The second physical moment of the heavy quark vector correlator at O(alpha_s^3)

TL;DR

This work delivers the second moment of the heavy-quark vector correlator at four-loop order ($O(\alpha_s^3)$), including singlet contributions, to refine charm and bottom mass extractions from QCD sum rules. Using advanced multi-loop techniques, it provides the analytic structure and numerical values of the four-loop coefficient across flavor/color sectors, and demonstrates a small but meaningful shift in extracted quark masses with a markedly reduced perturbative uncertainty. The results are consistent with earlier first-moment analyses and help optimize the choice of moments for precise mass determinations, particularly favoring higher moments for the bottom quark and confirming reliability for the charm quark with the second moment. Overall, the study strengthens the theoretical foundation for quark-mass extractions from low-energy expansions of heavy-quark vector correlators.

Abstract

The second moment of the heavy quark vector correlator at O(alpha_s^3) is presented. The implications of this result on recent determinations of the charm and bottom quark mass are discussed.