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<h2>Particle Decays</h2>

The <code>ParticleDecays</code> class performs the sequential decays of 
all unstable hadrons produced in the string fragmentation stage,
i.e. up to and including <i>b</i> hadrons and their decay products, 
such as the <i>tau</i> lepton. It is not to be used for the decay of 
more massive <a href="ResonanceDecays.html" target="page">resonances</a>, such as top, 
<i>Z^0</i> or SUSY, where decays must be performed already at the 
<code>ProcessLevel</code> of the event generation.

<p/>
The decay description essentially copies the one present in 
PYTHIA since many years, but with some improvements, e.g. in the decay
tables and the number of decay models available. Recently a more
sophisticated handling of <i>tau</i> decays has also been introduced.
Some issues may need further polishing.

<h3>Variables determining whether a particle decays</h3>

Before a particle is actually decayed, a number of checks are made.

<p/>
(i) Decay modes must have been defined for the particle kind;    
tested by the <code>canDecay()</code> method of <code>Event</code> 
(and <code>ParticleData</code>).        

<p/>
(ii) The main switch for allowing this particle kind to decay must 
be on; tested by the <code>mayDecay()</code> method of <code>Event</code> 
(and <code>ParticleData</code>). 

<p/>
(iii) Particles may be requested to have a nominal proper lifetime 
<i>tau0</i> below a threshold.

<p/><code>flag&nbsp; </code><strong> ParticleDecays:limitTau0 &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
When on, only particles with <i>tau0 &lt; tau0Max</i> are decayed.
  

<p/><code>parm&nbsp; </code><strong> ParticleDecays:tau0Max &nbsp;</strong> 
 (<code>default = <strong>10.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>tau0Max</i>, expressed in mm/c.
  

<p/>
(iv) Particles may be requested to have an actual proper lifetime 
<i>tau</i> below a threshold.

<p/><code>flag&nbsp; </code><strong> ParticleDecays:limitTau &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
When on, only particles with <i>tau &lt; tauMax</i> are decayed.
  

<p/><code>parm&nbsp; </code><strong> ParticleDecays:tauMax &nbsp;</strong> 
 (<code>default = <strong>10.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>tauMax</i>, expressed in mm/c.<br/>
In order for this and the subsequent tests to work, a <i>tau</i> 
is selected and stored for each particle, whether in the end it
decays or not. (If each test would use a different temporary 
<i>tau</i> it would lead to inconsistencies.)
  

<p/>
(v) Particles may be requested to decay within a given distance 
of the origin.

<p/><code>flag&nbsp; </code><strong> ParticleDecays:limitRadius &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
When on, only particles with a decay within a radius <i>r &lt; rMax</i> 
are decayed. There is assumed to be no magnetic field or other 
detector effects.
  

<p/><code>parm&nbsp; </code><strong> ParticleDecays:rMax &nbsp;</strong> 
 (<code>default = <strong>10.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>rMax</i>, expressed in mm.
   

<p/>
(vi) Particles may be requested to decay within a given cylindrical 
volume around the origin.

<p/><code>flag&nbsp; </code><strong> ParticleDecays:limitCylinder &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
When on, only particles with a decay within a volume limited by
<i>rho = sqrt(x^2 + y^2) &lt; xyMax</i> and <i>|z| &lt; zMax</i> 
are decayed. There is assumed to be no magnetic field or other 
detector effects.
  

<p/><code>parm&nbsp; </code><strong> ParticleDecays:xyMax &nbsp;</strong> 
 (<code>default = <strong>10.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>xyMax</i>, expressed in mm.
   

<p/><code>parm&nbsp; </code><strong> ParticleDecays:zMax &nbsp;</strong> 
 (<code>default = <strong>10.</strong></code>; <code>minimum = 0.</code>)<br/>
The above <i>zMax</i>, expressed in mm.
   

<h3>Mixing</h3>

<p/><code>flag&nbsp; </code><strong> ParticleDecays:mixB &nbsp;</strong> 
 (<code>default = <strong>on</strong></code>)<br/>
Allow or not <i>B^0 - B^0bar</i> and <i>B_s^0 - B_s^0bar</i> mixing.
  

<p/><code>parm&nbsp; </code><strong> ParticleDecays:xBdMix &nbsp;</strong> 
 (<code>default = <strong>0.776</strong></code>; <code>minimum = 0.74</code>; <code>maximum = 0.81</code>)<br/>
The mixing parameter <i>x_d = Delta(m_B^0)/Gamma_B^0</i> in the 
<i>B^0 - B^0bar</i> system. (Default from RPP2006.)
   

