[1] | 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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