answer += -2.0 / 3.0 * (sigW * sBreitWigner(pM[2], pM[4], s3, sigM, sigG) |
---|
| 1298 | + f0W * sBreitWigner(pM[2], pM[4], s3, f0M, f0G)); |
---|
| 1299 | answer += f2W * (0.5 * (s4 - s3) |
---|
| 1300 | * dBreitWigner(pM[3], pM[4], s2, f2M, f2G) |
---|
| 1301 | - 1.0 / (18 * s3) * (4 * pow2(pM[2]) - s3) |
---|
| 1302 | * (s1 + s3 - pow2(pM[2])) |
---|
| 1303 | * dBreitWigner(pM[2], pM[4], s3, f2M, f2G)); |
---|
| 1304 | } |
---|
| 1305 | |
---|
| 1306 | // Two neutral and one charged pion decay. |
---|
| 1307 | else { |
---|
| 1308 | for (unsigned int i = 0; i < rhoM.size(); i++) { |
---|
| 1309 | answer += rhoWp[i] * pBreitWigner(pM[3], pM[4], s2, rhoM[i], rhoG[i]) |
---|
| 1310 | - rhoWd[i] / 3.0 * pBreitWigner(pM[2], pM[4], s3, rhoM[i], rhoG[i]) |
---|
| 1311 | * (s4 - s2 - pow2(pM[4]) + pow2(pM[2])); |
---|
| 1312 | } |
---|
| 1313 | answer += 2.0 / 3.0 * (sigW * sBreitWigner(pM[2], pM[3], s4, sigM, sigG) |
---|
| 1314 | + f0W * sBreitWigner(pM[2], pM[3], s4, f0M, f0G)); |
---|
| 1315 | answer += f2W / (18 * s4) * (s1 - pow2(pM[4]) + s4) |
---|
| 1316 | * (4 * pow2(pM[2]) - s4) * dBreitWigner(pM[2], pM[3], s4, f2M, f2G); |
---|
| 1317 | } |
---|
| 1318 | return a1BW * answer; |
---|
| 1319 | |
---|
| 1320 | } |
---|
| 1321 | |
---|
| 1322 | //-------------------------------------------------------------------------- |
---|
| 1323 | |
---|
| 1324 | // Return the second form factor. |
---|
| 1325 | |
---|
| 1326 | complex HMETau2ThreePions::F2() { |
---|
| 1327 | |
---|
| 1328 | complex answer(0,0); |
---|
| 1329 | |
---|
| 1330 | // Three charged pion decay. |
---|
| 1331 | if (mode == PimPimPip) { |
---|
| 1332 | for (unsigned int i = 0; i < rhoM.size(); i++) { |
---|
| 1333 | answer += -rhoWp[i] * pBreitWigner(pM[2], pM[4], s3, rhoM[i], rhoG[i]) |
---|
| 1334 | - rhoWd[i] / 3.0 * pBreitWigner(pM[3], pM[4], s2, rhoM[i], rhoG[i]) |
---|
| 1335 | * (s3 - s4); |
---|
| 1336 | } |
---|
| 1337 | answer += -2.0 / 3.0 * (sigW * sBreitWigner(pM[3], pM[4], s2, sigM, sigG) |
---|
| 1338 | + f0W * sBreitWigner(pM[3], pM[4], s2, f0M, f0G)); |
---|
| 1339 | answer += f2W * (0.5 * (s4 - s2) |
---|
| 1340 | * dBreitWigner(pM[2], pM[4], s3, f2M, f2G) |
---|
| 1341 | - 1.0 / (18 * s2) * (4 * pow2(pM[2]) - s2) * (s1 + s2 - pow2(pM[2])) |
---|
| 1342 | * dBreitWigner(pM[3], pM[4], s2, f2M, f2G)); |
---|
| 1343 | } |
---|
| 1344 | |
---|
| 1345 | // Two neutral and one charged pion decay. |
---|
| 1346 | else { |
---|
| 1347 | for (unsigned int i = 0; i < rhoM.size(); i++) { |
---|
| 1348 | answer += -rhoWp[i] / 3.0 * |
---|
| 1349 | pBreitWigner(pM[2], pM[4], s3, rhoM[i], rhoG[i]) - |
---|
| 1350 | rhoWd[i] * pBreitWigner(pM[3], pM[4], s2, rhoM[i], rhoG[i]) * |
---|
| 1351 | (s4 - s3 - pow2(pM[4]) + pow2(pM[3])); |
---|
| 1352 | } |
---|
| 1353 | answer += 2.0 / 3.0 * (sigW * sBreitWigner(pM[2], pM[3], s4, sigM, sigG) |
---|
| 1354 | + f0W * sBreitWigner(pM[2], pM[3], s4, f0M, f0G)); |
---|
| 1355 | answer += f2W / (18 * s4) * (s1 - pow2(pM[4]) + s4) * |
---|
| 1356 | (4 * pow2(pM[2]) - s4) * dBreitWigner(pM[2], pM[3], s4, f2M, f2G); |
---|
| 1357 | } |
---|
| 1358 | return -a1BW * answer; |
---|
| 1359 | |
---|
| 1360 | } |
---|
| 1361 | |
---|
| 1362 | //-------------------------------------------------------------------------- |
---|
| 1363 | |
---|
| 1364 | // Return the third form factor. |
---|
| 1365 | |
---|
| 1366 | complex HMETau2ThreePions::F3() { |
---|
| 1367 | |
---|
| 1368 | complex answer(0,0); |
---|
| 1369 | |
---|
| 1370 | // Three charged pion decay. |
---|
| 1371 | if (mode == PimPimPip) { |
---|
| 1372 | for (unsigned int i = 0; i < rhoM.size(); i++) { |
---|
| 1373 | answer += -rhoWd[i] * (1.0 / 3.0 * (s3 - s4) * |
---|
| 1374 | pBreitWigner(pM[3], pM[4], s2, rhoM[i], rhoG[i]) |
---|
| 1375 | - 1.0 / 3.0 * (s2 - s4) * |
---|
| 1376 | pBreitWigner(pM[2], pM[4], s3, rhoM[i], |
---|
| 1377 | rhoG[i])); |
---|
| 1378 | } |
---|
| 1379 | answer += -2.0 / 3.0 * (sigW * sBreitWigner(pM[3], pM[4], s2, sigM, sigG) |
---|
| 1380 | + f0W * sBreitWigner(pM[3], pM[4], s2, f0M, f0G)); |
---|
| 1381 | answer += 2.0 / 3.0 * (sigW * sBreitWigner(pM[2], pM[4], s3, sigM, sigG) |
---|
| 1382 | + f0W * sBreitWigner(pM[2], pM[4], s3, f0M, f0G)); |
---|
| 1383 | answer += f2W * (-1.0 / (18 * s2) * (4 * pow2(pM[2]) - s2) * |
---|
| 1384 | (s1 + s2 - pow2(pM[2])) * |
---|
| 1385 | dBreitWigner(pM[3], pM[4], s2, f2M, f2G) + |
---|
| 1386 | 1.0 / (18 * s3) * (4 * pow2(pM[2]) - s3) * |
---|
| 1387 | (s1 + s3 - pow2(pM[2])) * |
---|
| 1388 | dBreitWigner(pM[2], pM[4], s3, f2M, f2G)); |
---|
| 1389 | } |
---|
| 1390 | |
---|
| 1391 | // Two neutral and one charged pion decay. |
---|
| 1392 | else { |
---|
| 1393 | for (unsigned int i = 0; i < rhoM.size(); i++) { |
---|
| 1394 | answer += rhoWd[i] * (-1.0 / 3.0 * |
---|
| 1395 | (s4 - s3 - pow2(pM[4]) + pow2(pM[3])) * |
---|
| 1396 | pBreitWigner(pM[3], pM[4], s2, rhoM[i], rhoG[i]) + |
---|
| 1397 | 1.0 / 3.0 * (s4 - s2 - pow2(pM[4]) + pow2(pM[2])) |
---|
| 1398 | * pBreitWigner(pM[2], pM[4], s3, rhoM[i], |
---|
| 1399 | rhoG[i])); |
---|
| 1400 | } |
---|
| 1401 | answer += -f2W / 2.0 * (s2 - s3) * |
---|
| 1402 | dBreitWigner(pM[2], pM[3], s4, f2M, f2G); |
---|
| 1403 | } |
---|
| 1404 | return a1BW * answer; |
---|
| 1405 | |
---|
| 1406 | } |
---|
| 1407 | |
---|
| 1408 | //-------------------------------------------------------------------------- |
---|
| 1409 | |
---|
| 1410 | // Return the running width for the a1 (multiplied by a factor of a1M). |
---|
| 1411 | |
---|
| 1412 | double HMETau2ThreePions::a1PhaseSpace(double s) { |
---|
| 1413 | |
---|
| 1414 | double picM = 0.1753; // (m_pi^- + m_pi^- + m_pi^+)^2 |
---|
| 1415 | double pinM = 0.1676; // (m_pi^0 + m_pi^0 + m_pi^-)^2 |
---|
| 1416 | double kM = 0.496; // K mass. |
---|
| 1417 | double ksM = 0.894; // K^* mass. |
---|
| 1418 | double picG = 0; // Width contribution from three charged pions. |
---|
| 1419 | double pinG = 0; // Width contribution from two neutral one charged. |
---|
| 1420 | double kG = 0; // Width contributions from s-wave K K^*. |
---|
| 1421 | double piW = pow2(0.2384)/1.0252088; // Overall weight factor. |
---|
| 1422 | double kW = pow2(4.7621); // K K^* width weight factor. |
---|
| 1423 | |
---|
| 1424 | // Three charged pion width contribution. |
---|
| 1425 | if (s < picM) |
---|
| 1426 | picG = 0; |
---|
| 1427 | else if (s < 0.823) |
---|
| 1428 | picG = 5.80900 * pow3(s - picM) * (1.0 - 3.00980 * (s - picM) + |
---|
| 1429 | 4.5792 * pow2(s - picM)); |
---|
| 1430 | else |
---|
| 1431 | picG = -13.91400 + 27.67900 * s - 13.39300 * pow2(s) + 3.19240 * pow3(s) |
---|
| 1432 | - 0.10487 * pow4(s); |
---|
| 1433 | |
---|
| 1434 | // Two neutral and one charged pion width contribution. |
---|
| 1435 | if (s < pinM) |
