1 | <chapter name="Semi-Internal Resonances"> |
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2 | |
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3 | <h2>Semi-Internal Resonances</h2> |
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4 | |
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5 | The introduction of a new <aloc href="SemiInternalProcesses"> |
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6 | semi-internal process</aloc> may also involve a new particle, |
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7 | not currently implemented in PYTHIA. Often it is then enough to |
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8 | use the <aloc href="ParticleDataScheme">standard machinery</aloc> |
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9 | to introduce a new particle (<code>id:all = ...</code>) and new |
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10 | decay channels (<code>id:addChannel = ...</code>). By default this |
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11 | only allows you to define a fixed total width and fixed branching |
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12 | ratios. Using <code><aloc href="ResonanceDecays">meMode</aloc></code> |
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13 | values 100 or bigger provides the possibility of a very |
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14 | simple threshold behaviour. |
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15 | |
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16 | <p/> |
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17 | If you want to have complete freedom, however, there are two |
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18 | ways to go. One is that you make the resonance decay part of the |
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19 | hard process itself, either using the |
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20 | <aloc href="LesHouchesAccord">Les Houches interface</aloc> or |
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21 | a semi-internal process. The other is for you to create a new |
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22 | <code>ResonanceWidths</code> object, where you write the code |
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23 | needed for a calculation of the partial width of a particular |
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24 | channel. |
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25 | |
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26 | <p/> |
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27 | Here we will explain what is involved in setting up a resonance. |
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28 | Should you actually go ahead with this, it is strongly recommended |
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29 | to use an existing resonance as a template, to get the correct |
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30 | structure. There also exists a sample main program, |
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31 | <code>main22.cc</code>, that illustrates how you could combine |
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32 | a new process and a new resonance. |
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33 | |
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34 | <p/> |
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35 | There are three steps involved in implementing a new resonance: |
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36 | <br/>1) providing the standard particle information, as already |
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37 | outlined above (<code>id:all = ...</code>, |
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38 | <code>id:addChannel = ...</code>), except that now branching |
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39 | ratios need not be specified, since they anyway will be overwritten |
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40 | by the dynamically calculated values. |
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41 | <br/>2) writing the class that calculates the partial widths. |
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42 | <br/>3) handing in a pointer to an instance of this class to PYTHIA. |
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43 | <br/>We consider the latter two aspects in turn. |
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44 | |
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45 | <h3>The ResonanceWidths Class</h3> |
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46 | |
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47 | The resonance-width calculation has to be encoded in a new class. |
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48 | The relevant code could either be put before the main program in the |
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49 | same file, or be stored separately, e.g. in a matched pair |
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50 | of <code>.h</code> and <code>.cc</code> files. The latter may be more |
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51 | convenient, in particular if the calculations are lengthy, or |
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52 | likely to be used in many different runs, but of course requires |
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53 | that these additional files are correctly compiled and linked. |
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54 | |
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55 | <p/> |
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56 | The class has to be derived from the <code>ResonanceWidths</code> |
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57 | base class. It can implement a number of methods. The constructor |
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58 | and the <code>calcWidth</code> ones are always needed, while others |
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59 | are for convenience. Much of the administrativ machinery is handled |
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60 | by methods in the base class. |
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61 | |
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62 | <p/>Thus, in particular, you must implement expressions for all |
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63 | possible final states, whether switched on in the current run or not, |
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64 | since all contribute to the total width needed in the denominator of |
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65 | the Breit-Wigner expression. Then the methods in the base class take |
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66 | care of selecting only allowed channels where that is required, and |
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67 | also of including effects of closed channels in secondary decays. |
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68 | These methods can be accessed indirectly via the |
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69 | <code><aloc href="ResonanceDecays">res...</aloc></code> |
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70 | methods of the normal |
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71 | <code><aloc href="ParticleDataScheme">particle database</aloc></code>. |
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72 | |
