Low energy moments of heavy quark current correlators at four loops

TL;DR

This paper introduces advanced techniques for calculating multi-loop integrals and applies them to compute four-loop corrections to heavy quark current correlators, aiding precise determinations of quark masses and the strong coupling constant.

Contribution

It presents the first four-loop corrections to low-energy moments of heavy quark current correlators, enhancing theoretical precision in quark mass and coupling constant determinations.

Findings

Four-loop corrections to second and third moments of correlators.

Third and fourth moments for pseudo-scalar correlator derived via Ward identity.

Implications for charm quark mass and strong coupling constant measurements.

Abstract

We describe several techniques for the calculation of multi-loop integrals and their application to heavy quark current correlators. As new results, we present the four-loop correction to the second and third physical moment in the low-energy expansions of vector, axial-vector and scalar quark current correlators. Using a Ward identity, we obtain the third and fourth moment for the pseudo-scalar correlator. We briefly discuss the impact of these results on the determination of the charm quark mass and the strong coupling constant using lattice simulations for the current correlators and of the charm- and bottom-quark mass from experimental data for \sigma(e^+ e^- -> hadrons).