---|
| 1436 | pinG = 0; |
---|
| 1437 | else if (s < 0.823) |
---|
| 1438 | pinG = 6.28450 * pow3(s - pinM) * (1.0 - 2.95950 * (s - pinM) + |
---|
| 1439 | 4.33550 * pow2(s - pinM)); |
---|
| 1440 | else |
---|
| 1441 | pinG = -15.41100 + 32.08800 * s - 17.66600 * pow2(s) + 4.93550 * pow3(s) |
---|
| 1442 | - 0.37498 * pow4(s); |
---|
| 1443 | |
---|
| 1444 | // K and K^* width contribution. |
---|
| 1445 | if (s > pow2(ksM + kM)) |
---|
| 1446 | kG = 0.5 * sqrt((s - pow2(ksM + kM)) * (s - pow2(ksM - kM))) / s; |
---|
| 1447 | return piW*(picG + pinG + kW*kG); |
---|
| 1448 | |
---|
| 1449 | } |
---|
| 1450 | |
---|
| 1451 | //-------------------------------------------------------------------------- |
---|
| 1452 | |
---|
| 1453 | // Return the Breit-Wigner for the a1. |
---|
| 1454 | |
---|
| 1455 | complex HMETau2ThreePions::a1BreitWigner(double s) { |
---|
| 1456 | |
---|
| 1457 | double a1M = 1.331; // Mass of the a1. |
---|
| 1458 | return a1M*a1M/(a1M*a1M - s - complex(0,1)*a1PhaseSpace(s)); |
---|
| 1459 | |
---|
| 1460 | } |
---|
| 1461 | |
---|
| 1462 | //========================================================================== |
---|
| 1463 | |
---|
| 1464 | // Tau decay matrix element for tau decay into three mesons with kaons. The form |
---|
| 1465 | // factors are taken from hep-ph/9503474. |
---|
| 1466 | |
---|
| 1467 | // rhoMa(v): on-shell masses for the axial (vector) rho resonances |
---|
| 1468 | // rhoGa(v): widths for the axial (vector) rho resonances |
---|
| 1469 | // rhoWa(v): weights for the axial (vector) rho resonances |
---|
| 1470 | // kstarXa(v): on-shell masses, widths, and weights for the K* resonances |
---|
| 1471 | // k1Xa(b): on-shell masses, width, and weight for the K1 resonances, |
---|
| 1472 | // the a constants are for K1 -> K* pi, K* -> K pi |
---|
| 1473 | // the b constants are for K1 -> rho K, rho -> pi pi |
---|
| 1474 | // omegaX: on-shell masses, width, and weights for the omega reosnances |
---|
| 1475 | // kM: kaon mass |
---|
| 1476 | // piM: charged pion mass |
---|
| 1477 | // piW: pion coupling, f_W |
---|
| 1478 | |
---|
| 1479 | //-------------------------------------------------------------------------- |
---|
| 1480 | |
---|
| 1481 | // Initialize resonance constants for the helicity matrix element. |
---|
| 1482 | |
---|
| 1483 | void HMETau2ThreeMesonsWithKaons::initResonances() { |
---|
| 1484 | |
---|
| 1485 | // K-, pi-, K+ decay. |
---|
| 1486 | if (mode == PimKmKp) DECAYWEIGHTMAX = 130; |
---|
| 1487 | // K0, pi-, Kbar0 decay. |
---|
| 1488 | else if (mode == PimK0bK0) DECAYWEIGHTMAX = 115; |
---|
| 1489 | // K_S0, pi-, K_S0 and K_L0, pi-, K_L0 decay. |
---|
| 1490 | else if (mode == PimKsKs || mode == KlKlPim) DECAYWEIGHTMAX = 230; |
---|
| 1491 | // K_S0, pi-, K_L0 decay. |
---|
| 1492 | else if (mode == KlPimKs) DECAYWEIGHTMAX = 230; |
---|
| 1493 | // K-, pi0, K0 decay. |
---|
| 1494 | else if (mode == Pi0K0Km) DECAYWEIGHTMAX = 125; |
---|
| 1495 | // pi0, pi0, K- decay. |
---|
| 1496 | else if (mode == Pi0Pi0Km) DECAYWEIGHTMAX = 2.5e4; |
---|
| 1497 | // K-, pi-, pi+ decay. |
---|
| 1498 | else if (mode == PimPipKm) DECAYWEIGHTMAX = 1.8e4; |
---|
| 1499 | // pi-, Kbar0, pi0 decay. |
---|
| 1500 | else if (mode == Pi0PimK0b) DECAYWEIGHTMAX = 3.9e4; |
---|
| 1501 | |
---|
| 1502 | // Clear the vectors from previous decays. |
---|
| 1503 | rhoMa.clear(); rhoGa.clear(); rhoWa.clear(); |
---|
| 1504 | rhoMv.clear(); rhoGv.clear(); rhoWv.clear(); |
---|
| 1505 | kstarMa.clear(); kstarGa.clear(); kstarWa.clear(); |
---|
| 1506 | kstarMv.clear(); kstarGv.clear(); kstarWv.clear(); |
---|
| 1507 | k1Ma.clear(); k1Ga.clear(); k1Wa.clear(); |
---|
| 1508 | k1Mb.clear(); k1Gb.clear(); k1Wb.clear(); |
---|
| 1509 | omegaM.clear(); omegaG.clear(); omegaW.clear(); |
---|
| 1510 | |
---|
| 1511 | // Rho parameters. |
---|
| 1512 | rhoMa.push_back(0.773); rhoGa.push_back(0.145); rhoWa.push_back(1); |
---|
| 1513 | rhoMa.push_back(1.370); rhoGa.push_back(0.510); rhoWa.push_back(-0.145); |
---|
| 1514 | rhoMv.push_back(0.773); rhoGv.push_back(0.145); rhoWv.push_back(1); |
---|
| 1515 | rhoMv.push_back(1.500); rhoGv.push_back(0.220); rhoWv.push_back(-6.5 / 26.0); |
---|
| 1516 | rhoMv.push_back(1.750); rhoGv.push_back(0.120); rhoWv.push_back(-1.0 / 26.0); |
---|
| 1517 | |
---|
| 1518 | // Kstar parameters. |
---|
| 1519 | kstarMa.push_back(0.892); kstarGa.push_back(0.050); |
---|
| 1520 | kstarMa.push_back(1.412); kstarGa.push_back(0.227); |
---|
| 1521 | kstarWa.push_back(1); |
---|
| 1522 | kstarWa.push_back(-0.135); |
---|
| 1523 | kstarMv.push_back(0.892); kstarGv.push_back(0.050); |
---|
| 1524 | kstarMv.push_back(1.412); kstarGv.push_back(0.227); |
---|
| 1525 | kstarMv.push_back(1.714); kstarGv.push_back(0.323); |
---|
| 1526 | kstarWv.push_back(1); |
---|
| 1527 | kstarWv.push_back(-6.5 / 26.0); |
---|
| 1528 | kstarWv.push_back(-1.0 / 26.0); |
---|
| 1529 | |
---|
| 1530 | // K1 parameters. |
---|
| 1531 | k1Ma.push_back(1.270); k1Ga.push_back(0.090); k1Wa.push_back(0.33); |
---|
| 1532 | k1Ma.push_back(1.402); k1Ga.push_back(0.174); k1Wa.push_back(1); |
---|
| 1533 | k1Mb.push_back(1.270); k1Gb.push_back(0.090); k1Wb.push_back(1); |
---|
| 1534 | |
---|
| 1535 | // Omega and phi parameters. |
---|
| 1536 | omegaM.push_back(0.782); omegaG.push_back(0.00843); omegaW.push_back(1); |
---|
| 1537 | omegaM.push_back(1.020); omegaG.push_back(0.00443); omegaW.push_back(0.05); |
---|
| 1538 | |
---|
| 1539 | // Kaon and pion parameters |
---|
| 1540 | kM = 0.49765; piM = 0.13957; piW = 0.0942; |
---|
| 1541 | |
---|
| 1542 | } |
---|
| 1543 | |
---|
| 1544 | //-------------------------------------------------------------------------- |
---|
| 1545 | |
---|
| 1546 | // Return the first form factor. |
---|
| 1547 | |
---|
| 1548 | complex HMETau2ThreeMesonsWithKaons::F1() { |
---|
| 1549 | |
---|
| 1550 | complex answer; |
---|
| 1551 | // K-, pi-, K+ decay. |
---|
| 1552 | if (mode == PimKmKp) |
---|
| 1553 | answer = a1BW * T(piM, kM, s2, kstarMa, kstarGa, kstarWa) / 2.0; |
---|
| 1554 | // K0, pi-, Kbar0 decay. |
---|
| 1555 | else if (mode == PimK0bK0) |
---|
| 1556 | answer = a1BW * T(piM, kM, s2, kstarMa, kstarGa, kstarWa) / 2.0; |
---|
| 1557 | // K_S0, pi-, K_S0 decay and K_L0, pi-, K_L0 decay. |
---|
| 1558 | else if (mode == PimKsKs || mode == KlKlPim) |
---|
| 1559 | answer = -a1BW * (T(piM, kM, s2, kstarMa, kstarGa, kstarWa) |
---|
| 1560 | + T(piM, kM, s4, kstarMa, kstarGa, kstarWa)) / 2.0; |
---|
| 1561 | // K_S0, pi-, K_L0 decay. |
---|
| 1562 | else if (mode == KlPimKs) |
---|
| 1563 | answer = a1BW * (T(piM, kM, s2, kstarMa, kstarGa, kstarWa) |
---|
| 1564 | - T(piM, kM, s4, kstarMa, kstarGa, kstarWa)) / 2.0; |
---|
| 1565 | // K-, pi0, K0 decay. |
---|
