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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