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63ba5337 | 1 | <chapter name="Semi-Internal Resonances"> |
2 | ||
3 | <h2>Semi-Internal Resonances</h2> | |
4 | ||
5 | The introduction of a new <aloc href="SemiInternalProcesses"> | |
6 | semi-internal process</aloc> may also involve a new particle, | |
7 | not currently implemented in PYTHIA. Often it is then enough to | |
8 | use the <aloc href="ParticleDataScheme">standard machinery</aloc> | |
9 | to introduce a new particle (<code>id:all = ...</code>) and new | |
10 | decay channels (<code>id:addChannel = ...</code>). By default this | |
11 | only allows you to define a fixed total width and fixed branching | |
12 | ratios. Using <code><aloc href="ResonanceDecays">meMode</aloc></code> | |
13 | values 100 or bigger provides the possibility of a very | |
14 | simple threshold behaviour. | |
15 | ||
16 | <p/> | |
17 | If you want to have complete freedom, however, there are two | |
18 | ways to go. One is that you make the resonance decay part of the | |
19 | hard process itself, either using the | |
20 | <aloc href="LesHouchesAccord">Les Houches interface</aloc> or | |
21 | a semi-internal process. The other is for you to create a new | |
22 | <code>ResonanceWidths</code> object, where you write the code | |
23 | needed for a calculation of the partial width of a particular | |
24 | channel. | |
25 | ||
26 | <p/> | |
27 | Here we will explain what is involved in setting up a resonance. | |
28 | Should you actually go ahead with this, it is strongly recommended | |
29 | to use an existing resonance as a template, to get the correct | |
30 | structure. There also exists a sample main program, | |
31 | <code>main22.cc</code>, that illustrates how you could combine | |
32 | a new process and a new resonance. | |
33 | ||
34 | <p/> | |
35 | There are three steps involved in implementing a new resonance: | |
36 | <br/>1) providing the standard particle information, as already | |
37 | outlined above (<code>id:all = ...</code>, | |
38 | <code>id:addChannel = ...</code>), except that now branching | |
39 | ratios need not be specified, since they anyway will be overwritten | |
40 | by the dynamically calculated values. | |
41 | <br/>2) writing the class that calculates the partial widths. | |
42 | <br/>3) handing in a pointer to an instance of this class to PYTHIA. | |
43 | <br/>We consider the latter two aspects in turn. | |
44 | ||
45 | <h3>The ResonanceWidths Class</h3> | |
46 | ||
47 | The resonance-width calculation has to be encoded in a new class. | |
48 | The relevant code could either be put before the main program in the | |
49 | same file, or be stored separately, e.g. in a matched pair | |
50 | of <code>.h</code> and <code>.cc</code> files. The latter may be more | |
51 | convenient, in particular if the calculations are lengthy, or | |
52 | likely to be used in many different runs, but of course requires | |
53 | that these additional files are correctly compiled and linked. | |
54 | ||
55 | <p/> | |
56 | The class has to be derived from the <code>ResonanceWidths</code> | |
57 | base class. It can implement a number of methods. The constructor | |
58 | and the <code>calcWidth</code> ones are always needed, while others | |
59 | are for convenience. Much of the administrativ machinery is handled | |
60 | by methods in the base class. | |
61 | ||
62 | <p/>Thus, in particular, you must implement expressions for all | |
63 | possible final states, whether switched on in the current run or not, | |
64 | since all contribute to the total width needed in the denominator of | |
65 | the Breit-Wigner expression. Then the methods in the base class take | |
66 | care of selecting only allowed channels where that is required, and | |
67 | also of including effects of closed channels in secondary decays. | |
68 | These methods can be accessed indirectly via the | |
69 | <code><aloc href="ResonanceDecays">res...</aloc></code> | |
70 | methods of the normal | |
71 | <code><aloc href="ParticleDataScheme">particle database</aloc></code>. | |
72 | ||
73 | <p/> | |
