5.15. QED corrections¶

Higher order QED corrections are effected both on hard interaction and, upon their formation, on each hadron’s subsequent decay. The Photons [SK08a] module is called in both cases for this task. It employes a YFS-type resummation [YFS61] of all infrared singular terms to all orders and is equipped with complete first order corrections for the most relevant cases (all other ones receive approximate real emission corrections built up by Catani-Seymour splitting kernels). The module is also equipped with an algorithm to allow any photons produced to split into charged particle pairs.

5.15.1. General Switches ¶

The relevant switches to steer the higher order QED corrections are collected in the YFS settings group and are modified like this:

YFS:
  <option1>: <value1>
  <option2>: <value2>
  ...

The options are

5.15.1.1. MODE ¶

The keyword MODE determines the mode of operation of Photons. MODE: None switches Photons off. Consequently, neither the hard interaction nor any hadron decay will be corrected for soft or hard photon emission. MODE: Soft sets the mode to “soft only”, meaning soft emissions will be treated correctly to all orders but no hard emission corrections will be included. With MODE: Full these hard emission corrections will also be included up to first order in alpha_QED. This is the default setting.

5.15.1.2. USE_ME ¶

The switch USE_ME tells Photons how to correct hard emissions to first order in alpha_QED. If USE_ME: 0, then Photons will use collinearly approximated real emission matrix elements. Virtual emission matrix elements of order alpha_QED are ignored. If, however, YFS_USE_ME=1, then exact real and/or virtual emission matrix elements are used wherever possible. These are presently available for V->FF, V->SS, S->FF, S->SS, S->Slnu, S->Vlnu type decays, Z->FF decays and leptonic tau and W decays. For all other decay types general collinearly approximated matrix elements are used. In both approaches all hadrons are treated as point-like objects. The default setting is USE_ME: 1. This switch is only effective if MODE: Full.

5.15.1.3. IR_CUTOFF ¶

IR_CUTOFF sets the infrared cut-off dividing the real emission in two regions, one containing the infrared divergence, the other the “hard” emissions. This cut-off is currently applied in the rest frame of the multipole of the respective decay. It also serves as a minimum photon energy in this frame for explicit photon generation for the event record. In contrast, all photons below with energy less than this cut-off will be assumed to have negligible impact on the final-state momentum distributions. The default is IR_CUTOFF: 1E-3 (GeV). Of course, this switch is only effective if Photons is switched on, i.e. MODE is not set to None.

5.15.1.4. PHOTON_SPLITTER_MODE ¶

The parameter PHOTON_SPLITTER_MODE determines which particles, if any, may be produced in photon splittings:

0
All photon splitting functions are turned off.

1
Photons may split into electron-positron pairs;

2
muons;

4
tau leptons;

8
light hadrons up to PHOTON_SPLITTER_MAX_HADMASS.

The settings are additive, e.g. PHOTON_SPLITTER_MODE: 3 allows splittings into electron-positron and muon-antimuon pairs. The default is PHOTON_SPLITTER_MODE: 15 (all splittings turned on). This parameter is of course only effective if the Photons module is switched on using the MODE keyword.

5.15.1.5. PHOTON_SPLITTER_MAX_HADMASS ¶

PHOTON_SPLITTER_MAX_HADMASS sets the mass (in GeV) of the heaviest hadron which may be produced in photon splittings. Note that vector splitting functions are currently not implemented: only fermions, scalars and pseudoscalars up to this cutoff will be considered. The default is 0.5 GeV.

5.15.2. QED Corrections to the Hard Interaction ¶

The switches to steer QED corrections to the hard scattering are collected in the ME_QED settings group and are modified like this:

ME_QED:
  <option1>: <value1>
  <option2>: <value2>
  ...

The following options can be customised:

5.15.2.1. ENABLED ¶

ENABLED: false turns the higher order QED corrections to the matrix element off. The default is true. Switching QED corrections to the matrix element off has no effect on QED Corrections to Hadron Decays. The QED corrections to the matrix element will only be effected on final state not strongly interacting particles. If a resonant production subprocess for an unambiguous subset of all such particles is specified via the process declaration (cf. Processes) this can be taken into account and dedicated higher order matrix elements can be used (if YFS: { MODE: Full, USE_ME: 1 }).

5.15.2.2. CLUSTERING_ENABLED ¶

CLUSTERING_ENABLED: false switches the phase space point dependent identification of possible resonances within the hard matrix element on or off, respectively. The default is true. Resonances are identified by recombining the electroweak final state of the matrix element into resonances that are allowed by the model. Competing resonances are identified by their on-shell-ness, i.e. the distance of the decay product’s invariant mass from the nominal resonance mass in units of the resonance width.

5.15.2.3. CLUSTERING_THRESHOLD ¶

Sets the maximal distance of the decay product invariant mass from the nominal resonance mass in units of the resonance width in order for the resonance to be identified. The default is CLUSTERING_THRESHOLD: 10.0.

5.15.3. QED Corrections to Hadron Decays ¶

If the Photons module is switched on, all hadron decays are corrected for higher order QED effects.

5.15.4. QED Corrections for Lepton-Lepton Collisions ¶

The YFS resummation can be enabled for lepton-lepton scattering by setting MODE to ISR.

The options are

5.15.4.1. BETA ¶

Higher order matrix element corrections can be included by setting BETA to either 1/2 to the desired order of accuray. For example BETA: 0 disables all higer-order corrections:cite:Jadach:2000ir

5.15.4.2. COULOMB ¶

The Coulomb threshold corrections [BBD93] [FKM93] to the \(W^+W^-\) threshold can be included with COULOMB: True. Double counting of the virtual corrections with the YFS form-factor is avoided by using analytical subtraction in the threshold limit [KPSchonherr22].