5.9. Hard decays

The handler for decays of particles produced in the hard scattering process (e.g. W, Z, top, Higgs) can be enabled and configured using the HARD_DECAYS collection of settings (and a small number of other other top-level settings). Which (anti)particles IDs should be treated as unstable is determined by the PARTICLE_DATA:<id>:Stable switch described in Models.

The syntax to configure HARD_DECAYS sub-settings is:

HARD_DECAYS:
  <sub-setting>: <value>
  # more sub-settings ...
  Channels:
    "<channel id>":
      <channel sub-setting>: <value>
      # more sub-settings for <channel>
    # more channels ...

The channel ID codes are of the form a -> b c .... The particle IDs for the decay channels can be found in the decay table printed to screen during the run.

This decay module can also be used on top of NLO matrix elements, but it does not include any NLO corrections in the decay matrix elements themselves.

Note that the decay handler is an afterburner at the event generation level. It does not affect the calculation and integration of the hard scattering matrix elements. The cross section is thus unaffected during integration, and the branching ratios (if any decay channels have been disabled) are only taken into account for the event weights and cross section output at the end of event generation (if not disabled with the HARD_DECAYS:Apply_Branching_Ratios option, cf. below). Furthermore any cuts or scale definitions are not affected by decays and operate only on the inclusively produced particles before decays.

5.9.1. Status

This sub-setting to each channel defined in HARD_DECAYS:Channels allows to explicitly force or disable a decay channel. The status can take the following values:

Status: -1

Decay channel is disabled and does not contribute to total width.

Status: 0

Decay channel is disabled but contributes to total width.

Status: 1 (default)

Decay channel is enabled.

Status: 2

Decay channel is forced.

For example, to disable the hadronic decay channels of the W boson one would use:

HARD_DECAYS:
  Channels:
    "24 -> 2 -1":  { Status: 0 }
    "24 -> 4 -3":  { Status: 0 }
    "-24 -> -2 1": { Status: 0 }
    "-24 -> -4 3": { Status: 0 }

In the same way, the bottom decay mode of the Higgs could be forced using:

"25 -> 5 -5":  { Status: 2 }

Note that the ordering of the decay products in <idcode> is important and has to be identical to the ordering in the decay table printed to screen. It is also possible to request multiple forced decay channels (@option{Status: 2}) for the same particle, all other channels will then automatically be disabled.

5.9.2. Width

This option allows to overwrite the calculated partial width (in GeV) of a given decay channel, and even to add new inactive channels which contribute to the total width. This is useful to adjust the branching ratios, which are used for the relative contributions of different channels and also influence the cross section during event generation, as well as the total width which is used for the lineshape of the resonance.

An example to set (/add) the partial widths of the H->ff, H->gg and H->yy channels can be seen in the following. The values have been taken from LHCHXSWG):

PARTICLE_DATA:
  25:
    Mass: 125
    Width: 0.00407

HARD_DECAYS:
  Enabled: true
  Channels:
    "25 -> 5 -5":   { Width: 2.35e-3 }
    "25 -> 15 -15": { Width: 2.57e-4 }
    "25 -> 13 -13": { Width: 8.91e-7 }
    "25 -> 4 -4":   { Width: 1.18e-4 }
    "25 -> 3 -3":   { Width: 1.00e-6 }
    "25 -> 21 21":  { Width: 3.49e-4 }
    "25 -> 22 22":  { Width: 9.28e-6 }

Another example, setting the leptonic and hadronic decay channels of W and Z bosons to the PDG values, would be specified as follows:

HARD_DECAYS:
  Enabled: true
  Channels:
    "24 -> 2 -1":    { Width: 0.7041 }
    "24 -> 4 -3":    { Width: 0.7041 }
    "24 -> 12 -11":  { Width: 0.2256 }
    "24 -> 14 -13":  { Width: 0.2256 }
    "24 -> 16 -15":  { Width: 0.2256 }
    "-24 -> -2 1":   { Width: 0.7041 }
    "-24 -> -4 3":   { Width: 0.7041 }
    "-24 -> -12 11": { Width: 0.2256 }
    "-24 -> -14 13": { Width: 0.2256 }
    "-24 -> -16 15": { Width: 0.2256 }
    "23 -> 1 -1":    { Width: 0.3828 }
    "23 -> 2 -2":    { Width: 0.2980 }
    "23 -> 3 -3":    { Width: 0.3828 }
    "23 -> 4 -4":    { Width: 0.2980 }
    "23 -> 5 -5":    { Width: 0.3828 }
    "23 -> 11 -11":  { Width: 0.0840 }
    "23 -> 12 -12":  { Width: 0.1663 }
    "23 -> 13 -13":  { Width: 0.0840 }
    "23 -> 14 -14":  { Width: 0.1663 }
    "23 -> 15 -15":  { Width: 0.0840 }
    "23 -> 16 -16":  { Width: 0.1663 }

5.9.3. HARD_SPIN_CORRELATIONS

Spin correlations between the hard scattering process and the following decay processes are enabled by default. If you want to disable them, e.g. for spin correlation studies, you can specify the option HARD_SPIN_CORRELATIONS: 0. This is a top-level setting as opposed to the other HARD_DECAYS-related settings.