| 1566 | else if (mode == Pi0K0Km) |
---|
| 1567 | answer = a1BW * (T(piM, kM, s2, kstarMa, kstarGa, kstarWa) |
---|
| 1568 | - T(piM, kM, s4, kstarMa, kstarGa, kstarWa)) / 2.0; |
---|
| 1569 | // pi0, pi0, K- decay. |
---|
| 1570 | else if (mode == Pi0Pi0Km) |
---|
| 1571 | answer = T(s1, k1Ma, k1Ga, k1Wa) |
---|
| 1572 | * T(piM, kM, s2, kstarMa, kstarGa, kstarWa); |
---|
| 1573 | // K-, pi-, pi+ decay. |
---|
| 1574 | else if (mode == PimPipKm) |
---|
| 1575 | answer = T(s1, k1Mb, k1Gb, k1Wb) |
---|
| 1576 | * T(piM, piM, s2, rhoMa, rhoGa, rhoWa); |
---|
| 1577 | // pi-, Kbar0, pi0 decay. |
---|
| 1578 | else if (mode == Pi0PimK0b) |
---|
| 1579 | answer = T(s1, k1Ma, k1Ga, k1Wa) |
---|
| 1580 | * (T(piM, kM, s2, kstarMa, kstarGa, kstarWa) |
---|
| 1581 | - T(piM, kM, s4, kstarMa, kstarGa, kstarWa)); |
---|
| 1582 | return -1.0 / 3.0 * answer; |
---|
| 1583 | } |
---|
| 1584 | |
---|
| 1585 | //-------------------------------------------------------------------------- |
---|
| 1586 | |
---|
| 1587 | // Return the second form factor. |
---|
| 1588 | |
---|
| 1589 | complex HMETau2ThreeMesonsWithKaons::F2() { |
---|
| 1590 | |
---|
| 1591 | complex answer; |
---|
| 1592 | // K-, pi-, K+ decay. |
---|
| 1593 | if (mode == PimKmKp) |
---|
| 1594 | answer = a1BW * T(piM, piM, s3, rhoMa, rhoGa, rhoWa) / 2.0; |
---|
| 1595 | // K0, pi-, Kbar0 decay. |
---|
| 1596 | else if (mode == PimK0bK0) |
---|
| 1597 | answer = a1BW * T(piM, piM, s3, rhoMa, rhoGa, rhoWa) / 2.0; |
---|
| 1598 | // K_S0, pi-, K_S0 decay and K_L0, pi-, K_L0 decay. |
---|
| 1599 | else if (mode == PimKsKs || mode == KlKlPim) |
---|
| 1600 | answer = a1BW * T(piM, kM, s4, kstarMa, kstarGa, kstarWa) / 2.0; |
---|
| 1601 | // K_S0, pi-, K_L0 decay. |
---|
| 1602 | else if (mode == KlPimKs) |
---|
| 1603 | answer = a1BW * (2.0 * T(piM, piM, s3, rhoMa, rhoGa, rhoWa) |
---|
| 1604 | + T(piM, kM, s4, kstarMa, kstarGa, kstarWa)) / 2.0; |
---|
| 1605 | // K-, pi0, K0 decay. |
---|
| 1606 | else if (mode == Pi0K0Km) |
---|
| 1607 | answer = a1BW * (2.0 * T(piM, piM, s3, rhoMa, rhoGa, rhoWa) |
---|
| 1608 | + T(piM, kM, s4, kstarMa, kstarGa, kstarWa)) / 2.0; |
---|
| 1609 | // pi0, pi0, K- decay. |
---|
| 1610 | else if (mode == Pi0Pi0Km) |
---|
| 1611 | answer = T(s1, k1Ma, k1Ga, k1Wa) |
---|
| 1612 | * T(piM, kM, s3, kstarMa, kstarGa, kstarWa); |
---|
| 1613 | // K-, pi-, pi+ decay. |
---|
| 1614 | else if (mode == PimPipKm) |
---|
| 1615 | answer = T(s1, k1Ma, k1Ga, k1Wa) |
---|
| 1616 | * T(piM, kM, s3, kstarMa, kstarGa, kstarWa); |
---|
| 1617 | // pi-, Kbar0, pi0 decay. |
---|
| 1618 | else if (mode == Pi0PimK0b) |
---|
| 1619 | answer = 2.0 * T(s1, k1Mb, k1Gb, k1Wb) |
---|
| 1620 | * T(piM, piM, s3, rhoMa, rhoGa, rhoWa) |
---|
| 1621 | + T(s1, k1Ma, k1Ga, k1Wa) * T(piM, kM, s4, kstarMa, kstarGa, kstarWa); |
---|
| 1622 | return 1.0 / 3.0 * answer; |
---|
| 1623 | |
---|
| 1624 | } |
---|
| 1625 | |
---|
| 1626 | //-------------------------------------------------------------------------- |
---|
| 1627 | |
---|
| 1628 | // Return the fourth form factor. |
---|
| 1629 | |
---|
| 1630 | complex HMETau2ThreeMesonsWithKaons::F4() { |
---|
| 1631 | |
---|
| 1632 | complex answer; |
---|
| 1633 | // K-, pi-, K+ decay. |
---|
| 1634 | if (mode == PimKmKp) |
---|
| 1635 | answer = (sqrt(2) - 1) * T(piM, piM, s1, rhoMv, rhoGv, rhoWv) |
---|
| 1636 | * (sqrt(2) * T(s3, omegaM, omegaG, omegaW) |
---|
| 1637 | + T(piM, kM, s2, kstarMa, kstarGa, kstarWa)); |
---|
| 1638 | // K0, pi-, Kbar0 decay. |
---|
| 1639 | else if (mode == PimK0bK0) |
---|
| 1640 | answer = -(sqrt(2) - 1) * T(piM, piM, s1, rhoMv, rhoGv, rhoWv) |
---|
| 1641 | * (sqrt(2) * T(s3, omegaM, omegaG, omegaW) |
---|
| 1642 | + T(piM, kM, s2, kstarMa, kstarGa, kstarWa)); |
---|
| 1643 | // K_S0, pi-, K_S0 decay and K_L0, pi-, K_L0 decay. |
---|
| 1644 | else if (mode == PimKsKs || mode == KlKlPim) |
---|
| 1645 | answer = (sqrt(2) - 1) * T(piM, piM, s1, rhoMv, rhoGv, rhoWv) |
---|
| 1646 | * (T(piM, kM, s2, kstarMa, kstarGa, kstarWa) |
---|
| 1647 | - T(piM, kM, s4, kstarMa, kstarGa, kstarWa)); |
---|
| 1648 | // K_S0, pi-, K_L0 decay. |
---|
| 1649 | else if (mode == KlPimKs) |
---|
| 1650 | answer = -(sqrt(2) - 1) * T(piM, piM, s1, rhoMv, rhoGv, rhoWv) |
---|
| 1651 | * (2 * sqrt(2) * T(s3, omegaM, omegaG, omegaW) |
---|
| 1652 | + T(piM, kM, s2, kstarMa, kstarGa, kstarWa) |
---|
| 1653 | + T(piM, kM, s4, kstarMa, kstarGa, kstarWa)); |
---|
| 1654 | // K-, pi0, K0 decay. |
---|
| 1655 | else if (mode == Pi0K0Km) |
---|
| 1656 | answer = -(sqrt(2) - 1) * T(piM, piM, s1, rhoMv, rhoGv, rhoWv) |
---|
| 1657 | * (T(piM, kM, s4, kstarMa, kstarGa, kstarWa) |
---|
| 1658 | - T(piM, kM, s2, kstarMa, kstarGa, kstarWa)); |
---|
| 1659 | // pi0, pi0, K- decay. |
---|
| 1660 | else if (mode == Pi0Pi0Km) |
---|
| 1661 | answer = T(piM, kM, s1, kstarMv, kstarGv, kstarWv) |
---|
| 1662 | * (T(piM, kM, s2, kstarMa, kstarGa, kstarWa) |
---|
| 1663 | - T(piM, kM, s3, kstarMa, kstarGa, kstarWa)); |
---|
| 1664 | // K-, pi-, pi+ decay. |
---|
| 1665 | else if (mode == PimPipKm) |
---|
| 1666 | answer = -T(piM, kM, s1, kstarMv, kstarGv, kstarWv) |
---|
| 1667 | * (T(piM, piM, s2, rhoMa, rhoGa, rhoWa) |
---|
| 1668 | + T(piM, kM, s3, kstarMa, kstarGa, kstarWa)); |
---|
| 1669 | // pi-, Kbar0, pi0 decay. |
---|
| 1670 | else if (mode == Pi0PimK0b) |
---|
| 1671 | answer = T(piM, kM, s1, kstarMv, kstarGv, kstarWv) |
---|
| 1672 | * (2.0 * T(piM, piM, s3, rhoMa, rhoGa, rhoWa) |
---|
| 1673 | + T(piM, kM, s2, kstarMa, kstarGa, kstarWa) |
---|
| 1674 | + T(piM, kM, s4, kstarMa, kstarGa, kstarWa)); |
---|
| 1675 | return 1.0 / (8.0 * M_PI * M_PI * piW * piW) * answer; |
---|
| 1676 | |
---|
| 1677 | } |
---|
| 1678 | |
---|
| 1679 | //========================================================================== |
---|
| 1680 | |
---|
| 1681 | // Tau decay matrix element for tau decay into three mesons. The form |
---|
| 1682 | // factors are taken from Comp. Phys. Com. 76 (1993) 361-380. |
---|
| 1683 | |
---|
| 1684 | // rhoMa(v): on-shell masses for the axial (vector) rho resonances |
---|
| 1685 | // rhoGa(v): widths for the axial (vector) rho resonances |
---|
| 1686 | // rhoWa(v): weights for the axial (vector) rho resonances |
---|
| 1687 | // kstarX: on-shell masses, widths, and weights for the K* resonances |
---|
| 1688 | // k1X: on-shell masses, width, and weight for the K1 resonances |
---|
| 1689 | // kM: kaon mass |
---|
| 1690 | // piM: charged pion mass |
---|
| 1691 | // piW: pion coupling, f_W |
---|
| 1692 | |
---|
| 1693 | //-------------------------------------------------------------------------- |
---|
| 1694 | |
---|
| 1695 | // Initialize resonances for the helicity matrix element. |
---|
| 1696 | |
---|
