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<h2>Semi-Internal Resonances</h2>
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The introduction of a new <?php $filepath = $_GET["filepath"];
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echo "<a href='SemiInternalProcesses.php?filepath=".$filepath."' target='page'>";?>
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semi-internal process</a> may also involve a new particle,
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not currently implemented in PYTHIA. Often it is then enough to
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use the <?php $filepath = $_GET["filepath"];
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echo "<a href='ParticleDataScheme.php?filepath=".$filepath."' target='page'>";?>standard machinery</a>
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to introduce a new particle (<code>id:all = ...</code>) and new
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decay channels (<code>id:addChannel = ...</code>). By default this
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only allows you to define a fixed total width and fixed branching
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ratios. Using <code><?php $filepath = $_GET["filepath"];
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echo "<a href='ResonanceDecays.php?filepath=".$filepath."' target='page'>";?>meMode</a></code>
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values 100 or bigger provides the possibility of a very
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simple threshold behaviour.
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If you want to have complete freedom, however, there are two
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ways to go. One is that you make the resonance decay part of the
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hard process itself, either using the
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<?php $filepath = $_GET["filepath"];
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echo "<a href='LesHouchesAccord.php?filepath=".$filepath."' target='page'>";?>Les Houches interface</a> or
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a semi-internal process. The other is for you to create a new
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<code>ResonanceWidths</code> object, where you write the code
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needed for a calculation of the partial width of a particular
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Here we will explain what is involved in setting up a resonance.
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Should you actually go ahead with this, it is strongly recommended
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to use an existing resonance as a template, to get the correct
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structure. There also exists a sample main program,
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<code>main22.cc</code>, that illustrates how you could combine
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a new process and a new resonance.
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There are three steps involved in implementing a new resonance:
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<br/>1) providing the standard particle information, as already
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outlined above (<code>id:all = ...</code>,
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<code>id:addChannel = ...</code>), except that now branching
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ratios need not be specified, since they anyway will be overwritten
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by the dynamically calculated values.
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<br/>2) writing the class that calculates the partial widths.
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<br/>3) handing in a pointer to an instance of this class to PYTHIA.
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<br/>We consider the latter two aspects in turn.
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<h3>The ResonanceWidths Class</h3>
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The resonance-width calculation has to be encoded in a new class.
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The relevant code could either be put before the main program in the
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same file, or be stored separately, e.g. in a matched pair
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of <code>.h</code> and <code>.cc</code> files. The latter may be more
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convenient, in particular if the calculations are lengthy, or
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likely to be used in many different runs, but of course requires
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that these additional files are correctly compiled and linked.
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The class has to be derived from the <code>ResonanceWidths</code>
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base class. It can implement a number of methods. The constructor
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and the <code>calcWidth</code> ones are always needed, while others
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are for convenience. Much of the administrativ machinery is handled
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by methods in the base class.
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<p/>Thus, in particular, you must implement expressions for all
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possible final states, whether switched on in the current run or not,
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since all contribute to the total width needed in the denominator of
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the Breit-Wigner expression. Then the methods in the base class take
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care of selecting only allowed channels where that is required, and
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also of including effects of closed channels in secondary decays.
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These methods can be accessed indirectly via the
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<code><?php $filepath = $_GET["filepath"];
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echo "<a href='ResonanceDecays.php?filepath=".$filepath."' target='page'>";?>res...</a></code>
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methods of the normal
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<code><?php $filepath = $_GET["filepath"];
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echo "<a href='ParticleDataScheme.php?filepath=".$filepath."' target='page'>";?>particle database</a></code>.
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A <b>constructor</b> for the derived class obviously must be available.
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Here you are quite free to allow a list of arguments, to set
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the parameters of your model. The constructor must call the
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base-class <code>initBasic(idResIn)</code> method, where the argument
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<code>idResIn</code> is the PDG-style identity code you have chosen
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for the new resonance. When you create several related resonances
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as instances of the same class you would naturally make
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<code>idResIn</code> an argument of the constructor; for the
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PYTHIA classes this convention is used also in cases when it is
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<br/>The <code>initBasic(...)</code> method will
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hook up the <code>ResonanceWidths</code> object with the corresponding
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entry in the generic particle database, i.e. with the normal particle
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information you set up in point 1) above. It will store, in base-class
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member variables, a number of quantities that you later may find useful:
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<br/><code>idRes</code> : the identity code you provide;
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<br/><code>hasAntiRes</code> : whether there is an antiparticle;
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<br/><code>mRes</code> : resonance mass;
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<br/><code>GammaRes</code> resonance width;
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<br/><code>m2Res</code> : the squared mass;
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<br/><code>GamMRat</code> : the ratio of width to mass.
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A <b>destructor</b> is only needed if you plan to delete the resonance
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before the natural end of the run, and require some special behaviour
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at that point. If you call such a destructor you will leave a pointer
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dangling inside the <code>Pythia</code> object you gave it in to,
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if that still exists.
