Setting coupling orders in MadGraph5_aMC@NLO

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• Example: generate p p > t t~ e+ e- QED<=4 QCD=0
• The QED=X and QCD=Y orders correspond to the powers of the electroweak/yukawa coupling (e, g, g′, y, etc) and the strong coupling constant (g-strong), respectively, at the diagram level (i.e., amplitude level, not amplitude-squared level).
• If no coupling orders are given, MG5 will try to determine orders to ensure maximum number of QCD vertices.
• Allowed coupling operators are: "==", "=", "<=" and ">". The difference between "==" and "=" is that the former imposes exactly that number of couplings, while "=" is interpreted as "<=".
• Desired coupling order combinations can be specified directly for the amplitude-squared by appending "^2" to the coupling name. For example, "p p > j j QED^2==2 QCD^2==2" selects the QED-QCD interference terms only. The other operators, "=", "<=" and ">", are also supported.
• In order to facilitate the use of couplings at the amplitude-squared level, one can also use "aS=X" and "aEW=Y" to determine the maximum power of alpha-S and alpha-EW to appear at the amplitude-squared level. (These are interpreted as "QCD^2=2X" and "QED^2=2Y" by the MG5_aMC interface, respectively).
• In general, restricting couplings at the diagram level is not consistent for NLO processes. It is strongly advised to use the "aS=X" and "aEW=Y" sytnax to set the restriction on the powers of alpha-S and alpha-EW at the amplitude-squared level. (The main exception to this rule would be to restrict the number of higher-dimensional interactions appearing in EFT models).

Comments regarding The automation of next-to-leading order electroweak calculations, arXiv:1804.10017

• The syntax used in that paper is no longer compatible with the current version of the MadGraph5_aMC@NLO code (>v3.1). In the paper, all the coupling orders had been understood at the amplitude-squared level, while, if the same syntax used in 1804.10017 were employed literally with the current version of the code, they would been applied at the diagram level. This obsolete syntax was only used in the v3.0.X beta versions of the code.
• In the whole paper, for all the process's syntax, all the instances of QCD=X and QED=Y need to replaced by aS=X and aEW=Y, respectively, to make them compatible with the v3.1 syntax.