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73 | <p/> |
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74 | A <b>constructor</b> for the derived class obviously must be available. |
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75 | Here you are quite free to allow a list of arguments, to set |
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76 | the parameters of your model. The constructor must call the |
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77 | base-class <code>initBasic(idResIn)</code> method, where the argument |
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78 | <code>idResIn</code> is the PDG-style identity code you have chosen |
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79 | for the new resonance. When you create several related resonances |
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80 | as instances of the same class you would naturally make |
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81 | <code>idResIn</code> an argument of the constructor; for the |
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82 | PYTHIA classes this convention is used also in cases when it is |
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83 | not needed. |
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84 | <br/>The <code>initBasic(...)</code> method will |
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85 | hook up the <code>ResonanceWidths</code> object with the corresponding |
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86 | entry in the generic particle database, i.e. with the normal particle |
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87 | information you set up in point 1) above. It will store, in base-class |
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88 | member variables, a number of quantities that you later may find useful: |
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89 | <br/><code>idRes</code> : the identity code you provide; |
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90 | <br/><code>hasAntiRes</code> : whether there is an antiparticle; |
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91 | <br/><code>mRes</code> : resonance mass; |
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92 | <br/><code>GammaRes</code> resonance width; |
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93 | <br/><code>m2Res</code> : the squared mass; |
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94 | <br/><code>GamMRat</code> : the ratio of width to mass. |
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95 | |
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96 | <p/> |
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97 | A <b>destructor</b> is only needed if you plan to delete the resonance |
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98 | before the natural end of the run, and require some special behaviour |
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99 | at that point. If you call such a destructor you will leave a pointer |
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100 | dangling inside the <code>Pythia</code> object you gave it in to, |
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101 | if that still exists. |
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102 | |
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103 | <method name="void ResonanceWidths::initConstants()"> |
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104 | is called once during initialization, and can then be used to set up |
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105 | further parameters specific to this particle species, such as couplings, |
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106 | and perform calculations that need not be repeated for each new event, |
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107 | thereby saving time. This method needs not be implemented. |
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108 | </method> |
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109 | |
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110 | <method name="void ResonanceWidths::calcPreFac(bool calledFromInit = false)"> |
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111 | is called once a mass has been chosen for the resonance, but before |
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112 | a specific final state is considered. This routine can therefore |
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113 | be used to perform calculations that otherwise might have to be repeated |
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114 | over and over again in <code>calcWidth</code> below. It is optional |
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115 | whether you want to use this method, however, or put |
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116 | everything in <code>calcWidth()</code>. |
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117 | <br/>The optional argument will have the value <code>true</code> when |
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118 | the resonance is initialized, and then be <code>false</code> throughout |
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119 | the event generation, should you wish to make a distinction. |
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120 | In PYTHIA such a distinction is made for <ei>gamma^*/Z^0</ei> and |
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121 | <ei>gamma^*/Z^0/Z'^0</ei>, owing to the necessity of a special |
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122 | description of interference effects, but not for other resonances. |
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123 | <br/>In addition to the base-class member variables already described |
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124 | above, <code>mHat</code> contains the current mass of the resonance. |
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125 | At initialization this agrees with the nominal mass <code>mRes</code>, |
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126 | but during the run it will not (in general). |
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127 | </method> |
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128 | |
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129 | <method name="void ResonanceWidths::calcWidth(bool calledFromInit = false)"> |
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130 | is the key method for width calculations and returns a partial width |
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131 | value, as further described below. It is called for a specific |
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132 | final state, typically in a loop over all allowed final states, |
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133 | subsequent to the <code>calcPreFac(...)</code> call above. |
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134 | Information on the final state is stored in a number of base-class |
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135 | variables, for you to use in your calculations: |
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136 | <br/><code>iChannel</code> : the channel number in the list of |
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137 | possible decay channels; |
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138 | <br/><code>mult</code> : the number of decay products; |
