Strange quark condensate from QCD sum rules to five loops

TL;DR

This paper uses advanced QCD sum rules with polynomial kernels to accurately determine the ratio of strange to non-strange quark condensates, providing bounds on the strange quark mass with reduced systematic uncertainties.

Contribution

It introduces a new set of QCD Finite Energy Sum Rules with polynomial kernels to improve the precision of quark condensate ratio and strange quark mass estimates.

Findings

Established an upper bound on the strange quark mass: 121 MeV at 2 GeV.

Reduced systematic uncertainties in spectral function integration.

Provided a more reliable determination of the quark condensate ratio.

Abstract

It is argued that it is valid to use QCD sum rules to determine the scalar and pseudoscalar two-point functions at zero momentum, which in turn determine the ratio of the strange to non-strange quark condensates $R_{su} = \frac{<\bar{s} s>}{<\bar{q} q>}$ with ($q=u,d$). This is done in the framework of a new set of QCD Finite Energy Sum Rules (FESR) that involve as integration kernel a second degree polynomial, tuned to reduce considerably the systematic uncertainties in the hadronic spectral functions. As a result, the parameters limiting the precision of this determination are $\Lambda_{QCD}$, and to a major extent the strange quark mass. From the positivity of $R_{su}$ there follows an upper bound on the latter: $\bar{m_{s}} (2 {GeV}) \leq 121 (105) {MeV}$, for $\Lambda_{QCD} = 330 (420) {MeV} .$