Three loop QCD corrections to the heavy-light form factors in the color-planar limit

TL;DR

This paper provides three-loop QCD corrections to heavy-light form factors in the color-planar limit, enhancing precision in top quark and flavor physics predictions by deriving analytic expressions and studying their asymptotic behavior.

Contribution

It presents the first analytic three-loop results for heavy-light form factors in the color-planar limit, including master integrals and Sudakov behavior analysis.

Findings

Analytic expressions for three-loop form factors in terms of harmonic polylogarithms.

Ultraviolet renormalization of all fields and parameters performed.

Insights into the asymptotic Sudakov behavior and higher-loop contributions.

Abstract

We present the analytic expressions for the color-planar contributions to the heavy-light form factors at three loops in perturbative QCD. These form factors play an important role in the precision predictions of various observables in top quark and flavour physics. We compute the master integrals using the method of differential equations. We perform the ultraviolet renormalization for all the appearing fields and parameters. The analytic results for the renormalized form factors are expressed in terms of generalized harmonic polylogarithms. We also study the Sudakov behaviour of these form factors in the asymptotic limit, which enables us to obtain the complete logarithmic three-loop and partial four-loop contributions.