| 1697 | void HMETau2ThreeMesonsGeneric::initResonances() { |
---|
| 1698 | |
---|
| 1699 | // pi-, pi-, pi+ decay and pi0, pi0, pi- decay. |
---|
| 1700 | if (mode == PimPimPip || mode == Pi0Pi0Pim) DECAYWEIGHTMAX = 1.3e4; |
---|
| 1701 | // K-, pi-, K+ decay. |
---|
| 1702 | else if (mode == PimKmKp) DECAYWEIGHTMAX = 330; |
---|
| 1703 | // K0, pi-, Kbar0 decay. |
---|
| 1704 | else if (mode == PimK0bK0) DECAYWEIGHTMAX = 300; |
---|
| 1705 | // K-, pi0, K0 decay. |
---|
| 1706 | else if (mode == Pi0K0Km) DECAYWEIGHTMAX = 40; |
---|
| 1707 | // pi0, pi0, K- decay. |
---|
| 1708 | else if (mode == Pi0Pi0Km) DECAYWEIGHTMAX = 9.4e4; |
---|
| 1709 | // K-, pi-, pi+ decay. |
---|
| 1710 | else if (mode == PimPipKm) DECAYWEIGHTMAX = 9.0e3; |
---|
| 1711 | // pi-, Kbar0, pi0 decay. |
---|
| 1712 | else if (mode == Pi0PimK0b) DECAYWEIGHTMAX = 1.2e4; |
---|
| 1713 | // pi-, pi0, eta decay. |
---|
| 1714 | else if (mode == Pi0PimEta) DECAYWEIGHTMAX = 360; |
---|
| 1715 | |
---|
| 1716 | // Clear the vectors from previous decays. |
---|
| 1717 | rhoMa.clear(); rhoGa.clear(); rhoWa.clear(); |
---|
| 1718 | rhoMv.clear(); rhoGv.clear(); rhoWv.clear(); |
---|
| 1719 | kstarM.clear(); kstarG.clear(); kstarW.clear(); |
---|
| 1720 | k1M.clear(); k1G.clear(); k1W.clear(); |
---|
| 1721 | |
---|
| 1722 | // Rho parameters. |
---|
| 1723 | rhoMa.push_back(0.773); rhoGa.push_back(0.145); rhoWa.push_back(1); |
---|
| 1724 | rhoMa.push_back(1.370); rhoGa.push_back(0.510); rhoWa.push_back(-0.145); |
---|
| 1725 | rhoMv.push_back(0.773); rhoGv.push_back(0.145); rhoWv.push_back(-26); |
---|
| 1726 | rhoMv.push_back(1.5); rhoGv.push_back(0.220); rhoWv.push_back(6.5); |
---|
| 1727 | rhoMv.push_back(1.75); rhoGv.push_back(0.120); rhoWv.push_back(1); |
---|
| 1728 | |
---|
| 1729 | // Kaon parameters. |
---|
| 1730 | kstarM.push_back(0.892); kstarG.push_back(0.0513); kstarW.push_back(1); |
---|
| 1731 | k1M.push_back(1.402); k1G.push_back(0.174); k1W.push_back(1); |
---|
| 1732 | |
---|
| 1733 | // Kaon and pion parameters |
---|
| 1734 | kM = 0.49765; piM = 0.13957; piW = 0.0942; |
---|
| 1735 | |
---|
| 1736 | } |
---|
| 1737 | |
---|
| 1738 | //-------------------------------------------------------------------------- |
---|
| 1739 | |
---|
| 1740 | // Return the first form factor. |
---|
| 1741 | |
---|
| 1742 | complex HMETau2ThreeMesonsGeneric::F1() { |
---|
| 1743 | |
---|
| 1744 | complex answer; |
---|
| 1745 | // pi-, pi-, pi+ decay and pi0, pi0, pi- decay. |
---|
| 1746 | if (mode == PimPimPip || mode == Pi0Pi0Pim) |
---|
| 1747 | answer = a1BW * T(piM, piM, s2, rhoMa, rhoGa, rhoWa); |
---|
| 1748 | // K-, pi-, K+ decay. |
---|
| 1749 | else if (mode == PimKmKp) |
---|
| 1750 | answer = -a1BW * T(piM, kM, s2, kstarM, kstarG, kstarW) / 3.0; |
---|
| 1751 | // K0, pi-, Kbar0 decay. |
---|
| 1752 | else if (mode == PimK0bK0) |
---|
| 1753 | answer = -a1BW * T(piM, kM, s2, kstarM, kstarG, kstarW) / 3.0; |
---|
| 1754 | // K-, pi0, K0 decay. |
---|
| 1755 | else if (mode == Pi0K0Km) |
---|
| 1756 | answer = 0; |
---|
| 1757 | // pi0, pi0, K- decay. |
---|
| 1758 | else if (mode == Pi0Pi0Km) |
---|
| 1759 | answer = T(s1, k1M, k1G, k1W) * T(piM, kM, s2, kstarM, kstarG, kstarW); |
---|
| 1760 | // K-, pi-, pi+ decay. |
---|
| 1761 | else if (mode == PimPipKm) |
---|
| 1762 | answer = -T(s1, k1M, k1G, k1W) * T(piM, piM, s2, rhoMa, rhoGa, rhoWa) / 3.0; |
---|
| 1763 | // pi-, Kbar0, pi0 decay. |
---|
| 1764 | else if (mode == Pi0PimK0b) |
---|
| 1765 | answer = 0; |
---|
| 1766 | // pi-, pi0, eta decay. |
---|
| 1767 | else if (mode == Pi0PimEta) |
---|
| 1768 | answer = 0; |
---|
| 1769 | return answer; |
---|
| 1770 | |
---|
| 1771 | } |
---|
| 1772 | |
---|
| 1773 | //-------------------------------------------------------------------------- |
---|
| 1774 | |
---|
| 1775 | // Return the second form factor. |
---|
| 1776 | |
---|
| 1777 | complex HMETau2ThreeMesonsGeneric::F2() { |
---|
| 1778 | |
---|
| 1779 | complex answer; |
---|
| 1780 | // pi-, pi-, pi+ decay and pi0, pi0, pi- decay. |
---|
| 1781 | if (mode == PimPimPip || mode == Pi0Pi0Pim) |
---|
| 1782 | answer = -a1BW * T(piM, piM, s3, rhoMa, rhoGa, rhoWa); |
---|
| 1783 | // K-, pi-, K+ decay. |
---|
| 1784 | else if (mode == PimKmKp) |
---|
| 1785 | answer = a1BW * T(piM, piM, s3, rhoMa, rhoGa, rhoWa) / 3.0; |
---|
| 1786 | // K0, pi-, Kbar0 decay. |
---|
| 1787 | else if (mode == PimK0bK0) |
---|
| 1788 | answer = a1BW * T(piM, piM, s3, rhoMa, rhoGa, rhoWa) / 3.0; |
---|
| 1789 | // K-, pi0, K0 decay. |
---|
| 1790 | else if (mode == Pi0K0Km) |
---|
| 1791 | answer = a1BW * T(piM, piM, s3, rhoMa, rhoGa, rhoWa); |
---|
| 1792 | // pi0, pi0, K- decay. |
---|
| 1793 | else if (mode == Pi0Pi0Km) |
---|
| 1794 | answer = -T(s1, k1M, k1G, k1W) * T(piM, kM, s3, kstarM, kstarG, kstarW); |
---|
| 1795 | // K-, pi-, pi+ decay. |
---|
| 1796 | else if (mode == PimPipKm) |
---|
| 1797 | answer = T(s1, k1M, k1G, k1W) |
---|
| 1798 | * T(piM, kM, s3, kstarM, kstarG, kstarW) / 3.0; |
---|
| 1799 | // pi-, Kbar0, pi0 decay. |
---|
| 1800 | else if (mode == Pi0PimK0b) |
---|
| 1801 | answer = T(s1, k1M, k1G, k1W) * T(piM, piM, s3, rhoMa, rhoGa, rhoWa); |
---|
| 1802 | // pi-, pi0, eta decay. |
---|
| 1803 | else if (mode == Pi0PimEta) |
---|
| 1804 | answer = 0; |
---|
| 1805 | return answer; |
---|
| 1806 | |
---|
| 1807 | } |
---|
| 1808 | |
---|
| 1809 | //-------------------------------------------------------------------------- |
---|
| 1810 | |
---|
| 1811 | // Return the fourth form factor. |
---|
| 1812 | |
---|
| 1813 | complex HMETau2ThreeMesonsGeneric::F4() { |
---|
| 1814 | |
---|
| 1815 | complex answer; |
---|
| 1816 | // pi-, pi-, pi+ decay and pi0, pi0, pi- decay. |
---|
| 1817 | if (mode == PimPimPip || mode == Pi0Pi0Pim) |
---|
| 1818 | answer = 0; |
---|
| 1819 | // K-, pi-, K+ decay. |
---|
| 1820 | else if (mode == PimKmKp) |
---|
| 1821 | answer = T(piM, piM, s1, rhoMv, rhoGv, rhoWv) |
---|
| 1822 | * (T(piM, piM, s3, rhoMa, rhoGa, rhoWa) |
---|
| 1823 | - 0.2 * T(piM, kM, s2, kstarM, kstarG, kstarW)) * (1.25); |
---|
| 1824 | // K0, pi-, Kbar0 decay. |
---|
| 1825 | else if (mode == PimK0bK0) |
---|
| 1826 | answer = -T(piM, piM, s1, rhoMv, rhoGv, rhoWv) |
---|
| 1827 | * (T(piM, piM, s3, rhoMa, rhoGa, rhoWa) |
---|
| 1828 | - 0.2 * T(piM, kM, s2, kstarM, kstarG, kstarW)) * (1.25); |
---|
| 1829 | // K-, pi0, K0 decay. |
---|
| 1830 | else if (mode == Pi0K0Km) |
---|
| 1831 | answer = 0; |
---|
| 1832 | // pi0, pi0, K- decay. |
---|
| 1833 | else if (mode == Pi0Pi0Km) |
---|
| 1834 | answer = 0; |
---|
| 1835 | // K-, pi-, pi+ decay. |
---|
| 1836 | else if (mode == PimPipKm) |
---|
| 1837 | answer = -T(piM, kM, s1, kstarM, kstarG, kstarW) |
---|
| 1838 | * (T(piM, piM, s2, rhoMa, rhoGa, rhoWa) |
---|