5.9.4. Store_Results

The decay table and partial widths are calculated on-the-fly during the initialization phase of Sherpa from the given model and its particles and interaction vertices. To store these results in the Results/Decays directory, one has to specify HARD_DECAYS: { Store_Results: 1 }. In case existing decay tables are to be read in the same configuration should be done. Please note, that Sherpa will delete decay channels present in the read in results but not in the present model with present parameters by default. To prevent Sherpa from updating the decay table files accordingly specify HARD_DECAYS: { Store_Results: 2 }.

5.9.5. Result_Directory

Specifies the name of the directory where the decay results are to be stored. Defaults to the value of the top-level setting RESULT_DIRECTORY.

5.9.6. Set_Widths

The decay handler computes LO partial and total decay widths and generates decays with corresponding branching fractions, independently from the particle widths specified by PARTICLE_DATA:<id>:Width. The latter are relevant only for the core process and should be set to zero for all unstable particles appearing in the core-process final state. This guarantees on-shellness and gauge invariance of the core process, and subsequent decays can be handled by the afterburner. In constrast, PARTICLE_DATA:<id>:Width should be set to the physical width when unstable particles appear (only) as intermediate states in the core process, i.e. when production and decay are handled as a full process or using Decay/DecayOS. In this case, the option HARD_DECAYS: { Set_Widths: true } permits to overwrite the PARTICLE_DATA:<id>:Width values of unstable particles by the LO widths computed by the decay handler.

5.9.7. Apply_Branching_Ratios

By default (HARD_DECAYS: { Apply_Branching_Ratios: true }), weights for events which involve a hard decay are multiplied with the corresponding branching ratios (if decay channels have been disabled). This also means that the total cross section at the end of the event generation run already includes the appropriate BR factors. If you want to disable that, e.g. because you want to multiply with your own modified BR, you can set the option {HARD_DECAYS: { Apply_Branching_Ratios: false }.

5.9.8. Mass_Smearing

With the default of HARD_DECAYS: { Mass_Smearing: 1 } the kinematic mass of the unstable propagator is distributed according to a Breit-Wigner shape a posteriori. All matrix elements are still calculated in the narrow-width approximation with onshell particles. Only the kinematics are affected. To keep all intermediate particles onshell {HARD_DECAYS: { Mass_Smearing: 0 }.

5.9.9. Resolve_Decays

There are different options how to decide when a 1->2 process should be replaced by the respective 1->3 processes built from its decaying daughter particles.

Resolve_Decays: Threshold

(default) Only when the sum of decay product masses exceeds the decayer mass.

Resolve_Decays: ByWidth

As soon as the sum of 1->3 partial widths exceeds the 1->2 partial width.

Resolve_Decays: None

No 1->3 decays are taken into account.

In all cases, one can exclude the replacement of a particle below a given width threshold using Min_Prop_Width: (default 0.0). Both settings are sub-settings of HARD_DECAYS:

HARD_DECAYS:
  Resolve_Decays: <mode>
  Min_Prop_Width: <threshold>

5.9.10. Decay_Tau

By default, the tau lepton is decayed by the hadron decay module, Hadron decays, which includes not only the leptonic decay channels but also the hadronic modes. If Decay_Tau: true is specified, the tau lepton will be decayed in the hard decay handler, which only takes leptonic and partonic decay modes into account. Note, that in this case the tau needs to also be set massive:

PARTICLE_DATA:
  15:
    Massive: true
HARD_DECAYS:
  Decay_Tau: true

5.9.11. Decay table integration settings

Three parameters can be used to steer the accuracy and time consumption of the calculation of the partial widths in the decay table: Int_Accuracy: 0.01 specifies a relative accuracy for the integration. The corresponding target reference is either the given total width of the decaying particle (Int_Target_Mode: 0, default) or the calculated partial decay width (Int_Target_Mode: 1). The option Int_NIter: 2500 can be used to change the number of points per integration iteration, and thus also the minimal number of points to be used in an integration. All decay table integration settings are sub-settings of HARD_DECAYS.