[1] | 1 | <chapter name="Couplings and Scales"> |
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| 2 | |
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| 3 | <h2>Couplings and Scales</h2> |
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| 4 | |
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| 5 | Here is collected some possibilities to modify the scale choices |
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| 6 | of couplings and parton densities for all internally implemented |
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| 7 | hard processes. This is based on them all being derived from the |
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| 8 | <code>SigmaProcess</code> base class. The matrix-element coding is |
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| 9 | also used by the multiparton-interactions machinery, but there with a |
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| 10 | separate choice of <ei>alpha_strong(M_Z^2)</ei> value and running, |
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| 11 | and separate PDF scale choices. Also, in <ei>2 -> 2</ei> and |
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| 12 | <ei>2 -> 3</ei> processes where resonances are produced, their |
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| 13 | couplings and thereby their Breit-Wigner shapes are always evaluated |
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| 14 | with the resonance mass as scale, irrespective of the choices below. |
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| 15 | |
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| 16 | <h3>Couplings and K factor</h3> |
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| 17 | |
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| 18 | The size of QCD cross sections is mainly determined by |
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| 19 | <parm name="SigmaProcess:alphaSvalue" default="0.1265" |
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| 20 | min="0.06" max="0.25"> |
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| 21 | The <ei>alpha_strong</ei> value at scale <ei>M_Z^2</ei>. |
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| 22 | </parm> |
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| 23 | |
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| 24 | <p/> |
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| 25 | The actual value is then regulated by the running to the <ei>Q^2</ei> |
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| 26 | renormalization scale, at which <ei>alpha_strong</ei> is evaluated |
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| 27 | <modepick name="SigmaProcess:alphaSorder" default="1" min="0" max="2"> |
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| 28 | Order at which <ei>alpha_strong</ei> runs, |
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| 29 | <option value="0">zeroth order, i.e. <ei>alpha_strong</ei> is kept |
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| 30 | fixed.</option> |
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| 31 | <option value="1">first order, which is the normal value.</option> |
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| 32 | <option value="2">second order. Since other parts of the code do |
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| 33 | not go to second order there is no strong reason to use this option, |
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| 34 | but there is also nothing wrong with it.</option> |
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| 35 | </modepick> |
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| 36 | |
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| 37 | <p/> |
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| 38 | QED interactions are regulated by the <ei>alpha_electromagnetic</ei> |
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| 39 | value at the <ei>Q^2</ei> renormalization scale of an interaction. |
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| 40 | <modepick name="SigmaProcess:alphaEMorder" default="1" min="-1" max="1"> |
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| 41 | The running of <ei>alpha_em</ei> used in hard processes. |
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| 42 | <option value="1">first-order running, constrained to agree with |
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| 43 | <code>StandardModel:alphaEMmZ</code> at the <ei>Z^0</ei> mass. |
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| 44 | </option> |
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| 45 | <option value="0">zeroth order, i.e. <ei>alpha_em</ei> is kept |
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| 46 | fixed at its value at vanishing momentum transfer.</option> |
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| 47 | <option value="-1">zeroth order, i.e. <ei>alpha_em</ei> is kept |
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| 48 | fixed, but at <code>StandardModel:alphaEMmZ</code>, i.e. its value |
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| 49 | at the <ei>Z^0</ei> mass. |
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| 50 | </option> |
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| 51 | </modepick> |
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| 52 | |
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| 53 | <p/> |
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| 54 | In addition there is the possibility of a global rescaling of |
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| 55 | cross sections (which could not easily be accommodated by a |
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| 56 | changed <ei>alpha_strong</ei>, since <ei>alpha_strong</ei> runs) |
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| 57 | <parm name="SigmaProcess:Kfactor" default="1.0" min="0.5" max="4.0"> |
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| 58 | Multiply almost all cross sections by this common fix factor. Excluded |
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| 59 | are only unresolved processes, where cross sections are better |
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| 60 | <aloc href="TotalCrossSections">set directly</aloc>, and |
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| 61 | multiparton interactions, which have a separate <ei>K</ei> factor |
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| 62 | <aloc href="MultipartonInteractions">of their own</aloc>. |
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| 63 | This degree of freedom is primarily intended for hadron colliders, and |
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| 64 | should not normally be used for <ei>e^+e^-</ei> annihilation processes. |
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| 65 | </parm> |
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| 66 | |
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| 67 | <h3>Renormalization scales</h3> |
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| 68 | |
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| 69 | The <ei>Q^2</ei> renormalization scale can be chosen among a few different |
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| 70 | alternatives, separately for <ei>2 -> 1</ei>, <ei>2 -> 2</ei> and two |
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| 71 | different kinds of <ei>2 -> 3</ei> processes. In addition a common |