| 1839 | - 0.2 * T(piM, kM, s3, kstarM, kstarG, kstarW)) * (1.25); |
---|
| 1840 | // pi-, Kbar0, pi0 decay. |
---|
| 1841 | else if (mode == Pi0PimK0b) |
---|
| 1842 | answer = 2.0 * T(piM, kM, s1, kstarM, kstarG, kstarW) |
---|
| 1843 | * (T(piM, piM, s3, rhoMa, rhoGa, rhoWa) |
---|
| 1844 | - 0.2 * T(piM, kM, s2, kstarM, kstarG, kstarW)) * (1.25); |
---|
| 1845 | // pi-, pi0, eta decay. |
---|
| 1846 | else if (mode == Pi0PimEta) |
---|
| 1847 | answer = T(piM, piM, s1, rhoMv, rhoGv, rhoWv) |
---|
| 1848 | * T(piM, piM, s4, rhoMa, rhoGa, rhoWa); |
---|
| 1849 | return 1.0 / (4.0 * M_PI * M_PI * piW * piW) * answer; |
---|
| 1850 | |
---|
| 1851 | } |
---|
| 1852 | |
---|
| 1853 | //========================================================================== |
---|
| 1854 | |
---|
| 1855 | // Tau decay matrix element for tau decay into two pions with a photons taken |
---|
| 1856 | // from Comp. Phys. Com. 76 (1993) 361-380. Because a photon is in the final |
---|
| 1857 | // state the matrix element is reimplented to handle the two spin states. |
---|
| 1858 | |
---|
| 1859 | // F(s, M, G, W): form factor for resonance |
---|
| 1860 | // rhoM: on-shell mass of the rho resonances |
---|
| 1861 | // rhoG: width of the rho resonances |
---|
| 1862 | // rhoW: weight of the rho resonances |
---|
| 1863 | // omegaX: on-shell mass, width, and weight of the omega resonances |
---|
| 1864 | // piM: charged pion mass |
---|
| 1865 | |
---|
| 1866 | //-------------------------------------------------------------------------- |
---|
| 1867 | |
---|
| 1868 | // Initialize constants for the helicity matrix element. |
---|
| 1869 | |
---|
| 1870 | void HMETau2TwoPionsGamma::initConstants() { |
---|
| 1871 | |
---|
| 1872 | DECAYWEIGHTMAX = 4e4; |
---|
| 1873 | |
---|
| 1874 | // Clear the vectors from previous decays. |
---|
| 1875 | rhoM.clear(); rhoG.clear(); rhoW.clear(); |
---|
| 1876 | omegaM.clear(); omegaG.clear(); omegaW.clear(); |
---|
| 1877 | |
---|
| 1878 | // Set parameters. |
---|
| 1879 | rhoM.push_back(0.773); rhoG.push_back(0.145); rhoW.push_back(1); |
---|
| 1880 | rhoM.push_back(1.7); rhoG.push_back(0.26); rhoW.push_back(-0.1); |
---|
| 1881 | omegaM.push_back(0.782); omegaG.push_back(0.0085); omegaW.push_back(1); |
---|
| 1882 | piM = 0.13957; |
---|
| 1883 | |
---|
| 1884 | } |
---|
| 1885 | |
---|
| 1886 | //-------------------------------------------------------------------------- |
---|
| 1887 | |
---|
| 1888 | // Initialize wave functions for the helicity matrix element. |
---|
| 1889 | void HMETau2TwoPionsGamma::initWaves(vector<HelicityParticle>& p) { |
---|
| 1890 | |
---|
| 1891 | // Calculate the hadronic current. |
---|
| 1892 | u.clear(); |
---|
| 1893 | pMap.resize(p.size()); |
---|
| 1894 | setFermionLine(0, p[0], p[1]); |
---|
| 1895 | |
---|
| 1896 | // Calculate the hadronic current. |
---|
| 1897 | vector< Wave4 > u2; |
---|
| 1898 | Wave4 q(p[2].p() + p[3].p() + p[4].p()); |
---|
| 1899 | Wave4 q2(p[2].p()), q3(p[3].p()), q4(p[4].p()); |
---|
| 1900 | double s1 = m2(q); |
---|
| 1901 | double s2 = m2(q3 + q2); |
---|
| 1902 | complex f = F(s1, rhoM, rhoG, rhoW) * F(0, rhoM, rhoG, rhoW) |
---|
| 1903 | * F(s2, omegaM, omegaG, omegaW); |
---|
| 1904 | double q4q2 = m2(q4, q2); |
---|
| 1905 | double q4q3 = m2(q4, q3); |
---|
| 1906 | double q3q2 = m2(q3, q2); |
---|
| 1907 | for (int h = 0; h < 2; h++) { |
---|
| 1908 | Wave4 e = p[2].wave(h); |
---|
| 1909 | complex q4e = q4*gamma[4]*e; |
---|
| 1910 | complex q3e = q3*gamma[4]*e; |
---|
| 1911 | u2.push_back(f * (e * (piM*piM*q4q2 - q3q2*(q4q3 - q4q2)) |
---|
| 1912 | - q3 * (q3e*q4q2 - q4e*q3q2) |
---|
| 1913 | + q2 * (q3e*q4q3 - q4e*(piM*piM + q3q2)))); |
---|
| 1914 | } |
---|
| 1915 | u.push_back(u2); |
---|
| 1916 | |
---|
| 1917 | } |
---|
| 1918 | |
---|
| 1919 | //-------------------------------------------------------------------------- |
---|
| 1920 | |
---|
| 1921 | // Return element for the helicity matrix element. |
---|
| 1922 | complex HMETau2TwoPionsGamma::calculateME(vector<int> h) { |
---|
| 1923 | |
---|
| 1924 | complex answer(0,0); |
---|
| 1925 | for (int mu = 0; mu <= 3; mu++) { |
---|
| 1926 | answer += |
---|
| 1927 | (u[1][h[pMap[1]]] * gamma[mu] * (1 - gamma[5]) * u[0][h[pMap[0]]]) |
---|
| 1928 | * gamma[4](mu,mu) * u[2][h[2]](mu); |
---|
| 1929 | } |
---|
| 1930 | return answer; |
---|
| 1931 | |
---|
| 1932 | } |
---|
| 1933 | |
---|
| 1934 | //-------------------------------------------------------------------------- |
---|
| 1935 | |
---|
| 1936 | // Return the form factor. |
---|
| 1937 | complex HMETau2TwoPionsGamma::F(double s, vector<double> M, vector<double> G, |
---|
| 1938 | vector<double> W) { |
---|
| 1939 | |
---|
| 1940 | complex answer(0, 0); |
---|
| 1941 | for (unsigned int i = 0; i < M.size(); i++) |
---|
| 1942 | answer += W[i] / (M[i]*M[i] - s - complex(0, 1) * M[i] * G[i]); |
---|
| 1943 | return answer; |
---|
| 1944 | |
---|
| 1945 | } |
---|
| 1946 | |
---|
| 1947 | //========================================================================== |
---|
| 1948 | |
---|
| 1949 | // Tau decay matrix element for tau decay into pions using the Novosibirsk |
---|
| 1950 | // model of Comp. Phys. Com. 174 (2006) 818-835. |
---|
| 1951 | |
---|
| 1952 | // G(i,s): G-factor for index 1, 2, or 3 |
---|
| 1953 | // tX(q,q1,q2,q3,q4): combined resonance current |
---|
| 1954 | // a1D(s): a1 Breit-Wigner denominator |
---|
| 1955 | // rhoD(s): rho Breit-Wigner denominator |
---|
| 1956 | // sigD(s): sigma Breit-Wigner denominator |
---|
| 1957 | // omeD(s): omega Breit-Wigner denominator |
---|
| 1958 | // a1FormFactor(s): form factor for the a1 resonance |
---|
| 1959 | // rhoFormFactor1(2)(s): form factor for the rho resonance |
---|
| 1960 | // omeFormFactor(s): form factor for the omega resonance |
---|
| 1961 | // sigM: on-shell mass of the sigma resonance |
---|
| 1962 | // sigG: width of the sigma resonance |
---|
| 1963 | // sigA: amplitude of the sigma resonance |
---|
| 1964 | // sigP: phase of the sigma resonance |
---|
| 1965 | // sigW: weight of the sigma resonance (from amplitude and weight) |
---|
| 1966 | // omeX: mass, width, amplitude, phase, and weight of the omega resonance |
---|
| 1967 | // a1X: mass and width of the a1 resonance |
---|
| 1968 | // rhoX: mass and width of the rho resonance |
---|
| 1969 | // picM: charge pion mass |
---|
| 1970 | // pinM: neutral pion mass |
---|
| 1971 | // lambda2: a1 form factor cut-off |
---|
| 1972 | |
---|
| 1973 | //-------------------------------------------------------------------------- |
---|
| 1974 | |
---|
| 1975 | // Initialize constants for the helicity matrix element. |
---|
| 1976 | |
---|
| 1977 | void HMETau2FourPions::initConstants() { |
---|
| 1978 | |
---|
