Particle Decays

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

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. Some issues may need further polishing.

Variables determining whether a particle decays

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

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

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

(iii) Particles may be requested to have a nominal proper lifetime tau0 below a threshold.

flag ParticleDecays:limitTau0 (default = off)
When on, only particles with tau0 < tau0Max are decayed.

parm ParticleDecays:tau0Max (default = 1.; minimum = 0.)
The above tau0Max, expressed in mm/c.

(iv) Particles may be requested to have an actual proper lifetime tau below a threshold.

flag ParticleDecays:limitTau (default = off)
When on, only particles with tau < tauMax are decayed.

parm ParticleDecays:tauMax (default = 1.; minimum = 0.)
The above tauMax, expressed in mm/c.
In order for this and the subsequent tests to work, a tau is selected and stored for each particle, whether in the end it decays or not. (If each test would use a different temporary tau it would lead to inconsistencies.)

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

flag ParticleDecays:limitRadius (default = off)
When on, only particles with a decay within a radius r < rMax are decayed. There is assumed to be no magnetic field or other detector effects.

parm ParticleDecays:rMax (default = 1.; minimum = 0.)
The above rMax, expressed in mm/c.

(vi) Particles may be requested to decay within a given cylidrical volume around the origin.

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

parm ParticleDecays:xyMax (default = 1.; minimum = 0.)
The above xyMax, expressed in mm/c.

parm ParticleDecays:zMax (default = 1.; minimum = 0.)
The above zMax, expressed in mm/c.

Mixing

flag ParticleDecays:mixB (default = on)
Allow or not B^0 - B^0bar and B_s^0 - B_s^0bar mixing.

parm ParticleDecays:xBdMix (default = 0.776; minimum = 0.74; maximum = 0.81)
The mixing parameter x_d = Delta(m_B^0)/Gamma_B^0 in the B^0 - B^0bar system. (Default from RPP2006.)

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

Other variables

parm ParticleDecays:mSafety (default = 0.0005; minimum = 0.; maximum = 0.01)
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.

parm ParticleDecays:sigmaSoft (default = 0.5; minimum = 0.2; maximum = 2.)
In semileptonic decays to more than one hadron, such as B -> nu l D pi, decay products after the first three are dampened in momentum by an explicit weight factor exp(-p^2/sigmaSoft^2), where p 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.

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 n_p normal particles and n_q quarks the average value is chosen as
n_p/ 2 + n_q/4 + multIncrease * ln ( mDiff / multRefMass)
with mDiff the difference between the decaying particle mass and the sum of the normal-particle masses and the constituent quark masses. For gluonic systems multGoffset offers and optional additional term to the multiplicity. The lowest possible multiplicity is n_p + n_q/2 (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.

parm ParticleDecays:multIncrease (default = 4.5; minimum = 3.; maximum = 6.)
The above multIncrease parameter.

parm ParticleDecays:multRefMass (default = 0.7; minimum = 0.2; maximum = 2.0)
The above multRefMass parameter.

parm ParticleDecays:multGoffset (default = 0.5; minimum = 0.0; maximum = 2.0)
The above multGoffset parameter.

parm ParticleDecays:colRearrange (default = 0.5; minimum = 0.; maximum = 1.0)
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 colRearrange is the probability that this original assignment is not respected, and default corresponds to no memory of this original colour topology.

flag ParticleDecays:FSRinDecays (default = true)
When a particle decays to q qbar, g g, g g g or gamma g g, with meMode > 90, allow or not a shower to develop from it, before the partonic system is hadronized. (The typical example is Upsilon decay.) In addition, some variables defined for string fragmentation and for flavour production are used also here.

Modes for Matrix Element Processing

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 signalled by a nonvanishing meMode() value for a decay mode in the particle data table. 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 meMode() codes:

0 : pure phace 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)
1 : omega and phi -> pi+ pi- pi0
2 : polarization in V -> PS + PS (V = vector, PS = pseudoscalar), when V is produced by PS -> PS + V or PS -> gamma + V
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)
12 : Dalitz decay into two or more particles in addition to the lepton pair
13 : double Dalitz decay into two lepton pairs
21 : decay to phase space, but weight up neutrino_tau spectrum in tau decay
22 : weak decay; if there is a quark spectator system it collapses to one hadron; for leptonic/semileptonic decays the V-A matrix element is used, for hadronic decays simple phase space
23 : as 22, but require at least three particles in decay
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
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 - 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
52 - 60 : as 42 - 50, with multiplicity between code - 50 and 10, but avoid already explicitly listed non-partonic channels
62 - 70 : as 42 - 50, but fixed multiplicity code - 60
72 - 80 : as 42 - 50, but fixed multiplicity code - 70, and avoid already explicitly listed non-partonic channels
91 : decay to q qbar or g g, which should shower and hadronize
92 : decay onium to g g g or g g gamma (with matrix element), which should shower and hadronize
100 - : reserved for the description of partial widths of resonances

Three special decay product identity codes are defined.

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.
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.
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. eta_c -> g g) and so have a somewhat higher average multiplicity than the simple string assumed for 82, see the ParticleDecays:multGoffset parameter above.