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<a name="method1"></a>
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<p/><strong>void ResonanceWidths::initConstants() </strong> <br/>
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is called once during initialization, and can then be used to set up
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further parameters specific to this particle species, such as couplings,
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and perform calculations that need not be repeated for each new event,
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thereby saving time. This method needs not be implemented.
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<a name="method2"></a>
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<p/><strong>void ResonanceWidths::calcPreFac(bool calledFromInit = false) </strong> <br/>
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is called once a mass has been chosen for the resonance, but before
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a specific final state is considered. This routine can therefore
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be used to perform calculations that otherwise might have to be repeated
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over and over again in <code>calcWidth</code> below. It is optional
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whether you want to use this method, however, or put
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everything in <code>calcWidth()</code>.
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<br/>The optional argument will have the value <code>true</code> when
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the resonance is initialized, and then be <code>false</code> throughout
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the event generation, should you wish to make a distinction.
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In PYTHIA such a distinction is made for <i>gamma^*/Z^0</i> and
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<i>gamma^*/Z^0/Z'^0</i>, owing to the necessity of a special
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description of interference effects, but not for other resonances.
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<br/>In addition to the base-class member variables already described
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above, <code>mHat</code> contains the current mass of the resonance.
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At initialization this agrees with the nominal mass <code>mRes</code>,
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but during the run it will not (in general).
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<a name="method3"></a>
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<p/><strong>void ResonanceWidths::calcWidth(bool calledFromInit = false) </strong> <br/>
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is the key method for width calculations and returns a partial width
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value, as further described below. It is called for a specific
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final state, typically in a loop over all allowed final states,
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subsequent to the <code>calcPreFac(...)</code> call above.
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Information on the final state is stored in a number of base-class
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variables, for you to use in your calculations:
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<br/><code>iChannel</code> : the channel number in the list of
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possible decay channels;
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<br/><code>mult</code> : the number of decay products;
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<br/><code>id1, id2, id3</code> : the identity code of up to the first
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three decay products, arranged in descending order of the absolute value
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of the identity code;
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<br/><code>id1Abs, id2Abs, id3Abs</code> : the absolute value of the
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above three identity codes;
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<br/><code>mHat</code> : the current resonance mass, which is the same
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as in the latest <code>calcPreFac(...)</code> call;
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<br/><code>mf1, mf2, mf3</code> : masses of the above decay products;
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<br/><code>mr1, mr2, mr3</code> : squared ratio of the product masses
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to the resonance mass;
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<br/><code>ps</code> : is only meaningful for two-body decays, where it
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gives the phase-space factor
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<i>ps = sqrt( (1. - mr1 - mr2)^2 - 4. * mr1 * mr2 )</i>;
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<br/>In two-body decays the third slot is zero for the above properties.
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Should there be more than three particles in the decay, you would have
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to take care of the subsequent products yourself, e.g. using
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<br/><code>particlePtr->decay[iChannel].product(j);</code>
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<br/>to extract the <code>j</code>'th decay products (with
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<code>j = 0</code> for the first, etc.). Currently we are not aware
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of any such examples.
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<br/>The base class also contains methods for <i>alpha_em</i> and
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<i>alpha_strong</i> evaluation, and can access many standard-model
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couplings; see the existing code for examples.
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<br/>The result of your calculation should be stored in
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<br/><code>widNow</code> : the partial width of the current channel,
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<a name="method4"></a>
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<p/><strong>double ResonanceWidths::widthChan( double mHat, int idAbs1, int idAbs2) </strong> <br/>
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is not normally used. In PYTHIA the only exception is Higgs decays,
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where it is used to define the width (except for colour factors)
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associated with a specific incoming/outgoing state. It allows the
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results of some loop expressions to be pretabulated.
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<h3>Access to resonance widths</h3>
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Once you have implemented a class, it is straightforward to
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make use of it in a run. Assume you have written a new class
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<code>MyResonance</code>, which inherits from
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<code>ResonanceWidths</code>. You then create an instance of
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this class and hand it in to a <code>pythia</code> object with
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ResonanceWidths* myResonance = new MyResonance();
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pythia.setResonancePtr( myResonance);
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If you have several resonances you can repeat the procedure any number
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of times. When <code>pythia.init(...)</code> is called these resonances
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are initialized along with all the internal resonances, and treated in
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exactly the same manner. See also the <?php $filepath = $_GET["filepath"];
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echo "<a href='ProgramFlow.php?filepath=".$filepath."' target='page'>";?>Program
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If the code should be of good quality and general usefulness,
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it would be simple to include it as a permanently available process
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in the standard program distribution. The final step of that integration
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ought to be left for the PYTHIA authors, but basically all that is
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needed is to add one line in
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<code>ParticleData::initResonances</code>, where one creates an
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instance of the resonance in the same way as for the resonances already
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there. In addition, the particle data and decay table for the new
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resonance has to be added to the permanent
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<?php $filepath = $_GET["filepath"];
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echo "<a href='ParticleData.php?filepath=".$filepath."' target='page'>";?>particle database</a>, and the code itself
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to <code>include/ResonanceWidths.h</code> and
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<code>src/ResonanceWidths.cc</code>.
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