| 1979 | if (abs(pID[3]) == 111) DECAYWEIGHTMAX = 5e8; |
---|
| 1980 | else DECAYWEIGHTMAX = 5e9; |
---|
| 1981 | pinM = particleDataPtr->m0(111); |
---|
| 1982 | picM = particleDataPtr->m0(211); |
---|
| 1983 | sigM = 0.8; omeM = 0.782; a1M = 1.23; rhoM = 0.7761; |
---|
| 1984 | sigG = 0.8; omeG = 0.00841; a1G = 0.45; rhoG = 0.1445; |
---|
| 1985 | sigP = 0.43585; omeP = 0.0; |
---|
| 1986 | sigA = 1.39987; omeA = 1.0; |
---|
| 1987 | sigW = sigA*(cos(sigP)+complex(0,1)*sin(sigP)); |
---|
| 1988 | omeW = omeA*(cos(omeP)+complex(0,1)*sin(omeP)); |
---|
| 1989 | lambda2 = 1.2; |
---|
| 1990 | |
---|
| 1991 | } |
---|
| 1992 | |
---|
| 1993 | //-------------------------------------------------------------------------- |
---|
| 1994 | |
---|
| 1995 | // Initialize the hadronic current for the helicity matrix element. |
---|
| 1996 | |
---|
| 1997 | void HMETau2FourPions::initHadronicCurrent(vector<HelicityParticle>& p) { |
---|
| 1998 | |
---|
| 1999 | vector< Wave4 > u2; |
---|
| 2000 | |
---|
| 2001 | // Create pion momenta. |
---|
| 2002 | Wave4 q(p[2].p() + p[3].p() + p[4].p()+ p[5].p()); |
---|
| 2003 | Wave4 q2(p[2].p()), q3(p[3].p()), q4(p[4].p()), q5(p[5].p()); |
---|
| 2004 | |
---|
| 2005 | // Calculate the four pion system energy. |
---|
| 2006 | double s = m2(q); |
---|
| 2007 | |
---|
| 2008 | // Create the hadronic current for the 3 neutral pion channel. |
---|
| 2009 | if (abs(pID[3]) == 111) |
---|
| 2010 | u2.push_back(G(1,s)*(t1(q,q3,q4,q5,q2) + t1(q,q3,q2,q5,q4) + |
---|
| 2011 | t1(q,q4,q3,q5,q2) + t1(q,q4,q2,q5,q3) + |
---|
| 2012 | t1(q,q2,q3,q5,q4) + t1(q,q2,q4,q5,q3) + |
---|
| 2013 | t2(q,q3,q5,q4,q2) + t2(q,q4,q5,q3,q2) + |
---|
| 2014 | t2(q,q2,q5,q4,q3) - t2(q,q5,q3,q4,q2) - |
---|
| 2015 | t2(q,q5,q4,q3,q2) - t2(q,q5,q2,q4,q3))); |
---|
| 2016 | |
---|
| 2017 | // Create the hadronic current for the 3 charged pion channel. |
---|
| 2018 | else if (abs(pID[3]) == 211) |
---|
| 2019 | u2.push_back(G(2,s)*(t1(q,q3,q5,q4,q2) + t1(q,q4,q5,q3,q2) + |
---|
| 2020 | t1(q,q3,q4,q5,q2) + t1(q,q4,q3,q5,q2) + |
---|
| 2021 | t1(q,q2,q4,q3,q5) + t1(q,q2,q3,q4,q5) + |
---|
| 2022 | t2(q,q2,q4,q3,q5) + t2(q,q2,q3,q4,q5) - |
---|
| 2023 | t2(q,q3,q2,q4,q5) - t2(q,q4,q2,q3,q5)) + |
---|
| 2024 | G(3,s)*(t3(q,q3,q5,q4,q2) + t3(q,q4,q5,q3,q2) - |
---|
| 2025 | t3(q,q3,q4,q5,q2) - t3(q,q4,q3,q5,q2) - |
---|
| 2026 | t3(q,q3,q2,q4,q5) - t3(q,q4,q2,q3,q5))); |
---|
| 2027 | u.push_back(u2); |
---|
| 2028 | |
---|
| 2029 | } |
---|
| 2030 | |
---|
| 2031 | //-------------------------------------------------------------------------- |
---|
| 2032 | |
---|
| 2033 | // Return the first t-vector. |
---|
| 2034 | |
---|
| 2035 | Wave4 HMETau2FourPions::t1(Wave4 &q, Wave4 &q1, Wave4 &q2, |
---|
| 2036 | Wave4 &q3, Wave4 &q4) { |
---|
| 2037 | |
---|
| 2038 | Wave4 a1Q(q2 + q3 + q4); |
---|
| 2039 | Wave4 rhoQ(q3 + q4); |
---|
| 2040 | double a1S = m2(a1Q); |
---|
| 2041 | double rhoS = m2(rhoQ); |
---|
| 2042 | |
---|
| 2043 | // Needed to match Herwig++. |
---|
| 2044 | double gM = sqrtpos(rhoM*rhoM - 4*picM*picM) * (rhoM*rhoM - 4*picM*picM) |
---|
| 2045 | / rhoM; |
---|
| 2046 | double dm = (rhoFormFactor1(0) - rhoFormFactor1(rhoM*rhoM) + |
---|
| 2047 | rhoM*rhoM * rhoFormFactor2(rhoM*rhoM)) / gM; |
---|
| 2048 | return - a1FormFactor(a1S) / (a1D(a1S) * rhoD(rhoS)) * pow2(a1M) * |
---|
| 2049 | (rhoM*rhoM + rhoM*rhoG*dm) * |
---|
| 2050 | (m2(q,a1Q) * (m2(q3,a1Q) * q4 - m2(q4,a1Q) * q3) + |
---|
| 2051 | (m2(q,q4) * m2(q1,q3) - m2(q,q3) * m2(q1,q4)) * a1Q); |
---|
| 2052 | |
---|
| 2053 | } |
---|
| 2054 | |
---|
| 2055 | //-------------------------------------------------------------------------- |
---|
| 2056 | |
---|
| 2057 | // Return the second t-vector. |
---|
| 2058 | |
---|
| 2059 | Wave4 HMETau2FourPions::t2(Wave4 &q, Wave4 &/*q1*/, Wave4 &q2, |
---|
| 2060 | Wave4 &q3, Wave4 &q4) { |
---|
| 2061 | |
---|
| 2062 | Wave4 a1Q(q2 + q3 + q4); |
---|
| 2063 | Wave4 sigQ(q3 + q4); |
---|
| 2064 | double a1S = m2(a1Q); |
---|
| 2065 | double sigS = m2(sigQ); |
---|
| 2066 | return sigW * a1FormFactor(a1S) / (a1D(a1S) * sigD(sigS)) * |
---|
| 2067 | pow2(a1M) * pow2(sigM) * (m2(q,a1Q) * a1S * q2 - m2(q,q2) * a1S * a1Q); |
---|
| 2068 | |
---|
| 2069 | } |
---|
| 2070 | |
---|
| 2071 | //-------------------------------------------------------------------------- |
---|
| 2072 | |
---|
| 2073 | // Return the third t-vector. |
---|
| 2074 | |
---|
| 2075 | Wave4 HMETau2FourPions::t3(Wave4 &q, Wave4 &q1, Wave4 &q2, |
---|
| 2076 | Wave4 &q3, Wave4 &q4) { |
---|
| 2077 | Wave4 omeQ(q2 + q3 + q4); |
---|
| 2078 | Wave4 rhoQ(q3 + q4); |
---|
| 2079 | double omeS = m2(omeQ); |
---|
| 2080 | double rhoS = m2(rhoQ); |
---|
| 2081 | |
---|
| 2082 | // Needed to match Herwig++. |
---|
| 2083 | double gM = sqrtpos(rhoM*rhoM - 4*picM*picM) * (rhoM*rhoM - 4*picM*picM) |
---|
| 2084 | / rhoM; |
---|
| 2085 | double dm = (rhoFormFactor1(0) - rhoFormFactor1(rhoM*rhoM) + |
---|
| 2086 | rhoM*rhoM * rhoFormFactor2(rhoM*rhoM)) / gM; |
---|
| 2087 | return omeW * omeFormFactor(omeS) / (omeD(omeS) * rhoD(rhoS)) * |
---|
| 2088 | pow2(omeM) * (rhoM*rhoM + rhoM*rhoG*dm) * |
---|
| 2089 | ((m2(q,q3) * m2(q1,q4) - m2(q,q4) * m2(q1,q3)) * q2 + |
---|
| 2090 | (m2(q,q4) * m2(q1,q2) - m2(q,q2) * m2(q1,q4)) * q3 + |
---|
| 2091 | (m2(q,q2) * m2(q1,q3) - m2(q,q3) * m2(q1,q2)) * q4); |
---|
| 2092 | |
---|
| 2093 | } |
---|
| 2094 | |
---|
| 2095 | //-------------------------------------------------------------------------- |
---|
| 2096 | |
---|
| 2097 | // Return the D function for the a1(1260). |
---|
| 2098 | |
---|
| 2099 | complex HMETau2FourPions::a1D(double s) { |
---|
| 2100 | |
---|
| 2101 | // rG is defined as the running width. |
---|
| 2102 | double rG = 0; |
---|
| 2103 | |
---|
| 2104 | // The rho and pion cut off thresholds defined in the fit. |
---|
| 2105 | double piM = 0.16960; |
---|
| 2106 | double rM = 0.83425; |
---|
| 2107 | |
---|
| 2108 | // Fit of width below three pion mass threshold. |
---|
| 2109 | if (s < piM) |
---|
| 2110 | rG = 0; |
---|
| 2111 | |
---|
| 2112 | // Fit of width below pion and rho mass threshold. |
---|
| 2113 | else if (s < rM) |
---|
| 2114 | rG = 0.003052*pow3(s - piM)*(1.0 + 151.088*(s - piM) + |
---|
| 2115 | 174.495*pow2(s - piM)); |
---|
| 2116 | |
---|
| 2117 | // Fit of width above pion and rho mass threshold. |
---|
| 2118 | else |
---|
| 2119 | rG = 2.60817 - 2.47790*s + 0.66539*pow2(s) - 0.0678183*pow3(s) + |
---|
| 2120 | 1.66577*(s-1.23701)/s; |
---|
| 2121 | return s - a1M*a1M + complex(0,1) * sqrtpos(s) * rG; |
---|
| 2122 | |
---|
| 2123 | } |
---|
| 2124 | |
---|
| 2125 | //-------------------------------------------------------------------------- |
---|
| 2126 | |
---|
| 2127 | // Return the D function for the rho(770). |
