Moments of heavy quark correlators with two masses: exact mass dependence to three loops

TL;DR

This paper calculates three-loop moments of heavy quark correlators with two different masses, providing exact mass dependence and useful results for electroweak parameters, applicable to scenarios with arbitrary quark masses.

Contribution

It presents the first exact three-loop calculations of non-diagonal heavy quark correlator moments with two masses without mass ratio restrictions.

Findings

Explicit three-loop results for two-mass correlator moments.

Analytical and numerical methods for two-scale master integrals.

Results applicable to electroweak $ ho$ parameter with arbitrary quark masses.

Abstract

We compute moments of non-diagonal correlators with two massive quarks. Results are obtained where no restriction on the ratio of the masses is assumed. Both analytical and numerical methods are applied in order to evaluate the two-scale master integrals at three loops. We provide explicit results for the latter which are useful for other calculations. As a by-product we obtain results for the electroweak $\rho$ parameter up to three loops which can be applied to a fourth generation of quarks with arbitrary masses.