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