---|
| 2128 | |
---|
| 2129 | complex HMETau2FourPions::rhoD(double s) { |
---|
| 2130 | |
---|
| 2131 | double gQ = sqrtpos(s - 4*picM*picM) * (s - 4*picM*picM) / sqrtpos(s); |
---|
| 2132 | double gM = sqrtpos(rhoM*rhoM - 4*picM*picM) * (rhoM*rhoM - 4*picM*picM) |
---|
| 2133 | / rhoM; |
---|
| 2134 | double dm = (rhoFormFactor1(s) - rhoFormFactor1(rhoM*rhoM) - |
---|
| 2135 | (s - rhoM*rhoM) * rhoFormFactor2(rhoM*rhoM)) / gM; |
---|
| 2136 | |
---|
| 2137 | // Ensure complex part is zero below available channel. |
---|
| 2138 | if (s < 4*picM*picM) gQ = 0; |
---|
| 2139 | return s - rhoM*rhoM - rhoM*rhoG*dm + complex(0,1)*rhoM*rhoG*(gQ/gM); |
---|
| 2140 | |
---|
| 2141 | } |
---|
| 2142 | |
---|
| 2143 | //-------------------------------------------------------------------------- |
---|
| 2144 | |
---|
| 2145 | // Return the D function for the sigma(800) (just s-wave running width). |
---|
| 2146 | |
---|
| 2147 | complex HMETau2FourPions::sigD(double s) { |
---|
| 2148 | |
---|
| 2149 | // Sigma decay to two neutral pions for three neutral pion channel. |
---|
| 2150 | double piM = abs(pID[3]) == 111 ? pinM : picM; |
---|
| 2151 | double gQ = sqrtpos(1.0 - 4*piM*piM/s); |
---|
| 2152 | double gM = sqrtpos(1.0 - 4*piM*piM/(sigM*sigM)); |
---|
| 2153 | return s - sigM*sigM + complex(0,1)*sigM*sigG*gQ/gM; |
---|
| 2154 | |
---|
| 2155 | } |
---|
| 2156 | |
---|
| 2157 | //-------------------------------------------------------------------------- |
---|
| 2158 | |
---|
| 2159 | // Return the D function for the omega(782). |
---|
| 2160 | |
---|
| 2161 | complex HMETau2FourPions::omeD(double s) { |
---|
| 2162 | |
---|
| 2163 | double g = 0; |
---|
| 2164 | double q = sqrtpos(s); |
---|
| 2165 | double x = q - omeM; |
---|
| 2166 | |
---|
| 2167 | // Fit of width given in TAUOLA. |
---|
| 2168 | if (s < 1) |
---|
| 2169 | g = 1 + 17.560*x + 141.110*pow2(x) + 894.884*pow3(x) + 4977.35*pow4(x) + |
---|
| 2170 | 7610.66*pow5(x) - 42524.4*pow6(x); |
---|
| 2171 | else |
---|
| 2172 | g = -1333.26 + 4860*q - 6000.81*pow2(q) + 2504.97*pow3(q); |
---|
| 2173 | if (g < 0) g = 0; |
---|
| 2174 | return s - omeM*omeM + complex(0,1)*omeM*omeG*g; |
---|
| 2175 | |
---|
| 2176 | } |
---|
| 2177 | |
---|
| 2178 | //-------------------------------------------------------------------------- |
---|
| 2179 | |
---|
| 2180 | // Return the form factor for the a1. |
---|
| 2181 | |
---|
| 2182 | double HMETau2FourPions::a1FormFactor(double s) { |
---|
| 2183 | |
---|
| 2184 | return pow2((1.0 + a1M*a1M/lambda2) / (1.0 + s/lambda2)); |
---|
| 2185 | |
---|
| 2186 | } |
---|
| 2187 | |
---|
| 2188 | //-------------------------------------------------------------------------- |
---|
| 2189 | |
---|
| 2190 | // Return the form factor for the rho(770) (equivalent to h(s) in TAUOLA). |
---|
| 2191 | |
---|
| 2192 | double HMETau2FourPions::rhoFormFactor1(double s) { |
---|
| 2193 | |
---|
| 2194 | double f = sqrtpos(1 - 4*picM*picM/s); |
---|
| 2195 | if (s > 4*picM*picM) |
---|
| 2196 | f = f * log((1 + f) / (1 - f)) * (s - 4*picM*picM) / M_PI; |
---|
| 2197 | else if (s < 0.0000001) |
---|
| 2198 | f = -8 * picM*picM / M_PI; |
---|
| 2199 | else |
---|
| 2200 | f = 0; |
---|
| 2201 | return f; |
---|
| 2202 | |
---|
| 2203 | } |
---|
| 2204 | |
---|
| 2205 | //-------------------------------------------------------------------------- |
---|
| 2206 | |
---|
| 2207 | // Return the form factor for the rho(770) (equivalent to h(s) derivative). |
---|
| 2208 | |
---|
| 2209 | double HMETau2FourPions::rhoFormFactor2(double s) { |
---|
| 2210 | |
---|
| 2211 | double f = sqrtpos(1 - 4*picM*picM/s); |
---|
| 2212 | if (s > 4*picM*picM) |
---|
| 2213 | f = f / (M_PI * s) * (s*f + (2*picM*picM + s)*log((1 + f) / (1 - f))); |
---|
| 2214 | else |
---|
| 2215 | f = 0; |
---|
| 2216 | return f; |
---|
| 2217 | |
---|
| 2218 | } |
---|
| 2219 | |
---|
| 2220 | //-------------------------------------------------------------------------- |
---|
| 2221 | |
---|
| 2222 | // Return the form factor for the omega(782). |
---|
| 2223 | |
---|
| 2224 | double HMETau2FourPions::omeFormFactor(double /*s*/) { |
---|
| 2225 | |
---|
| 2226 | return 1.0; |
---|
| 2227 | |
---|
| 2228 | } |
---|
| 2229 | |
---|
| 2230 | //-------------------------------------------------------------------------- |
---|
| 2231 | |
---|
| 2232 | // Return the G-functions given in TAUOLA using a piece-wise fit. |
---|
| 2233 | |
---|
| 2234 | double HMETau2FourPions::G(int i, double s) { |
---|
| 2235 | |
---|
| 2236 | // Break points for the fits. |
---|
| 2237 | double s0(0), s1(0), s2(0), s3(0), s4(0), s5(0); |
---|
| 2238 | |
---|
| 2239 | // Parameters for the fits. |
---|
| 2240 | double a1(0), b1(0); |
---|
| 2241 | double a2(0), b2(0), c2(0), d2(0), e2(0); |
---|
| 2242 | double a3(0), b3(0), c3(0), d3(0), e3(0); |
---|
| 2243 | double a4(0), b4(0); |
---|
| 2244 | double a5(0), b5(0); |
---|
| 2245 | |
---|
| 2246 | // Three neutral pion parameters. |
---|
| 2247 | if (i == 1) { |
---|
| 2248 | s0 = 0.614403; s1 = 0.656264; s2 = 1.57896; |
---|
| 2249 | s3 = 3.08198; s4 = 3.12825; s5 = 3.17488; |
---|
| 2250 | a1 = -23383.7; b1 = 38059.2; |
---|
| 2251 | a2 = 230.368; b2 = -4.39368; c2 = 687.002; |
---|
| 2252 | d2 = -732.581; e2 = 207.087; |
---|
| 2253 | a3 = 1633.92; b3 = -2596.21; c3 = 1703.08; |
---|
| 2254 | d3 = -501.407; e3 = 54.5919; |
---|
| 2255 | a4 = -2982.44; b4 = 986.009; |
---|
| 2256 | a5 = 6948.99; b5 = -2188.74; |
---|
| 2257 | } |
---|
| 2258 | |
---|
| 2259 | // Three charged pion parameters. |
---|
| 2260 | else if (i == 2) { |
---|
| 2261 | s0 = 0.614403; s1 = 0.635161; s2 = 2.30794; |
---|
| 2262 | s3 = 3.08198; s4 = 3.12825; s5 = 3.17488; |
---|
| 2263 | a1 = -54171.5; b1 = 88169.3; |
---|
| 2264 | a2 = 454.638; b2 = -3.07152; c2 = -48.7086; |
---|
| 2265 | d2 = 81.9702; e2 = -24.0564; |
---|
| 2266 | a3 = -162.421; b3 = 308.977; c3 = -27.7887; |
---|
| 2267 | d3 = -48.5957; e3 = 10.6168; |
---|
| 2268 | a4 = -2650.29; b4 = 879.776; |
---|
| 2269 | a5 = 6936.99; b5 = -2184.97; |
---|
| 2270 | } |
---|
| 2271 | |
---|
| 2272 | // Omega mediated three charged pion parameters. |
---|
| 2273 | else if (i == 3) { |
---|
| 2274 | s0 = 0.81364; s1 = 0.861709; s2 = 1.92621; |
---|
| 2275 | s3 = 3.08198; s4 = 3.12825; s5 = 3.17488; |
---|
| 2276 | a1 = -84888.9; b1 = 104332; |
---|
| 2277 | a2 = 2698.15; b2 = -3.08302; c2 = 1936.11; |
---|
| 2278 | d2 = -1254.59; e2 = 201.291; |
---|
| 2279 | a3 = 7171.65; b3 = -6387.9; c3 = 3056.27; |
---|
| 2280 | d3 = -888.63; e3 = 108.632; |
---|
| 2281 | a4 = -5607.48; b4 = 1917.27; |
---|
| 2282 | a5 = 26573; b5 = -8369.76; |
---|
| 2283 | } |
---|
| 2284 | |
---|
| 2285 | // Return the appropriate fit. |
---|
| 2286 | if (s < s0) |
