source: trunk/source/particles/management/src/G4MuonDecayChannelWithSpin.cc@ 1351

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1//
2// ********************************************************************
3// * License and Disclaimer *
4// * *
5// * The Geant4 software is copyright of the Copyright Holders of *
6// * the Geant4 Collaboration. It is provided under the terms and *
7// * conditions of the Geant4 Software License, included in the file *
8// * LICENSE and available at http://cern.ch/geant4/license . These *
9// * include a list of copyright holders. *
10// * *
11// * Neither the authors of this software system, nor their employing *
12// * institutes,nor the agencies providing financial support for this *
13// * work make any representation or warranty, express or implied, *
14// * regarding this software system or assume any liability for its *
15// * use. Please see the license in the file LICENSE and URL above *
16// * for the full disclaimer and the limitation of liability. *
17// * *
18// * This code implementation is the result of the scientific and *
19// * technical work of the GEANT4 collaboration. *
20// * By using, copying, modifying or distributing the software (or *
21// * any work based on the software) you agree to acknowledge its *
22// * use in resulting scientific publications, and indicate your *
23// * acceptance of all terms of the Geant4 Software license. *
24// ********************************************************************
25//
26// ------------------------------------------------------------
27// GEANT 4 class header file
28//
29// History:
30// 17 August 2004 P.Gumplinger and T.MacPhail
31// samples Michel spectrum including 1st order
32// radiative corrections
33// Reference: Florian Scheck "Muon Physics", in Physics Reports
34// (Review Section of Physics Letters) 44, No. 4 (1978)
35// 187-248. North-Holland Publishing Company, Amsterdam
36// at page 210 cc.
37//
38// W.E. Fisher and F. Scheck, Nucl. Phys. B83 (1974) 25.
39//
40// ------------------------------------------------------------
41//
42#include "G4MuonDecayChannelWithSpin.hh"
43
44#include "Randomize.hh"
45
46#include "G4DecayProducts.hh"
47#include "G4LorentzVector.hh"
48
49G4MuonDecayChannelWithSpin::G4MuonDecayChannelWithSpin(const G4String& theParentName,
50 G4double theBR)
51 : G4MuonDecayChannel(theParentName,theBR)
52{
53 EMMU = 0.*MeV;
54 EMASS = 0.*MeV;
55}
56
57G4MuonDecayChannelWithSpin::~G4MuonDecayChannelWithSpin()
58{
59}
60
61G4DecayProducts *G4MuonDecayChannelWithSpin::DecayIt(G4double)
62{
63 // This version assumes V-A coupling with 1st order radiative correctons,
64 // the standard model Michel parameter values, but
65 // gives incorrect energy spectrum for neutrinos
66
67#ifdef G4VERBOSE
68 if (GetVerboseLevel()>1) G4cout << "G4MuonDecayChannelWithSpin::DecayIt ";
69#endif
70
71 if (parent == 0) FillParent();
72 if (daughters == 0) FillDaughters();
73
74 // parent mass
75 G4double parentmass = parent->GetPDGMass();
76
77 EMMU = parentmass;
78
79 //daughters'mass
80 G4double daughtermass[3];
81 G4double sumofdaughtermass = 0.0;
82 for (G4int index=0; index<3; index++){
83 daughtermass[index] = daughters[index]->GetPDGMass();
84 sumofdaughtermass += daughtermass[index];
85 }
86
87 EMASS = daughtermass[0];
88
89 //create parent G4DynamicParticle at rest
90 G4ThreeVector dummy;
91 G4DynamicParticle * parentparticle = new G4DynamicParticle( parent, dummy, 0.0);
92 //create G4Decayproducts
93 G4DecayProducts *products = new G4DecayProducts(*parentparticle);
94 delete parentparticle;
95
96 // calcurate electron energy
97
98 G4double michel_rho = 0.75; //Standard Model Michel rho
99 G4double michel_delta = 0.75; //Standard Model Michel delta
100 G4double michel_xsi = 1.00; //Standard Model Michel xsi
101 G4double michel_eta = 0.00; //Standard Model eta
102
103 G4double rndm, x, ctheta;
104
105 G4double FG;
106 G4double FG_max = 2.00;
107
108 G4double W_mue = (EMMU*EMMU+EMASS*EMASS)/(2.*EMMU);
109 G4double x0 = EMASS/W_mue;
110
111 G4double x0_squared = x0*x0;
112
113 // ***************************************************
114 // x0 <= x <= 1. and -1 <= y <= 1
115 //
116 // F(x,y) = f(x)*g(x,y); g(x,y) = 1.+g(x)*y
117 // ***************************************************
118
119 // ***** sampling F(x,y) directly (brute force) *****
120
121 do{
122
123 // Sample the positron energy by sampling from F
