How to use the new functionalities of v3.5.0 for lepton collisions at NLO EW

This FAQ provides some guidance for the calculation of NLO EW corrections for processes at lepton colliders, which have been documented in https://arxiv.org/abs/2207.03265 .
As for the hadron-collider case, NLO EW corrections can be computed at fixed-order only, so no event-generation is possible.

The user should first install the code eMELA (https://github.com/gstagnit/eMELA/releases), which is a provider for leptonic parton densities.
The following flags should be provided to the cmake command (in addition to the one specifying the installation prefix)
-DSHARED=OFF -DWITH_LHAPDF=ON
(this assumes that a valid installation of LHAPDF6 is available on the system, and the PATH/LIBRARY_PATH/... variables are updated accordingly).

The path to emela_config (in the bin directory of the eMELA installation) should be made known to MG5_aMC, either editing input/mg5_configuration.txt before generating any process or inside Cards/amcatnlo_configuration.txt in the generated process folder

The syntax for process generation is the usual one (see the case with initial photons below for some caveats), e.g.
generate e+ e- > w+ w- [QED]
for W pair production.

The LHAID of the chosen PDF set can be specified in the run_card, by setting
pdlabel = emela
and
lhaid = LHAID

Furthermore, to tell the code that electron densities must be used, the variables lpp1, lpp2 must be set t -3, 3 respectively.

The user should not worry about the variable pdfscheme, as, when using eMELA, it is set automatically in a consistent manner with the chosen PDF.

- LIMITATIONS
At the moment the only limitation for EW corrections at lepton colliders is that the chosen process must not proceed via a resonating, pure s-channel (e.g. e+ e- > hadrons, or e+ e- > mu+ mu- with energy such that the Z resonance can be probed).
Such a limitation is due to the need for a specific phase-space mapping to deal with this case, which will be implemented in the future.
When the s-channel is not resonating (e.g. e+ e- > H Z) this limitation does not apply.

- RENORMALISATION SCHEMES AND MODEL
PDFs come in 3 different renormalization schemes: MSbar (with alpha running), alpha(MZ), and Gmu. For the second and the third scheme, the process must be generated with the corresponding model (loop_qcd_qed_sm and loop_qcd_qed_sm_Gmu, respectively). The code should raise an error if the wrong model is loaded, but we urge the user to pay attention to this.
For the MSbar renormalisation scheme, the model in the alpha(MZ) scheme should be used to generate the process.
The code will take care automatically to add an extra bit to the virtual amplitude to compensate for the difference in the finite part of the UV counterterm. However, the value of alpha entering the result is still the one from alpha(MZ). The user should then reweight separately the LO and NLO parts of the correction with the correct power of alpha. In general, we do not encourage the usage of such a scheme.

- FACTORISATION SCHEMES
The factorisation scheme of the chosen PDF set (LL-Running, NLL-MSbar or NLL-Delta) is communicated automatically to the code. Hence, nothing specific should be done by the user.

- BEAMSTRAHLUNG
At the moment, beamstrahlung is included only in the sets
137010 NLL_DELTA_MSBAR_ILC500
137011 NLL_DELTA_ALPMZ_ILC500
137012 NLL_DELTA_ALGMU_ILC500
137013 LL_MSBAR_ILC500
and it is modeled according to the ILC specifications at 500 GeV center-of-mass energy. The presence of beamstrahlung in a PDF set is detected automatically by the code.

- INITIAL-STATE PHOTONS
The PDFs provided by eMELA have a non-zero photonic density (and in principle also a non-zero contributions for other fermions, such as e-/quarks in e+, but these are set to zero in MG5_aMC) , whose impact is process- and configuration- (energy, cuts, ...) dependent.
A run_card variable (photons_from_leptons) controls whether their contributions must be retained (True) or discarded (False).
In the case the user's choice is to include the photon contribution, in order to ensure proper cancelation of IR divergencies, photons should be included also in the process definition, e.g. in the following way:

define ep = e+ a
define em = e- a

generate ep em > w+ w- [QED]

Given that the complexity of the final state significantly increases, the user should pay special attention in designing a set of IR-safe cuts and observables.