A numerical routine for the crossed vertex diagram with a massive-particle loop

Abstract

We present an evaluation of the two master integrals for the crossed vertex diagram with a closed loop of top quarks that allows for an easy numerical implementation. The differential equations obeyed by the master integrals are used to generate power series expansions centered around all the singular points. The different series are then matched numerically with high accuracy in intermediate points. The expansions allow a fast and precise numerical calculation of the two master integrals in all the regions of the phase space. A numerical routine that implements these expansions is presented. Program summaryProgram Title: ellipticProgram Files doi:http://dx.doi.org/10.17632/kybzy5d84t.1Licensing provisions: CC By 4.0Programming language: Fortran77Nature of problem: Numerical computation of the two master integrals for the crossed ladder vertex diagram with massive loop at two-loop level.Solution method: Power series expansions around singular and regular points for positive and negative values in x=−S∕m2, with m denoting the massive state in the loop and S the Madelstam invariant. The different series expansions are matched numerically.