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| 72 | multiplicative factor may be imposed. |
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| 73 | |
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| 74 | <modepick name="SigmaProcess:renormScale1" default="1" min="1" max="2"> |
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| 75 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 1</ei> processes. |
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| 76 | The same options also apply for those <ei>2 -> 2</ei> and <ei>2 -> 3</ei> |
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| 77 | processes that have been specially marked as proceeding only through |
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| 78 | an <ei>s</ei>-channel resonance, by the <code>isSChannel()</code> virtual |
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| 79 | method of <code>SigmaProcess</code>. |
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| 80 | <option value="1">the squared invariant mass, i.e. <ei>sHat</ei>. |
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| 81 | </option> |
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| 82 | <option value="2">fix scale set in <code>SigmaProcess:renormFixScale</code> |
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| 83 | below. |
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| 84 | </option> |
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| 85 | </modepick> |
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| 86 | |
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| 87 | <modepick name="SigmaProcess:renormScale2" default="2" min="1" max="5"> |
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| 88 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 2</ei> processes. |
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| 89 | <option value="1">the smaller of the squared transverse masses of the two |
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| 90 | outgoing particles, i.e. <ei>min(mT_3^2, mT_4^2) = |
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| 91 | pT^2 + min(m_3^2, m_4^2)</ei>. |
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| 92 | </option> |
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| 93 | <option value="2">the geometric mean of the squared transverse masses of |
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| 94 | the two outgoing particles, i.e. <ei>mT_3 * mT_4 = |
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| 95 | sqrt((pT^2 + m_3^2) * (pT^2 + m_4^2))</ei>. |
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| 96 | </option> |
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| 97 | <option value="3">the arithmetic mean of the squared transverse masses of |
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| 98 | the two outgoing particles, i.e. <ei>(mT_3^2 + mT_4^2) / 2 = |
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| 99 | pT^2 + 0.5 * (m_3^2 + m_4^2)</ei>. Useful for comparisons |
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| 100 | with PYTHIA 6, where this is the default. |
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| 101 | </option> |
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| 102 | <option value="4">squared invariant mass of the system, |
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| 103 | i.e. <ei>sHat</ei>. Useful for processes dominated by |
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| 104 | <ei>s</ei>-channel exchange. |
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| 105 | </option> |
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| 106 | <option value="5">fix scale set in <code>SigmaProcess:renormFixScale</code> |
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| 107 | below. |
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| 108 | </option> |
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| 109 | </modepick> |
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| 110 | |
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| 111 | <modepick name="SigmaProcess:renormScale3" default="3" min="1" max="6"> |
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| 112 | The <ei>Q^2</ei> renormalization scale for "normal" <ei>2 -> 3</ei> |
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| 113 | processes, i.e excepting the vector-boson-fusion processes below. |
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| 114 | Here it is assumed that particle masses in the final state either match |
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| 115 | or are heavier than that of any <ei>t</ei>-channel propagator particle. |
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| 116 | (Currently only <ei>g g / q qbar -> H^0 Q Qbar</ei> processes are |
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| 117 | implemented, where the "match" criterion holds.) |
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| 118 | <option value="1">the smaller of the squared transverse masses of the three |
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| 119 | outgoing particles, i.e. min(mT_3^2, mT_4^2, mT_5^2). |
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| 120 | </option> |
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| 121 | <option value="2">the geometric mean of the two smallest squared transverse |
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| 122 | masses of the three outgoing particles, i.e. |
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| 123 | <ei>sqrt( mT_3^2 * mT_4^2 * mT_5^2 / max(mT_3^2, mT_4^2, mT_5^2) )</ei>. |
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| 124 | </option> |
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| 125 | <option value="3">the geometric mean of the squared transverse masses of the |
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| 126 | three outgoing particles, i.e. <ei>(mT_3^2 * mT_4^2 * mT_5^2)^(1/3)</ei>. |
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| 127 | </option> |
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| 128 | <option value="4">the arithmetic mean of the squared transverse masses of |
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| 129 | the three outgoing particles, i.e. <ei>(mT_3^2 + mT_4^2 + mT_5^2)/3</ei>. |
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| 130 | </option> |
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| 131 | <option value="5">squared invariant mass of the system, |
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| 132 | i.e. <ei>sHat</ei>. |
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| 133 | </option> |
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| 134 | <option value="6">fix scale set in <code>SigmaProcess:renormFixScale</code> |
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| 135 | below. |
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| 136 | </option> |
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| 137 | </modepick> |
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| 138 | |
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| 139 | <modepick name="SigmaProcess:renormScale3VV" default="3" min="1" max="6"> |
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| 140 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 3</ei> |
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| 141 | vector-boson-fusion processes, i.e. <ei>f_1 f_2 -> H^0 f_3 f_4</ei> |
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| 142 | with <ei>Z^0</ei> or <ei>W^+-</ei> <ei>t</ei>-channel propagators. |