<p/><code>parm&nbsp; </code><strong> ParticleDecays:xBsMix &nbsp;</strong> 
 (<code>default = <strong>26.05</strong></code>; <code>minimum = 22.0</code>; <code>maximum = 30.0</code>)<br/>
The mixing parameter <i>x_s = Delta(m_B_s^0)/Gamma_B_s^0</i> in the 
<i>B_s^0 - B_s^0bar</i> system. (Delta-m from CDF hep-ex-0609040,
Gamma from RPP2006.)
   

<h3>Tau decays</h3>

A new machinery has been introduced to handle <i>tau</i> lepton decays, 
with helicity information related to the production process and with
the form of the hadronic current fitted to data. It is largely based
on the corresponding Herwig++ implementation [<a href="Bibliography.html" target="page">Gre07</a>], with
some input from Tauola [<a href="Bibliography.html" target="page">Jad90</a>]. A complete writeup is 
in preparation, but meanwhile a short summary can be found at
[<a href="Bibliography.html" target="page">Ilt12</a>]. 

<p/>
For <i>tau</i>s in external processes, interfaced with Les Houches 
Accord information available, e.g. via Les Houches Event Files (LHEF), 
the new machinery interprets the SPINUP number for <i>tau</i> leptons 
as giving their helicity, and decays them accordingly. The only exceptions 
are when a specific polarization is forced by the user (see below), 
which then overrides the SPINUP value, or when SPINUP has the special 
value 9 (unpolarized). In the latter case, PYTHIA defaults back to 
attempting to determine the helicity structure from the production 
process, in the same way as for internal processes.

<p/>
This new machinery is on by default, but it is possible to revert to 
the simpler old decay handling, e.g. to study differences. Furthermore
the spin tracing framework does not yet cover all possibilities; notably 
it cannot handle taus coming from SUSY decay chains 
(except via LHEF), so it makes sense 
to switch off the new machinery in such instances, for speed reasons if 
nothing else. In case only one tau mother species is undefined, the 
polarization involved can be set by hand.

<p/><code>mode&nbsp; </code><strong> ParticleDecays:sophisticatedTau &nbsp;</strong> 
 (<code>default = <strong>1</strong></code>; <code>minimum = 0</code>; <code>maximum = 3</code>)<br/>
Choice of <i>tau</i> decay model.
<br/><code>option </code><strong> 0</strong> : old decay model, with isotropic decays. 
When reading LHEF files, the SPINUP digit will be ignored.  
<br/><code>option </code><strong> 1</strong> : sophisticated decays where <i>tau</i> polarization is 
calculated from the <i>tau</i> production mechanism. 
When reading LHEF files, the SPINUP digit will be used.
  
<br/><code>option </code><strong> 2</strong> : sophisticated decays as above, but additionally <i>tau</i> 
polarization is set to <code>ParticleDecaus:tauPolarization</code> for 
<i>tau</i>s produced from <code>ParticleDecays:tauMother</code>. 
When reading LHEF files, this overrides the SPINUP digit. 
  
<br/><code>option </code><strong> 3</strong> : sophisticated decays where <i>tau</i> polarization is set 
to <code>ParticleDecaus:tauPolarization</code> for all <i>tau</i> decays. 
When reading LHEF files, this overrides the SPINUP digit. 
  
<br/><b>Note</b>: options <code>2</code> and <code>3</code>, 
to force a specific <i>tau</i> polarization, only affect the decay 
of the <i>tau</i>. The angular distribution of the <i>tau</i> itself, 
given by its production, is not modified by these options. If you want, e.g., 
a righthanded <i>W</i>, or a SUSY decay chain, the kinematics should 
be handled by the corresponding cross section class(es), supplemented by 
the resonance decay one(s). The options here could then still be used 
to ensure the correct polarization at the <i>tau</i> decay stage.
  

<p/><code>parm&nbsp; </code><strong> ParticleDecays:tauPolarization &nbsp;</strong> 
 (<code>default = <strong>0</strong></code>; <code>minimum = -1.</code>; <code>maximum = 1.</code>)<br/>
Polarization of the <i>tau</i> when mode <i>2</i> or <i>3</i> of 
<code>ParticleDecays:sophisticatedTau</code> is selected.
  

<p/><code>mode&nbsp; </code><strong> ParticleDecays:tauMother &nbsp;</strong> 
 (<code>default = <strong>0</strong></code>; <code>minimum = 0</code>)<br/>
Mother of the <i>tau</i> for forced polarization when mode <i>2</i> of 
<code>ParticleDecays:sophisticatedTau</code> is selected. You should give the
positive identity code; to the extent an antiparticle exists it will
automatically obtain the inverse polarization.
  