74 | A <b>constructor</b> for the derived class obviously must be available. | |
75 | Here you are quite free to allow a list of arguments, to set | |
76 | the parameters of your model. The constructor must call the | |
77 | base-class <code>initBasic(idResIn)</code> method, where the argument | |
78 | <code>idResIn</code> is the PDG-style identity code you have chosen | |
79 | for the new resonance. When you create several related resonances | |
80 | as instances of the same class you would naturally make | |
81 | <code>idResIn</code> an argument of the constructor; for the | |
82 | PYTHIA classes this convention is used also in cases when it is | |
83 | not needed. | |
84 | <br/>The <code>initBasic(...)</code> method will | |
85 | hook up the <code>ResonanceWidths</code> object with the corresponding | |
86 | entry in the generic particle database, i.e. with the normal particle | |
87 | information you set up in point 1) above. It will store, in base-class | |
88 | member variables, a number of quantities that you later may find useful: | |
89 | <br/><code>idRes</code> : the identity code you provide; | |
90 | <br/><code>hasAntiRes</code> : whether there is an antiparticle; | |
91 | <br/><code>mRes</code> : resonance mass; | |
92 | <br/><code>GammaRes</code> resonance width; | |
93 | <br/><code>m2Res</code> : the squared mass; | |
94 | <br/><code>GamMRat</code> : the ratio of width to mass. | |
95 | ||
96 | <p/> | |
97 | A <b>destructor</b> is only needed if you plan to delete the resonance | |
98 | before the natural end of the run, and require some special behaviour | |
99 | at that point. If you call such a destructor you will leave a pointer | |
100 | dangling inside the <code>Pythia</code> object you gave it in to, | |
101 | if that still exists. | |
102 | ||
103 | <method name="void ResonanceWidths::initConstants()"> | |
104 | is called once during initialization, and can then be used to set up | |
105 | further parameters specific to this particle species, such as couplings, | |
106 | and perform calculations that need not be repeated for each new event, | |
107 | thereby saving time. This method needs not be implemented. | |
108 | </method> | |
109 | ||
110 | <method name="void ResonanceWidths::calcPreFac(bool calledFromInit = false)"> | |
111 | is called once a mass has been chosen for the resonance, but before | |
112 | a specific final state is considered. This routine can therefore | |
113 | be used to perform calculations that otherwise might have to be repeated | |
114 | over and over again in <code>calcWidth</code> below. It is optional | |
115 | whether you want to use this method, however, or put | |
116 | everything in <code>calcWidth()</code>. | |
117 | <br/>The optional argument will have the value <code>true</code> when | |
118 | the resonance is initialized, and then be <code>false</code> throughout | |
119 | the event generation, should you wish to make a distinction. | |
120 | In PYTHIA such a distinction is made for <ei>gamma^*/Z^0</ei> and | |
121 | <ei>gamma^*/Z^0/Z'^0</ei>, owing to the necessity of a special | |
122 | description of interference effects, but not for other resonances. | |
123 | <br/>In addition to the base-class member variables already described | |
124 | above, <code>mHat</code> contains the current mass of the resonance. | |
125 | At initialization this agrees with the nominal mass <code>mRes</code>, | |
126 | but during the run it will not (in general). | |
127 | </method> | |
128 | ||
129 | <method name="void ResonanceWidths::calcWidth(bool calledFromInit = false)"> | |
130 | is the key method for width calculations and returns a partial width | |
131 | value, as further described below. It is called for a specific | |
132 | final state, typically in a loop over all allowed final states, | |
133 | subsequent to the <code>calcPreFac(...)</code> call above. | |
134 | Information on the final state is stored in a number of base-class | |
135 | variables, for you to use in your calculations: | |
136 | <br/><code>iChannel</code> : the channel number in the list of | |