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| 143 | Here the transverse masses of the outgoing fermions do not reflect the |
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| 144 | virtualities of the exchanged bosons. A better estimate is obtained |
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| 145 | by replacing the final-state fermion masses by the vector-boson ones |
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| 146 | in the definition of transverse masses. We denote these combinations |
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| 147 | <ei>mT_Vi^2 = m_V^2 + pT_i^2</ei>. |
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| 148 | <option value="1">the squared mass <ei>m_V^2</ei> of the exchanged |
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| 149 | vector boson. |
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| 150 | </option> |
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| 151 | <option value="2">the geometric mean of the two propagator virtuality |
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| 152 | estimates, i.e. <ei>sqrt(mT_V3^2 * mT_V4^2)</ei>. |
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| 153 | </option> |
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| 154 | <option value="3">the geometric mean of the three relevant squared |
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| 155 | transverse masses, i.e. <ei>(mT_V3^2 * mT_V4^2 * mT_H^2)^(1/3)</ei>. |
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| 156 | </option> |
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| 157 | <option value="4">the arithmetic mean of the three relevant squared |
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| 158 | transverse masses, i.e. <ei>(mT_V3^2 + mT_V4^2 + mT_H^2)/3</ei>. |
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| 159 | </option> |
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| 160 | <option value="5">squared invariant mass of the system, |
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| 161 | i.e. <ei>sHat</ei>. |
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| 162 | </option> |
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| 163 | <option value="6">fix scale set in <code>SigmaProcess:renormFixScale</code> |
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| 164 | below. |
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| 165 | </option> |
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| 166 | </modepick> |
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| 167 | |
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| 168 | <parm name="SigmaProcess:renormMultFac" default="1." min="0.1" max="10."> |
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| 169 | The <ei>Q^2</ei> renormalization scale for <ei>2 -> 1</ei>, |
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| 170 | <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes is multiplied by |
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| 171 | this factor relative to the scale described above (except for the options |
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| 172 | with a fix scale). Should be use sparingly for <ei>2 -> 1</ei> processes. |
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| 173 | </parm> |
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| 174 | |
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| 175 | <parm name="SigmaProcess:renormFixScale" default="10000." min="1."> |
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| 176 | A fix <ei>Q^2</ei> value used as renormalization scale for <ei>2 -> 1</ei>, |
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| 177 | <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes in some of the options above. |
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| 178 | </parm> |
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| 179 | |
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| 180 | <h3>Factorization scales</h3> |
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| 181 | |
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| 182 | Corresponding options exist for the <ei>Q^2</ei> factorization scale |
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| 183 | used as argument in PDF's. Again there is a choice of form for |
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| 184 | <ei>2 -> 1</ei>, <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes separately. |
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| 185 | For simplicity we have let the numbering of options agree, for each event |
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| 186 | class separately, between normalization and factorization scales, and the |
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| 187 | description has therefore been slightly shortened. The default values are |
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| 188 | <b>not</b> necessarily the same, however. |
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| 189 | |
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| 190 | <modepick name="SigmaProcess:factorScale1" default="1" min="1" max="2"> |
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| 191 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 1</ei> processes. |
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| 192 | The same options also apply for those <ei>2 -> 2</ei> and <ei>2 -> 3</ei> |
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| 193 | processes that have been specially marked as proceeding only through |
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| 194 | an <ei>s</ei>-channel resonance. |
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| 195 | <option value="1">the squared invariant mass, i.e. <ei>sHat</ei>. |
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| 196 | </option> |
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| 197 | <option value="2">fix scale set in <code>SigmaProcess:factorFixScale</code> |
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| 198 | below. |
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| 199 | </option> |
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| 200 | </modepick> |
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| 201 | |
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| 202 | <modepick name="SigmaProcess:factorScale2" default="1" min="1" max="5"> |
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| 203 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 2</ei> processes. |
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| 204 | <option value="1">the smaller of the squared transverse masses of the two |
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| 205 | outgoing particles. |
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| 206 | </option> |
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| 207 | <option value="2">the geometric mean of the squared transverse masses of |
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| 208 | the two outgoing particles. |
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| 209 | </option> |
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| 210 | <option value="3">the arithmetic mean of the squared transverse masses of |
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| 211 | the two outgoing particles. Useful for comparisons with PYTHIA 6, where |