<h3>QED radiation</h3>

So far PYTHIA does not have any generic machinery for handling QED radiation
in normal particle decays. In order to include this, a program like Photos 
[<a href="Bibliography.html" target="page">Bar94, Dav10</a>] could be used as an afterburner. In a few cases,
however, the existing shower machinery can be used also here: for 
two-body decays to a lepton pair (<i>l^+ l^-</i> or <i>l^+- nu_l</i>).
Such decays are mediated by <i>gamma^*/Z^0/W^+-</i> exchange, for
which PYTHIA does have an existing machinery that can be applied, 
including first-order matrix-element corrections for the first (hardest)
photon emission. 

<p/><code>flag&nbsp; </code><strong> ParticleDecays:allowPhotonRadiation &nbsp;</strong> 
 (<code>default = <strong>off</strong></code>)<br/>
Allow or not photon radiations in decays to a lepton pair, see above.
<br/><b>Note:</b> The current default is to have radiation switched off, 
in order to avoid double-counting of emissions if you link to an external 
QED-radiation program, as is the norm in many collaborations.
  

<h3>Other variables</h3>

<p/><code>parm&nbsp; </code><strong> ParticleDecays:mSafety &nbsp;</strong> 
 (<code>default = <strong>0.0005</strong></code>; <code>minimum = 0.</code>; <code>maximum = 0.01</code>)<br/>
Minimum mass difference required between the decaying mother mass 
and the sum of the daughter masses, kept as a safety margin to avoid
numerical problems in the decay generation.
   

<p/><code>parm&nbsp; </code><strong> ParticleDecays:sigmaSoft &nbsp;</strong> 
 (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.2</code>; <code>maximum = 2.</code>)<br/>
In semileptonic decays to more than one hadron, such as 
<i>B -> nu l D pi</i>, decay products after the first three are 
dampened in momentum by an explicit weight factor 
<i>exp(-p^2/sigmaSoft^2)</i>, where <i>p</i> is the 
three-momentum in the rest frame of the decaying particle.
This takes into account that such further particles come from the
fragmentation of the spectator parton and thus should be soft.   
   

<p/>
When a decay mode is defined in terms of a partonic content, a random 
multiplicity (and a random flavour set) of hadrons is to be picked, 
especially for some charm and bottom decays. This is done according to 
a Poissonian distribution, for <i>n_p</i> normal particles and 
<i>n_q</i> quarks the average value is chosen as  
<br/><i>
  n_p/ 2 + n_q/4 + multIncrease * ln ( mDiff / multRefMass)
</i><br/>
with <i>mDiff</i> the difference between the decaying particle mass 
and the sum of the normal-particle masses and the constituent quark masses. 
For gluon systems <i>multGoffset</i> offers and optional additional 
term to the multiplicity. The lowest possible multiplicity is 
<i>n_p + n_q/2</i> (but at least 2) and the highest possible 10.
If the picked hadrons have a summed mass above that of the mother a 
new try is made, including a new multiplicity. These constraints 
imply that the actual average multiplicity does not quite agree with
the formula above.

<p/><code>parm&nbsp; </code><strong> ParticleDecays:multIncrease &nbsp;</strong> 
 (<code>default = <strong>4.</strong></code>; <code>minimum = 2.</code>; <code>maximum = 6.</code>)<br/>
The above <i>multIncrease</i> parameter, except for 
<code>meMode = 23</code>.
   

<p/><code>parm&nbsp; </code><strong> ParticleDecays:multIncreaseWeak &nbsp;</strong> 
 (<code>default = <strong>2.5</strong></code>; <code>minimum = 1.</code>; <code>maximum = 4.</code>)<br/>
The above <i>multIncrease</i> parameter, specifically for 
<code>meMode = 23</code>. Here the weak decay implies that only the 
virtual W mass should contribute to the production of new particles, 
rather than the full meson mass.
   

<p/><code>parm&nbsp; </code><strong> ParticleDecays:multRefMass &nbsp;</strong> 
 (<code>default = <strong>0.7</strong></code>; <code>minimum = 0.2</code>; <code>maximum = 2.0</code>)<br/>
The above <i>multRefMass</i> parameter.
   

<p/><code>parm&nbsp; </code><strong> ParticleDecays:multGoffset &nbsp;</strong> 
 (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.0</code>; <code>maximum = 2.0</code>)<br/>
The above <i>multGoffset</i> parameter.
   

<p/><code>parm&nbsp; </code><strong> ParticleDecays:colRearrange &nbsp;</strong> 
 (<code>default = <strong>0.5</strong></code>; <code>minimum = 0.</code>; <code>maximum = 1.0</code>)<br/>
When a decay is given as a list of four partons to be turned into
hadrons (primarily for modes 41 - 80)  it is assumed that they are 
listed in pairs, as a first and a second colour singlet, which could 
give rise to separate sets of hadrons. Here <i>colRearrange</i> is 
the probability that this original assignment is not respected, and 
default corresponds to no memory of this original colour topology.
   