---|
| 2287 | return 0.0; |
---|
| 2288 | else if (s < s1) |
---|
| 2289 | return a1 + b1*s; |
---|
| 2290 | else if (s < s2) |
---|
| 2291 | return a2*pow(s,b2) + c2*pow2(s) + d2*pow3(s) + e2*pow4(s); |
---|
| 2292 | else if (s < s3) |
---|
| 2293 | return a3 + b3*s + c3*pow2(s) + d3*pow3(s) + e3*pow4(s); |
---|
| 2294 | else if (s < s4) |
---|
| 2295 | return a4 + b4*s; |
---|
| 2296 | else if (s < s5) |
---|
| 2297 | return a5 + b5*s; |
---|
| 2298 | else |
---|
| 2299 | return 0.0; |
---|
| 2300 | |
---|
| 2301 | } |
---|
| 2302 | |
---|
| 2303 | //========================================================================== |
---|
| 2304 | |
---|
| 2305 | // Tau decay matrix element for tau decay into five pions using the model given |
---|
| 2306 | // in hep-ph/0602162v1. |
---|
| 2307 | |
---|
| 2308 | // Ja(q,q1,q2,q3,q4,q5): current through rho and omega resonances |
---|
| 2309 | // Jb(q,q1,q2,q3,q4,q5): current through a1 and sigma resonances |
---|
| 2310 | // breitWigner(s,M,G): s-wave Breit-Wigner assuming massless products |
---|
| 2311 | // a1M: on-shell mass of the a1 resonance |
---|
| 2312 | // a1G: width of the a1 resonance |
---|
| 2313 | // rhoX: mass and width of the rho resonance |
---|
| 2314 | // omegaX: mass, width, and weight of the omega resonance |
---|
| 2315 | // sigmaX: mass, width, and weight of the sigma resonance |
---|
| 2316 | |
---|
| 2317 | //-------------------------------------------------------------------------- |
---|
| 2318 | |
---|
| 2319 | // Initialize constants for the helicity matrix element. |
---|
| 2320 | |
---|
| 2321 | void HMETau2FivePions::initConstants() { |
---|
| 2322 | |
---|
| 2323 | // pi-, pi-, pi+, pi+, pi- decay. |
---|
| 2324 | if (abs(pID[2]) == 211 && abs(pID[3]) == 211 && abs(pID[4]) == 211 && |
---|
| 2325 | abs(pID[5]) == 211 && abs(pID[6]) == 211) |
---|
| 2326 | DECAYWEIGHTMAX = 4e4; |
---|
| 2327 | // pi+, pi-, pi0, pi-, pi0 decay. |
---|
| 2328 | else if (abs(pID[2]) == 111 && abs(pID[3]) == 111 && abs(pID[4]) == 211 && |
---|
| 2329 | abs(pID[5]) == 211 && abs(pID[6]) == 211) |
---|
| 2330 | DECAYWEIGHTMAX = 1e7; |
---|
| 2331 | // pi0, pi0, pi-, pi0, pi0 decay. |
---|
| 2332 | else if (abs(pID[2]) == 111 && abs(pID[3]) == 111 && abs(pID[4]) == 111 && |
---|
| 2333 | abs(pID[5]) == 111 && abs(pID[6]) == 211) |
---|
| 2334 | DECAYWEIGHTMAX = 1e5; |
---|
| 2335 | |
---|
| 2336 | // Set resonances. |
---|
| 2337 | a1M = 1.260; a1G = 0.400; |
---|
| 2338 | rhoM = 0.776; rhoG = 0.150; |
---|
| 2339 | omegaM = 0.782; omegaG = 0.0085; omegaW = 11.5; |
---|
| 2340 | sigmaM = 0.800; sigmaG = 0.600; sigmaW = 1; |
---|
| 2341 | |
---|
| 2342 | } |
---|
| 2343 | |
---|
| 2344 | //-------------------------------------------------------------------------- |
---|
| 2345 | |
---|
| 2346 | // Initialize the hadronic current for the helicity matrix element. |
---|
| 2347 | |
---|
| 2348 | void HMETau2FivePions::initHadronicCurrent(vector<HelicityParticle>& p) { |
---|
| 2349 | |
---|
| 2350 | vector< Wave4 > u2; |
---|
| 2351 | |
---|
| 2352 | Wave4 q(p[2].p() + p[3].p() + p[4].p() + p[5].p() + p[6].p()); |
---|
| 2353 | Wave4 q2(p[2].p()), q3(p[3].p()), q4(p[4].p()), q5(p[5].p()), q6(p[6].p()); |
---|
| 2354 | // pi-, pi-, pi+, pi+, pi- decay. |
---|
| 2355 | if (abs(pID[2]) == 211 && abs(pID[3]) == 211 && abs(pID[4]) == 211 && |
---|
| 2356 | abs(pID[5]) == 211 && abs(pID[6]) == 211) |
---|
| 2357 | u2.push_back(Jb(q, q2, q3, q5, q6, q4) + Jb(q, q4, q3, q5, q6, q2) |
---|
| 2358 | + Jb(q, q2, q4, q5, q6, q3) + Jb(q, q2, q3, q6, q5, q4) |
---|
| 2359 | + Jb(q, q4, q3, q6, q5, q2) + Jb(q, q2, q4, q6, q5, q3)); |
---|
| 2360 | // pi+, pi-, pi0, pi-, pi0 decay. |
---|
| 2361 | else if (abs(pID[2]) == 111 && abs(pID[3]) == 111 && abs(pID[4]) == 211 && |
---|
| 2362 | abs(pID[5]) == 211 && abs(pID[6]) == 211) |
---|
| 2363 | u2.push_back(Ja(q, q6, q4, q2, q5, q3) + Ja(q, q6, q5, q2, q4, q3) |
---|
| 2364 | + Ja(q, q6, q4, q3, q5, q2) + Ja(q, q6, q5, q3, q4, q2) |
---|
| 2365 | + Jb(q, q4, q5, q6, q2, q3) + Jb(q, q2, q3, q4, q6, q5) |
---|
| 2366 | + Jb(q, q2, q3, q5, q6, q4)); |
---|
| 2367 | // pi0, pi0, pi-, pi0, pi0 decay. |
---|
| 2368 | else if (abs(pID[2]) == 111 && abs(pID[3]) == 111 && abs(pID[4]) == 111 && |
---|
| 2369 | abs(pID[5]) == 111 && abs(pID[6]) == 211) |
---|
| 2370 | u2.push_back(Jb(q, q2, q3, q6, q4, q5) + Jb(q, q5, q3, q6, q4, q2) |
---|
| 2371 | + Jb(q, q3, q4, q6, q2, q5) + Jb(q, q2, q4, q6, q3, q5) |
---|
| 2372 | + Jb(q, q2, q5, q6, q4, q3) + Jb(q, q4, q5, q6, q2, q3)); |
---|
| 2373 | |
---|
| 2374 | u.push_back(u2); |
---|
| 2375 | |
---|
| 2376 | } |
---|
| 2377 | |
---|
| 2378 | //-------------------------------------------------------------------------- |
---|
| 2379 | |
---|
| 2380 | // Return the omega-rho hadronic current. |
---|
| 2381 | |
---|
| 2382 | Wave4 HMETau2FivePions::Ja(Wave4 &q, Wave4 &q1, Wave4 &q2, |
---|
| 2383 | Wave4 &q3, Wave4 &q4, Wave4 &q5) { |
---|
| 2384 | |
---|
| 2385 | Wave4 j = epsilon(q1, q2, q3); |
---|
| 2386 | return omegaW * (breitWigner(m2(q), a1M, a1G) |
---|
| 2387 | * breitWigner(m2(q1 + q2 + q3), omegaM, omegaG) |
---|
| 2388 | * breitWigner(m2(q4 + q5), rhoM, rhoG) |
---|
| 2389 | * epsilon(q4 - q5, j, q) |
---|
| 2390 | * (breitWigner(m2(q2 + q3), rhoM, rhoG) |
---|
| 2391 | + breitWigner(m2(q1 + q3), rhoM, rhoG) |
---|
| 2392 | + breitWigner(m2(q1 + q2), rhoM, rhoG))); |
---|
| 2393 | |
---|
| 2394 | } |
---|
| 2395 | |
---|
| 2396 | //-------------------------------------------------------------------------- |
---|
| 2397 | |
---|
| 2398 | // Return the a1-sigma hadronic current. |
---|
| 2399 | |
---|
| 2400 | Wave4 HMETau2FivePions::Jb(Wave4 &q, Wave4 &q1, Wave4 &q2, |
---|
| 2401 | Wave4 &q3, Wave4 &q4, Wave4 &q5) { |
---|
| 2402 | |
---|
| 2403 | double s = m2(q); |
---|
| 2404 | Wave4 a1Q = q1 + q2 + q3; |
---|
| 2405 | double a1S = m2(a1Q); |
---|
| 2406 | Wave4 j = (m2(q2, q1 - q3) / a1S * a1Q - q1 + q3) |
---|
| 2407 | * breitWigner(m2(q1 + q3), rhoM, rhoG) |
---|
| 2408 | + (m2(q1, q2 - q3) / a1S * a1Q - q2 + q3) |
---|
| 2409 | * breitWigner(m2(q2 + q3), rhoM, rhoG); |
---|
| 2410 | j = (j * gamma[4] * q / s) * q - j; |
---|
| 2411 | return sigmaW * (breitWigner(s, a1M, a1G) * breitWigner(a1S, a1M, a1G) |
---|
| 2412 | * breitWigner(m2(q4 + q5), sigmaM, sigmaG) * j); |
---|
| 2413 | |
---|
| 2414 | } |
---|
| 2415 | |
---|
| 2416 | complex HMETau2FivePions::breitWigner(double s, double M, double G) { |
---|
| 2417 | |
---|
| 2418 | return M * M / (M * M - s - complex(0, 1) * M * G); |
---|
| 2419 | |
---|
| 2420 | } |
---|
| 2421 | |
---|
| 2422 | //========================================================================== |
---|
| 2423 | |
---|
| 2424 | } // end namespace Pythia8 |
---|