Resonance Decays

  1. Resonance Decays and Cross Sections
  2. Special properties and methods for resonances
  3. Modes for Matrix Element Processing
  4. Filter for Resonance Decays
The ResonanceDecays class performs the sequential decays of all resonances formed in the hard process. Note the important distinction between "resonances" and other "particles" made in PYTHIA. There is one ambiguous case in this classification, namely the photon. The gamma^*/Z^0 combination contains a low-mass peak when produced in a hard process. On the other hand, photons can participate in shower evolution, and therefore a photon originally assumed massless can be assigned an arbitrarily high mass when it is allowed to branch into a fermion pair. In some cases this could lead to double-counting, e.g. between processes such as f fbar → (gamma^*/Z^0) (gamma^*/Z^0), f fbar → (gamma^*/Z^0) gamma and f fbar → gamma gamma. Here it make sense to limit the lower mass allowed for the gamma^*/Z^0 combination, in 23:mMin, to be the same as the upper limit allowed for an off-shell photon in the shower evolution, in TimeShower:mMaxGamma. By default this matching is done at 10 GeV.

In spite of the above-mentioned differences, the resonances and the other particles are all stored in one common particle data table, so as to offer a uniform interface to setting and getting properties such as name, mass, charge and decay modes, also for the particle properties in the event record. Some methods are specific to resonances, however, in particular for the calculation of partial widths and thereby of branching ratio. For resonances these can be calculated dynamically, set up at initialization for the nominal mass and then updated to the current mass when these are picked according to a Breit-Wigner resonance shape.

Resonance Decays and Cross Sections

As already hinted above, you have the possibility to set the allowed decay channels of resonances, see Particle Data Scheme description. For instance, if you study the process q qbar → H^0 Z^0 you could specify that the Z^0 should decay only to lepton pairs, the H^0 only to W^+ W^-, the W^+ only to a muon and a neutrino, while the W^- can decay to anything. Unfortunately there are limits to the flexibility: you cannot set a resonance to have different properties in different places of a process, e.g. if instead H^0 → Z^0 Z^0 in the above process then the three Z^0's would all obey the same rules.

The restrictions on the allowed final states of a process is directly reflected in the cross section of it. That is, if some final states are excluded then the cross section is reduced accordingly. Such restrictions are built up recursively in cases of sequential decay chains. The restrictions are also reflected in the compositions of those events that actually do get to be generated. For instance, the relative rates of H^0 → W^+ W^- and H^0 → Z^0 Z^0 are shifted when the allowed sets of W^+- and Z^0 decay channels are changed.

We remind that only those particles that Pythia treat as resonances enjoy this property, and only those that are considered as part of the hard process and its associated resonance decays.

There is one key restriction on resonances:

parm  ResonanceWidths:minWidth   (default = 1.97e-19; minimum = 1e-30)
Minimal allowed width of a resonance, in GeV. If the width falls below this number the resonance is considered stable and will not be allowed to decay. This is mainly intended as a technical parameter, to avoid disasters in cases where no open decay channels exists at all. It could be used for real-life decisions as well, however. The default value corresponds to an average lifetime c * tau of 1 km, meaning such a particle would only rarely decay inside a typical detector. Special caution would be needed if coloured resonance particles were made stable, since the program would not necessarily know how to hadronize them, and therefore fail at that stage (see further the R-hadrons description).

In spite of this technical parameter choice, it is possible to set a lifetime for a resonance, and thereby to obtain displaced vertices. If a resonance is allowed to decay it will do so, irrespective of the location of the decay vertex. This is unlike normal particle decays, where it is possible to define some region around the primary vertex within which all decays should happen, with particles leaving that region considered stable. The logic is that resonances as a rule are too short-lived for secondary vertices, so if you pick a scenario with a long-lived but unstable resonance it is because you want to study secondary vertices. How to interface those decays to a detector simulation program then is another story, to be solved separately. Do note that a special treatment is needed for coloured long-lived resonances, that form R-hadrons, and where charge and flavour may change between the production and decay vertices.

Special properties and methods for resonances

The method ParticleData::isResonance(id) allows you to query whether a given particle species is considered a resonance or not. You can also change the default value of this flag in the normal way, e.g. pythia.readString("id:isResonance = true").

Resonances come in two kinds.

Sometimes experimentalists want to modify the physical width of a resonance, to understand how sensitive analyses are to this width, if at all. For the second, simpler kind of resonances, the id:mWidth can be changed right away, but for the first kind any change will be overwritten at initialization. To circumvent this problem, the id:doForceWidth flag can be changed from the default off to on. Then the width stored in id:mWidth is strictly used to describe the Breit-Wigner of the resonance. Partial widths are still recalculated to set the mass-dependent branching ratios, but then uniformly rescaled to the requested total width. The width can also run across the lineshape, so that it deviates from the nominal one in the wings of the Breit-Wigner.