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| 212 | this is the default. |
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| 213 | </option> |
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| 214 | <option value="4">squared invariant mass of the system, |
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| 215 | i.e. <ei>sHat</ei>. Useful for processes dominated by |
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| 216 | <ei>s</ei>-channel exchange. |
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| 217 | </option> |
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| 218 | <option value="5">fix scale set in <code>SigmaProcess:factorFixScale</code> |
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| 219 | below. |
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| 220 | </option> |
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| 221 | </modepick> |
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| 222 | |
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| 223 | <modepick name="SigmaProcess:factorScale3" default="2" min="1" max="6"> |
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| 224 | The <ei>Q^2</ei> factorization scale for "normal" <ei>2 -> 3</ei> |
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| 225 | processes, i.e excepting the vector-boson-fusion processes below. |
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| 226 | <option value="1">the smaller of the squared transverse masses of the three |
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| 227 | outgoing particles. |
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| 228 | </option> |
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| 229 | <option value="2">the geometric mean of the two smallest squared transverse |
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| 230 | masses of the three outgoing particles. |
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| 231 | </option> |
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| 232 | <option value="3">the geometric mean of the squared transverse masses of the |
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| 233 | three outgoing particles. |
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| 234 | </option> |
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| 235 | <option value="4">the arithmetic mean of the squared transverse masses of |
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| 236 | the three outgoing particles. |
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| 237 | </option> |
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| 238 | <option value="5">squared invariant mass of the system, |
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| 239 | i.e. <ei>sHat</ei>. |
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| 240 | </option> |
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| 241 | <option value="6">fix scale set in <code>SigmaProcess:factorFixScale</code> |
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| 242 | below. |
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| 243 | </option> |
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| 244 | </modepick> |
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| 245 | |
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| 246 | <modepick name="SigmaProcess:factorScale3VV" default="2" min="1" max="6"> |
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| 247 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 3</ei> |
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| 248 | vector-boson-fusion processes, i.e. <ei>f_1 f_2 -> H^0 f_3 f_4</ei> |
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| 249 | with <ei>Z^0</ei> or <ei>W^+-</ei> <ei>t</ei>-channel propagators. |
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| 250 | Here we again introduce the combinations <ei>mT_Vi^2 = m_V^2 + pT_i^2</ei> |
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| 251 | as replacements for the normal squared transverse masses of the two |
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| 252 | outgoing quarks. |
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| 253 | <option value="1">the squared mass <ei>m_V^2</ei> of the exchanged |
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| 254 | vector boson. |
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| 255 | </option> |
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| 256 | <option value="2">the geometric mean of the two propagator virtuality |
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| 257 | estimates. |
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| 258 | </option> |
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| 259 | <option value="3">the geometric mean of the three relevant squared |
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| 260 | transverse masses. |
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| 261 | </option> |
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| 262 | <option value="4">the arithmetic mean of the three relevant squared |
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| 263 | transverse masses. |
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| 264 | </option> |
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| 265 | <option value="5">squared invariant mass of the system, |
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| 266 | i.e. <ei>sHat</ei>. |
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| 267 | </option> |
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| 268 | <option value="6">fix scale set in <code>SigmaProcess:factorFixScale</code> |
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| 269 | below. |
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| 270 | </option> |
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| 271 | </modepick> |
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| 272 | |
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| 273 | <parm name="SigmaProcess:factorMultFac" default="1." min="0.1" max="10."> |
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| 274 | The <ei>Q^2</ei> factorization scale for <ei>2 -> 1</ei>, |
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| 275 | <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes is multiplied by |
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| 276 | this factor relative to the scale described above (except for the options |
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| 277 | with a fix scale). Should be use sparingly for <ei>2 -> 1</ei> processes. |
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| 278 | </parm> |
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| 279 | |
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| 280 | <parm name="SigmaProcess:factorFixScale" default="10000." min="1."> |
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| 281 | A fix <ei>Q^2</ei> value used as factorization scale for <ei>2 -> 1</ei>, |
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| 282 | <ei>2 -> 2</ei> and <ei>2 -> 3</ei> processes in some of the options above. |
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| 283 | </parm> |
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| 284 | |
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| 285 | </chapter> |
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| 286 | |
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| 287 | <!-- Copyright (C) 2012 Torbjorn Sjostrand --> |
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