Electroweak two-loop corrections to sin^2{\theta}(eff,bb) and R(b) using numerical Mellin-Barnes integrals

TL;DR

This paper applies numerical Mellin-Barnes integrals to compute electroweak two-loop corrections for key Z boson observables, providing new results for R(b) and confirming previous findings for sin^2{ heta}(eff,bb).

Contribution

It introduces a numerical Mellin-Barnes method for calculating electroweak two-loop corrections, including a new result for R(b) and a parametrization formula.

Findings

Good agreement with previous sin^2{ heta}(eff,bb) results

New calculation of R(b) with a simple approximation formula

Demonstrates effectiveness of Mellin-Barnes integrals for multi-loop electroweak corrections

Abstract

Multi-loop integrals can be evaluated numerically using Mellin-Barnes representations. Here this technique is applied to the calculation of electroweak two-loop correction with closed fermion loops for two observables: the effective weak mixing angle for bottom quarks, sin^2{\theta}(eff,bb), and the branching ratio of the Z boson into bottom quarks, R(b). Good agreement with a previous result for sin^2{\theta}(eff,bb) is found. The result for R(b) is new, and a simple parametrization formula is provided which approximates the full result within integration errors.