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139 | <br/><code>id1, id2, id3</code> : the identity code of up to the first |
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140 | three decay products, arranged in descending order of the absolute value |
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141 | of the identity code; |
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142 | <br/><code>id1Abs, id2Abs, id3Abs</code> : the absolute value of the |
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143 | above three identity codes; |
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144 | <br/><code>mHat</code> : the current resonance mass, which is the same |
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145 | as in the latest <code>calcPreFac(...)</code> call; |
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146 | <br/><code>mf1, mf2, mf3</code> : masses of the above decay products; |
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147 | <br/><code>mr1, mr2, mr3</code> : squared ratio of the product masses |
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148 | to the resonance mass; |
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149 | <br/><code>ps</code> : is only meaningful for two-body decays, where it |
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150 | gives the phase-space factor |
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151 | <ei>ps = sqrt( (1. - mr1 - mr2)^2 - 4. * mr1 * mr2 )</ei>; |
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152 | <br/>In two-body decays the third slot is zero for the above properties. |
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153 | Should there be more than three particles in the decay, you would have |
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154 | to take care of the subsequent products yourself, e.g. using |
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155 | <br/><code>particlePtr->decay[iChannel].product(j);</code> |
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156 | <br/>to extract the <code>j</code>'th decay products (with |
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157 | <code>j = 0</code> for the first, etc.). Currently we are not aware |
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158 | of any such examples. |
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159 | <br/>The base class also contains methods for <ei>alpha_em</ei> and |
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160 | <ei>alpha_strong</ei> evaluation, and can access many standard-model |
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161 | couplings; see the existing code for examples. |
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162 | <br/>The result of your calculation should be stored in |
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163 | <br/><code>widNow</code> : the partial width of the current channel, |
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164 | expressed in GeV. |
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165 | </method> |
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166 | |
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167 | <method name="double ResonanceWidths::widthChan( double mHat, |
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168 | int idAbs1, int idAbs2)"> |
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169 | is not normally used. In PYTHIA the only exception is Higgs decays, |
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170 | where it is used to define the width (except for colour factors) |
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171 | associated with a specific incoming/outgoing state. It allows the |
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172 | results of some loop expressions to be pretabulated. |
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173 | </method> |
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174 | |
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175 | <h3>Access to resonance widths</h3> |
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176 | |
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177 | Once you have implemented a class, it is straightforward to |
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178 | make use of it in a run. Assume you have written a new class |
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179 | <code>MyResonance</code>, which inherits from |
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180 | <code>ResonanceWidths</code>. You then create an instance of |
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181 | this class and hand it in to a <code>pythia</code> object with |
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182 | <pre> |
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183 | ResonanceWidths* myResonance = new MyResonance(); |
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184 | pythia.setResonancePtr( myResonance); |
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185 | </pre> |
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186 | If you have several resonances you can repeat the procedure any number |
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187 | of times. When <code>pythia.init(...)</code> is called these resonances |
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188 | are initialized along with all the internal resonances, and treated in |
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189 | exactly the same manner. See also the <aloc href="ProgramFlow">Program |
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190 | Flow</aloc> |
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191 | description. |
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192 | |
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193 | <p/> |
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194 | If the code should be of good quality and general usefulness, |
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195 | it would be simple to include it as a permanently available process |
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196 | in the standard program distribution. The final step of that integration |
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197 | ought to be left for the PYTHIA authors, but basically all that is |
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198 | needed is to add one line in |
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199 | <code>ParticleData::initResonances</code>, where one creates an |
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200 | instance of the resonance in the same way as for the resonances already |
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201 | there. In addition, the particle data and decay table for the new |
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202 | resonance has to be added to the permanent |
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203 | <aloc href="ParticleData">particle database</aloc>, and the code itself |
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204 | to <code>include/ResonanceWidths.h</code> and |
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205 | <code>src/ResonanceWidths.cc</code>. |
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206 | |
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207 | </chapter> |
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208 | |
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209 | <!-- Copyright (C) 2012 Torbjorn Sjostrand --> |
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