Particle Decays

1. Variables determining whether a particle decays
2. Mixing
3. Tau decays
4. QED radiation
5. Other variables
6. Modes for Matrix Element Processing

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 tau decays has also been introduced. Some issues may need further polishing.

Variables determining whether a particle decays

(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). By default this is defined as true for all particles with tau0 below 1000 mm, and false for ones above, see the Particle Data Scheme. This means that mu^+-, pi^+-, K^+-, K^0_L and n/nbar always remain stable unless decays are explicity switched on, e.g. 211:mayDecay = true.

(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 = 10.; 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 = 10.; 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 = 10.; minimum = 0.)
The above rMax, expressed in mm.

(vi) Particles may be requested to decay within a given cylindrical 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 = 10.; minimum = 0.)
The above xyMax, expressed in mm.

parm  ParticleDecays:zMax   (default = 10.; minimum = 0.)
The above zMax, expressed in mm.

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.)

Tau decays

The decays of tau leptons are categorized as correlated, where a tau pair is produced from a single process, or uncorrelated, where only one tau is produced. Currently, internally supported tau production mechanisms include correlated decays from gamma, Z^0, Z'^0, gamma^*/Z^0/Z'^0, Higgs bosons (CP-even, odd, or mixed), and t-channel gamma gamma → tau^+ tau^-; and uncorrelated decays from W^+-, W'^+-, B/D hadrons, and charged Higgs bosons. For all mechanisms except B/D hadrons, both the full process, e.g. q qbar → Z^0 → tau^+ tau^-, as well as just the decay of the boson with a given initial helicity state, e.g. Z^0 → tau^+ tau^-, can be handled. The axial and vector couplings of the Z'^0 and W'^0 are set from the relevant parameters in New Gauge Boson Processes. Note that the CP of the various Higgs bosons can be set with the options HiggsX:parity, HiggsX:etaParity, and HiggsX:phiParity as described in Higgs Processes where X is either H1, H2, or A3. Any tau produced from a helicity shower can also be handled.

The tau polarization and tau decay correlation mechanism can be determined either using internal matrix elements or external SPINUP information provided in the event, e.g. via Les Houches Event Files (LHEF). The SPINUP digit is interpreted as the particle helicity state in the lab frame: -1 and 1 are longitudinal and 0 is transverse. Other values are not valid. For internal determination any tau pair or single tau from the processes of the previous list can be handeled. For external determination of a single uncorrelated tau, its helicity state is set to its SPINUP information. When the SPINUP for the tau is not valid, e.g. when FSR is applied, the SPINUP for the first copy of that tau is used instead unless also invalid. While Pythia does not internally produce events with polarized beams, beam polarization for externally provided events is accounted for in tau decays when the beam SPINUP digits are set accordingly. For the external determination of a correlated tau pair the following options are available.

mode  TauDecays:externalMode   (default = 1; minimum = 0; maximum = 2)
Choice of the external polarization and correlation mechanism for correlated tau pairs.
option 0 : all correlated tau pairs are treated as uncorrelated tau leptons with their helicity state set via SPINUP.
option 1 : the mother of each tau pair is found and its helicity state set via SPINUP. If the mother is from the list of available internal correlated processes, a correlated decay is performed.
option 2 : nothing is done.
Note 1: here, SPINUP is always interpreted as a helicity state and must be -1, 0, or 1. Any other values are invalid and default behavior for the decay will be used instead, including using internal determination methods if configured accordingly.
Note 2: to enable correlated tau decays from helicity showers, mode 1 must be set.

A default behaviour is defined when the polarization and decay mechanism cannot be determined using either the internal or external methods. If the tau is known to be produced from a W^+-, gamma, or Z^0, the tau or tau pair is assumed to be produced from an unpolarized boson of this type. If the mediator is unknown but there is a correlated tau pair, the pair is assumed to be produced from an unpolarized photon and a warning is issued. Finally, if the tau is uncorrelated, an unpolarized and uncorrelated decay is performed and a warning is issued.

mode  TauDecays:mode   (default = 1; minimum = 0; maximum = 5)
Choice of tau decay model.
option 0 : old decay model, with isotropic decays.
option 1 : sophisticated decays where external and then internal determination is applied.
option 2 : sophisticated decays as above, but now taus with a mother TauDecays:tauMother are forced into an uncorrelated decay with a polarization set by TauDecays:tauPolarization.
option 3 : sophisticated decays where all taus, regardless of mother, are forced into an uncorrelated decay with a polarization set by TauDecays:tauPolarization.
option 4 : sophisticated decays where only internal determination is applied.
option 5 : sophisticated decays where only external (SPINUP) determination is applied.
Warning 1: options 2 and 3, to force a specific tau polarization, only affect the decay of the tau. The angular distribution of the tau itself, given by its production, is not modified by these options. If you want, e.g., a righthanded W, 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 tau decay stage.
Warning 2: for options 1 through 5, if the polarization and correlation mechanism for the tau cannot be determined (internally or externally) then the default behaviour described above is applied.

parm  TauDecays:tauPolarization   (default = 0; minimum = -1.; maximum = 1.)
Polarization of the tau when mode 2 or 3 of TauDecays:mode is selected. Note, this does not specific a helicity state, but rather a polarization probability.

mode  TauDecays:tauMother   (default = 0; minimum = 0)
Mother of the tau for forced polarization when mode 2 of TauDecays:mode is selected. You should give the positive identity code; to the extent an antiparticle exists it will automatically obtain the inverse polarization.

parm  TauDecays:mMinForZ   (default = -1)
Calculating the helicity matrix element for f fbar → gamma^*/Z^0 → tau^+ tau- production may be speeded up significantly by assuming massless fermions. If this value is positive, the massless fermion approximation is used when the mediator mass for the process is above this value.

QED radiation

flag  ParticleDecays:allowPhotonRadiation   (default = off)
Allow or not photon radiations in decays to a lepton pair, see above.
Note: 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.

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 gluon 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.; minimum = 2.; maximum = 6.)
The above multIncrease parameter, except for meMode = 23.

parm  ParticleDecays:multIncreaseWeak   (default = 2.5; minimum = 1.; maximum = 4.)
The above multIncrease parameter, specifically for meMode = 23. 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.

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 = on)
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

• 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)
• 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
• 3 - 7 : two-body decay of a hadron with mass-dependent width. The angular momentum of the outgoing two-body system is given by code - 3.
• 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
• 93 : decay of colour singlet to q qbar plus another singlet, flat in phase space (and arbitrarily ordered), where the q qbar pair should shower and hadronize
• 94 : same as 93, but weighted with V-A weak matrix element if the decay chain is of the type neutrino \rarr; dbar u lepton in that order
• 100 - : reserved for the description of partial widths of resonances

• 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.