124
125 rndm = G4UniformRand();
126
127 x = x0 + rndm*(1.-x0);
128
129 G4double x_squared = x*x;
130
131 G4double F_IS, F_AS, G_IS, G_AS;
132
133 F_IS = 1./6.*(-2.*x_squared+3.*x-x0_squared);
134 F_AS = 1./6.*std::sqrt(x_squared-x0_squared)*(2.*x-2.+std::sqrt(1.-x0_squared));
135
136 G_IS = 2./9.*(michel_rho-0.75)*(4.*x_squared-3.*x-x0_squared);
137 G_IS = G_IS + michel_eta*(1.-x)*x0;
138
139 G_AS = 3.*(michel_xsi-1.)*(1.-x);
140 G_AS = G_AS+2.*(michel_xsi*michel_delta-0.75)*(4.*x-4.+std::sqrt(1.-x0_squared));
141 G_AS = 1./9.*std::sqrt(x_squared-x0_squared)*G_AS;
142
143 F_IS = F_IS + G_IS;
144 F_AS = F_AS + G_AS;
145
146 // *** Radiative Corrections ***
147
148 G4double R_IS = F_c(x,x0);
149
150 G4double F = 6.*F_IS + R_IS/std::sqrt(x_squared-x0_squared);
151
152 // *** Radiative Corrections ***
153
154 G4double R_AS = F_theta(x,x0);
155
156 rndm = G4UniformRand();
157
158 ctheta = 2.*rndm-1.;
159
160 G4double G = 6.*F_AS - R_AS/std::sqrt(x_squared-x0_squared);
161
162 FG = std::sqrt(x_squared-x0_squared)*F*(1.+(G/F)*ctheta);
163
164 if(FG>FG_max){
165 G4cout<<"***Problem in Muon Decay *** : FG > FG_max"<<G4endl;
166 FG_max = FG;
167 }
168
169 rndm = G4UniformRand();
170
171 }while(FG<rndm*FG_max);
172
173 G4double energy = x * W_mue;
174
175 rndm = G4UniformRand();
176
177 G4double phi = twopi * rndm;
178
179 if(energy < EMASS) energy = EMASS;
180
181 // calculate daughter momentum
182 G4double daughtermomentum[3];
183
184 daughtermomentum[0] = std::sqrt(energy*energy - EMASS*EMASS);
185
186 G4double stheta = std::sqrt(1.-ctheta*ctheta);
187 G4double cphi = std::cos(phi);
188 G4double sphi = std::sin(phi);
189
190 //Coordinates of the decay positron with respect to the muon spin
191
192 G4double px = stheta*cphi;
193 G4double py = stheta*sphi;
194 G4double pz = ctheta;
195
196 G4ThreeVector direction0(px,py,pz);
197
198 direction0.rotateUz(parent_polarization);
199
200 G4DynamicParticle * daughterparticle0
201 = new G4DynamicParticle( daughters[0], daughtermomentum[0]*direction0);
202
203 products->PushProducts(daughterparticle0);
204
205
206 // daughter 1 ,2 (neutrinos)
207 // create neutrinos in the C.M frame of two neutrinos
208 G4double energy2 = parentmass*(1.0 - x/2.0);
209 G4double vmass = std::sqrt((energy2-daughtermomentum[0])*(energy2+daughtermomentum[0]));
210 G4double beta = -1.0*daughtermomentum[0]/energy2;
211 G4double costhetan = 2.*G4UniformRand()-1.0;
212 G4double sinthetan = std::sqrt((1.0-costhetan)*(1.0+costhetan));
213 G4double phin = twopi*G4UniformRand()*rad;
214 G4double sinphin = std::sin(phin);
215 G4double cosphin = std::cos(phin);
216
217 G4ThreeVector direction1(sinthetan*cosphin,sinthetan*sinphin,costhetan);
218 G4DynamicParticle * daughterparticle1
219 = new G4DynamicParticle( daughters[1], direction1*(vmass/2.));
220 G4DynamicParticle * daughterparticle2
221 = new G4DynamicParticle( daughters[2], direction1*(-1.0*vmass/2.));
222
223 // boost to the muon rest frame
224 G4LorentzVector p4;
225 p4 = daughterparticle1->Get4Momentum();
226 p4.boost( direction0.x()*beta, direction0.y()*beta, direction0.z()*beta);
227 daughterparticle1->Set4Momentum(p4);
228 p4 = daughterparticle2->Get4Momentum();
229 p4.boost( direction0.x()*beta, direction0.y()*beta, direction0.z()*beta);
230 daughterparticle2->Set4Momentum(p4);
231 products->PushProducts(daughterparticle1);
232 products->PushProducts(daughterparticle2);
233 daughtermomentum[1] = daughterparticle1->GetTotalMomentum();
234 daughtermomentum[2] = daughterparticle2->GetTotalMomentum();
235
236 // output message
237#ifdef G4VERBOSE
238 if (GetVerboseLevel()>1) {
239 G4cout << "G4MuonDecayChannelWithSpin::DecayIt ";
240 G4cout << " create decay products in rest frame " <<G4endl;
241 products->DumpInfo();
242 }
243#endif
244 return products;
245}
246
247G4double G4MuonDecayChannelWithSpin::R_c(G4double x){
248
249 G4int n_max = (int)(100.*x);
250
251 if(n_max<10)n_max=10;
252
253 G4double L2 = 0.0;
254
255 for(G4int n=1; n<=n_max; n++){
256 L2 += std::pow(x,n)/(n*n);
257 }
258
259 G4double omega = std::log(EMMU/EMASS);
260
261 G4double r_c;
262
263 r_c = 2.*L2-(pi*pi/3.)-2.;
264 r_c = r_c + omega * (1.5+2.*std::log((1.-x)/x));
265 r_c = r_c - std::log(x)*(2.*std::log(x)-1.);
266 r_c = r_c + (3.*std::log(x)-1.-1./x)*std::log(1.-x);
267
268 return r_c;
269}
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