Low- and High-Energy Expansion of Heavy-Quark Correlators at Next-To-Next-To-Leading Order

TL;DR

This paper computes three-loop corrections to heavy-quark current correlators in low- and high-energy regimes, providing extensive coefficients to enhance lattice QCD quark-mass determinations and correlator reconstructions.

Contribution

It presents the first comprehensive calculation of 60 expansion coefficients for various heavy-quark correlators at three-loop order, covering both diagonal and non-diagonal flavor structures.

Findings

Calculated 30 coefficients for low-energy scalar and vector correlators.

Computed 30 coefficients for high-energy diagonal correlators.

Results enable improved quark-mass determinations and correlator reconstructions.

Abstract

We calculate three-loop corrections to correlation functions of heavy-quark currents in the low- and high-energy regions. We present 30 coefficients both in the low-energy and the high-energy expansion of the scalar and the vector correlator with non-diagonal flavour structure. In addition we compute 30 coefficients in the high-energy expansion of the diagonal vector, axial-vector, scalar and pseudo-scalar correlators. Possible applications of our new results are improvements of lattice-based quark-mass determinations and the approximate reconstruction of the full momentum dependence of the correlators.