SmeftFR – Feynman rules generator for the Standard Model Effective Field Theory

Abstract

We present SmeftFR, a Mathematica package designed to generate the Feynman rules for the Standard Model Effective Field Theory (SMEFT) including the complete set of gauge invariant operators up to dimension 6. Feynman rules are generated with the use of FeynRules package, directly in the physical (mass eigenstates) basis for all fields. The complete set of interaction vertices can be derived including all or any chosen subset of SMEFT operators. As an option, the user can also choose preferred gauge fixing, generating Feynman rules in unitary or Rξ-gauges (the latter include generation of ghost vertices). Further options allow to treat neutrino fields as massless Weyl or massive Majorana fermions. The derived Lagrangian in the mass basis can be exported in various formats supported by FeynRules, such as UFO and FeynArts. Initialisation of numerical values of d=6 Wilson coefficients used by SmeftFR is interfaced to WCxf format. The package also includes dedicated Latex generator allowing to print the result in clear human-readable form. SmeftFR can be downloaded from the address www.fuw.edu.pl/smeft. Program summaryProgram Title:SmeftFR v2.0Program Files doi:http://dx.doi.org/10.17632/yyv9fpmwzv.1Licensing provisions: GPLv3Programming language: Mathematica 11.3 or later (earlier versions were reported to have problems running this code).Nature of problem: Standard Model Effective Field Theory (SMEFT) has become in recent years a commonly used model to parameterise the potential effects of New Physics. Calculation of physical observables within such a complicated theory requires large degree of automatisation, starting from the generation of Feynman rules in various formats, which could be further imported to Monte Carlo generators or symbolic packages calculating transition amplitudes. SmeftFR package generates such Feynman rules for SMEFT in physical (mass) field basis for the user defined subset of dimension 5 and 6 operators, in unitary or linear Rξ-gauges.Solution method: Implementation (as the Mathematica package) of the results of Ref. [1]. SmeftFR generates dynamically “model files” for the FeynRules package [2], based on user-defined set of options — most important are SMEFT operators subset, gauge fixing choice and numerical input for Wilson coefficients in the WCxf format [3]. Subsequently FeynRules engine is used to calculate SMEFT Feynman rules, which can be later manipulated or exported in several formats, such as UFO, FeynArts, Latex, WCxf and others, by SmeftFR auxiliary routines.Additional comments: Running the code requires prior installation of the FeynRules package [2], https://feynrules.irmp.ucl.ac.be.[1] A. Dedes, W. Materkowska, M. Paraskevas, J. Rosiek and K. Suxho, “Feynman rules for the Standard Model Effective Field Theory in Rξ-gauges,” JHEP 1706, 143 (2017).[2] A. Alloul, N. D. Christensen, C. Degrande, C. Duhr and B. Fuks, “FeynRules 2.0 - A complete toolbox for tree-level phenomenology,” Comput. Phys. Commun. 185, 2250 (2014).[3] J. Aebischer, et al., WCxf: an exchange format for Wilson coefficients beyond the Standard Model, Comput. Phys. Commun. 232 (2018) 71–83.