Light quark masses from QCD sum rules with minimal hadronic bias

TL;DR

This paper introduces a novel QCD sum rule method with an integration kernel to accurately determine light quark masses, significantly reducing hadronic spectral function uncertainties and providing precise values at 2 GeV.

Contribution

A new QCD Finite Energy Sum Rule with an integration kernel minimizes hadronic bias, improving the accuracy of light quark mass determinations from QCD sum rules.

Findings

Quark masses at 2 GeV: mu=2.9 MeV, md=5.3 MeV, ms=102 MeV.

Systematic uncertainty from unmeasured spectral functions is below 3%.

Results are consistent with previous estimates and can be refined further.

Abstract

The light quark masses are determined using a new QCD Finite Energy Sum Rule (FESR) in the pseudoscalar channel. This FESR involves an integration kernel designed to reduce considerably the contribution of the (unmeasured) hadronic resonance spectral functions. The QCD sector of the FESR includes perturbative QCD (PQCD) to five loop order, and the leading non-perturbative terms. In the hadronic sector the dominant contribution is from the pseudoscalar meson pole. Using Contour Improved Perturbation Theory (CIPT) the results for the quark masses at a scale of 2 GeV are $m_u(Q= 2 {GeV}) = 2.9 \pm 0.2 {MeV}$, $m_d(Q= 2 {GeV}) = 5.3 \pm 0.4 {MeV}$, and $m_s(Q= 2 {GeV}) = 102 \pm 8 {MeV}$, for $\Lambda = 381 \pm 16 {MeV}$, corresponding to $\alpha_s(M_\tau^2) = 0.344 \pm0.009$. In this framework the systematic uncertainty in the quark masses from the unmeasured hadronic resonance spectral function amounts to less than 2 - 3 %. The remaining uncertainties above arise from those in $\Lambda$, the unknown six-loop PQCD contribution, and the gluon condensate, which are all potentially subject to improvement.