TARCER — A mathematica program for the reduction of two-loop propagator integrals

Abstract

TARCER is an implementation of the recurrence algorithm of O.V. Tarasov for the reduction of two-loop propagator integrals with arbitrary masses to a small set of basis integrals. The tensor integral reduction scheme is adapted to moment integrals emerging in operator matrix element calculations.

Investigating the near-criticality of the Higgs boson

“…using the code Tarcer [105] that uses the Tarasov's algorithm [106] and it is now part of the Feyncalc [107] package. In order to extract the V W and B W terms in ∆r 0 from the relevant diagrams we used the projector presented in ref.…”

Two-loop contributions of the order O α t α s $$ \mathcal{O}\left({\alpha}_t{\alpha}_s\right) $$ to the masses of the Higgs bosons in the CP-violating NMSSM

“…The contraction of the Dirac and γ 5 matrices was done with FeynCalc [100]. The reduction to master integrals was performed using the program TARCER [101], which is based on a reduction algorithm proposed by Tarasov [102,103] and which is included in FeynCalc. Additional checks of the calculation of the self-energy diagrams have been carried out applying in-house mathematica routines for the evaluation of scalar self-energy diagrams but also using the programs OneCalc and TwoCalc [80,104] for the contraction of Dirac matrices, the evaluation of Dirac traces and the tensor reduction of the integrals in combination with the package FeynArts for the amplitude generation.…”

The m W − m Z interdependence in the Standard Model: a new scrutiny

“…All the diagrams entering the calculation ofα(m Z ), ∆r W ,ρ were generated using the Mathematica package Feynarts [45]. The reduction of the two-loop diagrams to scalar integrals was done using the code Tarcer [46] which uses the algorithm by Tarasov [47] and is now part of the Feyncalc [48] package. In order to extract the vertex and box contributions in ∆r W from the relevant diagrams, we used the projector presented in ref.…”