137 | possible decay channels; | |
138 | <br/><code>mult</code> : the number of decay products; | |
139 | <br/><code>id1, id2, id3</code> : the identity code of up to the first | |
140 | three decay products, arranged in descending order of the absolute value | |
141 | of the identity code; | |
142 | <br/><code>id1Abs, id2Abs, id3Abs</code> : the absolute value of the | |
143 | above three identity codes; | |
144 | <br/><code>mHat</code> : the current resonance mass, which is the same | |
145 | as in the latest <code>calcPreFac(...)</code> call; | |
146 | <br/><code>mf1, mf2, mf3</code> : masses of the above decay products; | |
147 | <br/><code>mr1, mr2, mr3</code> : squared ratio of the product masses | |
148 | to the resonance mass; | |
149 | <br/><code>ps</code> : is only meaningful for two-body decays, where it | |
150 | gives the phase-space factor | |
151 | <ei>ps = sqrt( (1. - mr1 - mr2)^2 - 4. * mr1 * mr2 )</ei>; | |
152 | <br/>In two-body decays the third slot is zero for the above properties. | |
153 | Should there be more than three particles in the decay, you would have | |
154 | to take care of the subsequent products yourself, e.g. using | |
155 | <br/><code>particlePtr->decay[iChannel].product(j);</code> | |
156 | <br/>to extract the <code>j</code>'th decay products (with | |
157 | <code>j = 0</code> for the first, etc.). Currently we are not aware | |
158 | of any such examples. | |
159 | <br/>The base class also contains methods for <ei>alpha_em</ei> and | |
160 | <ei>alpha_strong</ei> evaluation, and can access many standard-model | |
161 | couplings; see the existing code for examples. | |
162 | <br/>The result of your calculation should be stored in | |
163 | <br/><code>widNow</code> : the partial width of the current channel, | |
164 | expressed in GeV. | |
165 | </method> | |
166 | ||
167 | <method name="double ResonanceWidths::widthChan( double mHat, | |
168 | int idAbs1, int idAbs2)"> | |
169 | is not normally used. In PYTHIA the only exception is Higgs decays, | |
170 | where it is used to define the width (except for colour factors) | |
171 | associated with a specific incoming/outgoing state. It allows the | |
172 | results of some loop expressions to be pretabulated. | |
173 | </method> | |
174 | ||
175 | <h3>Access to resonance widths</h3> | |
176 | ||
177 | Once you have implemented a class, it is straightforward to | |
178 | make use of it in a run. Assume you have written a new class | |
179 | <code>MyResonance</code>, which inherits from | |
180 | <code>ResonanceWidths</code>. You then create an instance of | |
181 | this class and hand it in to a <code>pythia</code> object with | |
182 | <pre> | |
183 | ResonanceWidths* myResonance = new MyResonance(); | |
184 | pythia.setResonancePtr( myResonance); | |
185 | </pre> | |
186 | If you have several resonances you can repeat the procedure any number | |
187 | of times. When <code>pythia.init(...)</code> is called these resonances | |
188 | are initialized along with all the internal resonances, and treated in | |
189 | exactly the same manner. See also the <aloc href="ProgramFlow">Program | |
190 | Flow</aloc> | |
191 | description. | |
192 | ||
193 | <p/> | |
194 | If the code should be of good quality and general usefulness, | |
195 | it would be simple to include it as a permanently available process | |
196 | in the standard program distribution. The final step of that integration | |
197 | ought to be left for the PYTHIA authors, but basically all that is | |
198 | needed is to add one line in | |
199 | <code>ParticleData::initResonances</code>, where one creates an | |
200 | instance of the resonance in the same way as for the resonances already | |
201 | there. In addition, the particle data and decay table for the new | |
202 | resonance has to be added to the permanent | |
203 | <aloc href="ParticleData">particle database</aloc>, and the code itself | |
204 | to <code>include/ResonanceWidths.h</code> and | |
205 | <code>src/ResonanceWidths.cc</code>. | |
206 | ||
207 | </chapter> | |
208 | ||
209 | <!-- Copyright (C) 2012 Torbjorn Sjostrand --> |