Moments of Heavy Quark Current Correlators at Four-Loop Order in Perturbative QCD
Christian Sturm
TL;DR
This work computes the lowest moments of heavy-quark current correlators at four-loop order in perturbative QCD, focusing on the first moment of the scalar and axial-vector currents and providing detailed results for the pseudo-scalar case. A robust computational pipeline—diagram generation with QGRAF, IBP/Laporta reduction to master integrals, and algebraic evaluation with FORM—yields the low-energy expansions and four-loop coefficients, including explicit dependence on the numbers of light and heavy quark flavors. Analytic results are presented for the scalar and axial-vector first moments, with comprehensive numerical coefficients for all currents and complete analytic expressions for the pseudo-scalar case, all in the MS-bar scheme. These results reduce theoretical uncertainties in the determination of α_s and charm-quark mass from lattice QCD and establish a foundation for extending to higher moments.
Abstract
We present the result for the first moment of the scalar and axial-vector current correlator in third order of the strong coupling constant alpha_s and give the details of a recent evaluation of the pseudo-scalar correlator. The results can be used to reduce the theoretical uncertainty due to higher order corrections for the determination of fundamental parameters of QCD in the context of lattice calculations.