5.13. 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).

5.13.1. 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

5.13.1.1. 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.

5.13.1.2. 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.

5.13.1.3. 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.

5.13.2. 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:

5.13.2.1. 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 }).

5.13.2.2. 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.

5.13.2.3. 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.

5.13.3. QED Corrections to Hadron Decays

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

5.13.4. NNLO QED and NLO EW Corrections

The inclusion of NNLO QED and NLO EW ME corrections can be applied to leptonically decaying bosons with the YFS framework [KLLS19]. By default, these corrections are disabled and they can be enable during configuration with --enable-yfsnnlo. The NNLO QED corrections can be included with the switch YFS:NNLO_QED: 1. The NLO EW can be included by setting EW_CORRECTIONS: 1.