For processes that contain interference terms between resonances, notably gamma^*/Z^0 or gamma^*/Z^0/Z'^0, it is not obvious how these contributions should be modified consistently. Therefore it is necessary to set WeakZ0:gmZmode = 2 or Zprime:gmZmode = 3, to have a pure Z^0 or Z'^0, respectively, for width forcing to be allowed in these cases.

A warning is that the different processes have cross sections that rescale in different ways when the resonance width is varied. This depends on them not having been implemented in a guaranteed uniform way. To illustrate the point, consider the case of an s-channel resonance, where the cross section dependence on the width can be written as
sigmaHat(sHat) = constant * Gamma_in * Gamma_out / ((sHat - m^2)^2 + m^2 * Gamma^2)
Here the doForceWidth = on option ensures that the Gamma in the denominator is rescaled by some factor k relative to the natural width, but does not guarantee that Gamma_in and Gamma_out are rescaled as well. If all three are rescaled by the same factor k, as they should, then the integrated cross section also scales like k, assuming that the peak is reasonably narrow, so that the variation of PDF's across the Breit-Wigner can be neglected. This is the case for some processes. But in others either or both of the production and decay vertices can have been hardcoded, based on the coupling structure, and thus not scale with k. If only Gamma_out scales with k, say, the cross section remains (approximately) constant, and if neither scales the cross section will even go like 1/k. Such obvious normalization imperfections have to be corrected by hand.

Mainly for internal usage, the ParticleData contain some special methods that are only meaningful for resonances:

These methods actually provide an interface to the classes derived from the ResonanceWidths base class, to describe various resonances.

Modes for Matrix Element Processing

The meMode() value for a decay mode is used to specify nonisotropic decays or the conversion of a parton list into a set of hadrons in some channels of normal particles. For resonances it can also take a third function, namely to describe how the branching ratios and widths of a resonance should be rescaled as a function of the current mass of the decaying resonance. The rules are especially useful when new channels are added to an existing particle, or a completely new resonance added.

parm  ResonanceWidths:minThreshold   (default = 0.1; minimum = 0.01)
Used uniquely for meMode = 103 to set the minimal value assumed for the threshold factor, sqrt( (1 - m_1^2/m_2 - m_2^2/m^2)^2 - 4 m_1^2 m_2^2/m^4) for two-body decays and sqrt(1 - Sum_i m_i / m) for multibody ones. Thus the inverse of this number sets an upper limit for how much the partial width of a channel can increase from the on-shell value to the value for asymptotically large resonance masses. Is mainly intended as a safety measure, to avoid unintentionally large rescalings.

All of these meMode's may coexist for the same resonance. This would be the case e.g. if you want to add a few new channels to an already existing resonance, where the old partial widths come hardcoded while the new ones are read in from an external file. The typical example would be an MSSM Higgs sector, where partial widths to SM particles are already encoded, meMode = 0, while decay rates to sparticles are read in from some external calculation and maybe would be best approximated by using meMode = 103. Indeed the default particle table in PYTHIA uses 103 for all channels that are expected to be provided by external input.

Some further clarification may be useful. At initialization the existing total width and on-shell branching ratios will be updated. For channels with meMode < 100 the originally stored branching ratios are irrelevant, since the existing code will anyway be used to calculate the partial widths from scratch. For channels with meMode = 100 or bigger, instead the stored branching ratio is used together with the originally stored total width to define the correct on-shell partial width. The sum of partial widths then gives the new total width, and from there new branching ratios are defined.

In these operations the original sum of branching ratios need not be normalized to unity. For instance, you may at input have a stored total width of 1 GeV and a sum of branching ratios of 2. After initialization the width will then have been changed to 2 GeV and the sum of branching ratios rescaled to unity. This might happen e.g. if you add a few channels to an existing resonance, without changing the branching ratios of the existing channels or the total width of the resonance.

In order to simulate the Breit-Wigner shape correctly, it is important that all channels that contribute to the total width are included in the above operations. This must be kept separate from the issue of which channels you want to have switched on for a particular study, to be considered next.

In the event-generation process, when an off-shell resonance mass has been selected, the width and branching ratios are re-evaluated for this new mass. At this stage also the effects of restrictions on allowed decay modes are taken into account, as set by the onMode switch for each separate decay channel. Thus a channel may be on or off, with different choices of open channels between the particle and its antiparticle. In addition, even when a channel is on, the decay may be into another resonance with its selection of allowed channels. It is these kinds of restrictions that lead to the Gamma_out possibly being smaller than Gamma_tot. As a reminder, the Breit-Wigner for decays behaves like Gamma_out / ((s - m^2)^2 + s * Gamma_tot^2), where the width in the numerator is only to those channels being studied, but the one in the denominator to all channels of the particle. These ever-changing numbers are not directly visible to the user, but are only stored in a work area.

Filter for Resonance Decays

The UserHooks code ResonanceDecayFilterHooks available in include/Pythia8Plugins provides a convenient way to select a specific final state from resonance decays. For example, this could be applied to provide events from top pair production that include leptons + jets. The example main103 demonstrates how to use this user hook. Further documentation on the available settings can by found in the ResonanceDecayFilterHooks.h header file.