<p/><code>flag&nbsp; </code><strong> ParticleDecays:FSRinDecays &nbsp;</strong> 
 (<code>default = <strong>true</strong></code>)<br/>
When a particle decays to <i>q qbar</i>, <i>g g</i>, <i>g g g</i> 
or <i>gamma g g</i>, with <code>meMode > 90</code>, allow or not a 
shower to develop from it, before the partonic system is hadronized. 
(The typical example is <i>Upsilon</i> decay.)
  

In addition, some variables defined for string fragmentation and for
flavour production are used also here.
 
<h3>Modes for Matrix Element Processing</h3>

Some decays can be treated better than what pure phase space allows,
by reweighting with appropriate matrix elements. In others a partonic
content has to be converted to a set of hadrons. The presence of such
corrections is signaled by a nonvanishing <code>meMode()</code> value
for a decay mode in the <a href="ParticleDataScheme.html" target="page">particle
data table</a>. The list of allowed possibilities almost agrees with the 
PYTHIA 6 ones, but several obsolete choices have been removed, 
a few new introduced, and most have been moved for better consistency. 
Here is the list of currently allowed <code>meMode()</code> codes:
<ul>
<li>  0 : pure phase space of produced particles ("default");
input of partons is allowed and then the partonic content is 
converted into the minimal number of hadrons (i.e. one per
parton pair, but at least two particles in total)</li>
<li>  1 : <i>omega</i> and <i>phi -> pi+ pi- pi0</i></li>
<li>  2 : polarization in <i>V -> PS + PS</i> (<i>V</i> = vector, 
<i>PS</i> = pseudoscalar), when <i>V</i> is produced by 
<i>PS -> PS + V</i> or <i>PS -> gamma + V</i></li>
<li> 11 : Dalitz decay into one particle, in addition to the 
lepton pair (also allowed to specify a quark-antiquark pair that 
should collapse to a single hadron)</li>
<li> 12 : Dalitz decay into two or more particles in addition 
to the lepton pair</li>
<li> 13 : double Dalitz decay into two lepton pairs</li>
<li> 21 : decay to phase space, but weight up <i>neutrino_tau</i> spectrum
in <i>tau</i> decay</li>
<li> 22 : weak decay; if there is a quark spectator system it collapses to 
one hadron; for leptonic/semileptonic decays the <i>V-A</i> matrix element
is used, for hadronic decays simple phase space</li>
<li> 23 : as 22, but require at least three particles in decay</li>
<li> 31 : decays of type B -> gamma X, very primitive simulation where
X is given in terms of its flavour content, the X multiplicity is picked 
according to a geometrical distribution with average number 2, and 
the photon energy spectrum is weighted up relative to pure phase space</li>
<li> 42 - 50 : turn partons into a random number of hadrons, picked according 
to a Poissonian with average value as described above, but at least 
<code>code</code> - 40 and at most 10, and then distribute then in pure 
phase space; make a new try with another multiplicity if the sum of daughter
masses exceed the mother one </li>
<li> 52 - 60 : as 42 - 50, with multiplicity between <code>code</code> - 50 
and 10, but avoid already explicitly listed non-partonic channels</li>
<li> 62 - 70 : as 42 - 50, but fixed multiplicity <code>code</code> - 60</li>
<li> 72 - 80 : as 42 - 50, but fixed multiplicity <code>code</code> - 70,
and avoid already explicitly listed non-partonic channels</li>
<li> 91 : decay to <i>q qbar</i> or <i>g g</i>, which should shower 
and hadronize</li>
<li> 92 : decay onium to <i>g g g</i> or <i>g g gamma</i> 
(with matrix element), which should shower and hadronize</li>
<li> 100 - : reserved for the description of partial widths of 
<a href="ResonanceDecays.html" target="page">resonances</a></li>
</ul>

Three special decay product identity codes are defined.
<ul>
<li>81: remnant flavour. Used for weak decays of c and b hadrons, where the
c or b quark decays and the other quarks are considered as a spectator
remnant in this decay. In practice only used for baryons with multiple 
c and b quarks, which presumably would never be used, but have simple
(copied) just-in-case decay tables. Assumed to be last decay product.</li> 
<li>82: random flavour, picked by the standard fragmentation flavour
machinery, used to start a sequence of hadrons, for matrix element
codes in 41 - 80. Assumed to be first decay product, with -82 as second
and last. Where multiplicity is free to be picked it is selected as for
normal quarkonic systems. Currently unused.</li>  
<li>83: as for 82, with matched pair 83, -83 of decay products. The 
difference is that here the pair is supposed to come from a closed gluon 
loop (e.g. <i>eta_c -> g g</i>) and so have a somewhat higher average
multiplicity than the simple string assumed for 82, see the
<code>ParticleDecays:multGoffset</code> parameter above.</li>
</ul>

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