<chapter name="Mass-dependent hadron widths"> 
 
<h2>Mass-dependent hadron widths</h2> 
 
This page describes a model for mass-dependent hadron widths. This includes 
mass-dependent branching ratios for hadrons produced off-shell, and is a, 
important component of the 
<aloc href="HadronicRescattering">rescattering framework</aloc>. 
 
<p/> 
The mass-dependent widths are handled by the <code>HadronWidths</code> class. 
When running the program, the widths are precalculated and tabulated in order 
to improve efficiency, which is particularly important for rescattering. 
These precalculated values can be found in the <code>HadronWidths.dat</code> 
file. 
 
<p/> 
A prerequisite is that the space-time production vertices of hadrons 
from string fragmentation are known. This was implemented in 
<ref>Fer18</ref>, and is described separately on the 
<aloc href="HadronVertexInformation">Hadron Vertex Information</aloc> 
page. A smaller further smearing is obtained from the 
<aloc href="PartonVertexInformation">Parton Vertex Information</aloc> 
transverse displacement of separate MPI vertices. 
 
<h3>The <code>HadronWidths</code> class</h3> 
 
<p/> 
The following methods are found in the <code>HadronWidths</code> class. 
 
<method name="bool HadronWidths::check()"> 
run a check to validate the loaded hadron widths data. Returns whether 
successful. 
</method> 
 
<method name="set&lt;int&gt; HadronWidths::hasResonances(int idA, int idB)"> 
returns whether the two specified incoming particles can form 
resonances. 
</method> 
 
<method name="set&lt;int&gt; HadronWidths::getResonances()"> 
</method> 
<methodmore name="set&lt;int&gt; HadronWidths::getResonances(int idA, 
int idB)"> 
gets a list of the implemented resonance particles. If <code>idA</code> and 
<code>idB</code> are specified, it instead returns a list of resonances that 
can be formed by those particles. 
</methodmore> 
 
<method name="bool HadronWidths::hasData(int id)"> 
returns whether mass-dependent widths have been parameterized for the 
specified particle. If <code>id</code> is negative, it instead returns whether 
data exists for the corresponding absolute value. 
</method> 
 
<method name="bool HadronWidths::canDecay(int idR, int prodA, int prodB)"> 
returns whether data exists for the decay <ei>R &rarr; A + B</ei>. 
</method> 
 
<method name="double HadronWidths::width(int id, double m)"> 
returns the mass-dependent width of the specified particle at the given mass. 
If parameterized data does not exist for that particle, its nominal width is 
returned instead. 
</method> 
 
<method name="double HadronWidths::partialWidth(int idR, 
int prodA, int prodB, double m)"> 
</method> 
<methodmore name="double HadronWidths::br(int id, 
int prodA, int prodB, double m)"> 
returns the mass-dependent partial width or branching ratio of the decay 
<ei>R &rarr; A + B</ei>. 
</methodmore> 
 
<method name="double HadronWidths::mDistr(int id, double m)"> 
gives the mass distribution density for the specified particle. This is given 
by a Breit-Wigner function, using the mass-dependent width. 
</method> 
 
<method name="bool HadronWidths::pickMasses(int idA, int idB, double eCM, 
double& mAOut, double& mBOut, int lType = 1)"> 
given two particles produced at the specified CM energy, this method samples 
the masses of those two particles, according to their mass distributions and 
available phase space. If successful, the resulting masses are written to 
<code>mAOut</code> and <code>mBOut</code>, and the method returns true. 
The <code>lType</code> parameter is <ei>2l+1</ei>, where <ei>l</ei> is the 
angular momentum of the outgoing two-body system. 
</method> 
 
<method name="bool HadronWidths::pickDecay(int idDec, double m, 
int& idAOut, int& iBOut, double& mAOut, double& mBOut)"> 
pick a decay channel for the <code>idDec</code> particle with the specified 
mass, using mass-dependent branching ratios. If successful, the outgoing 
particle ids are written to <code>idAOut</code> and <code>idBOut</code>, 
and their corresponding masses are written to <code>mAOut</code> and 
<code>mBOut</code>. Returns whether successful. 
</method> 
 
<p/> 
In some cases, parameterized hadron widths are not available. This could 
happen for example if the user defines new particles or changes properties of 
existing resonance hadrons. In these cases, the following methods can be used 
to calculate new widths and generate parameterization data. 
 
<method name="double HadronWidths::widthCalc(int id, double m)"> 
</method> 
<methodmore name="double HadronWidths::widthCalc(int idR, 
int prodA, int prodB, double m)"> 
calculate the mass-dependent width of the particle at the specified mass, 
or the partial width of the decay <ei>R &rarr; A + B</ei>. 
This does not use the parameterized mass-dependent width for the resonance 
particle, even if it is defined. However, this is dependent on the mass 
distributions of the decay products, and these will be calculated using 
mass-dependent widths if they have been parameterized for those particles. 
</methodmore> 
 
<method name="bool HadronWidths::parameterize(int id, int precision)"> 
</method> 
<methodmore name="void HadronWidths::parameterizeAll(int precision)"> 
the <code>parameterize</code> method recalculates the widths of the specified 
particle. The widths are calculated at <code>precision</code> number of 
points, evenly spaced between the minimum and maxium mass of that particle. 
Note that this will use existing parameterizations for decay products, if 
available. 
The <code>parametizeAll</code> method clears all parameterized data and 
recalculates it for all particles in the event record that set 
<code>varWidth = on</code>. This is done in a way that ensures that if such a 
hadron decays into other hadrons with mass-dependent widths, then the widths 
of the decay products are parameterized first. 
</methodmore> 
 
<method name="bool HadronWidths::save(ostream& stream)"> 
</method> 
<methodmore name="bool HadronWidths::save(string 
file = &quot;HadronWidths.dat&quot;)"> 
write all parameterized mass-dependent widths in an xml format to the 
specified stream or file. 
</methodmore> 
 
</chapter> 
 
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