Light Quark Masses 99

TL;DR

This paper reviews the historical and current methods for determining light quark masses using QCD sum rules and lattice results, providing world averages and implications for CP violation parameters.

Contribution

It offers a critical review of quark mass determinations from QCD and lattice, proposing a QCD grand average and analyzing implications for CP violation.

Findings

World average for strange quark mass: 110.9±8.8 MeV at 2 GeV

Critical comparison of QCD sum rules and lattice results

Indications of deviation from 1/N predictions in CP-violating parameters

Abstract

I give a short historical and a critical review of the determinations of light quark masses from QCD at dawn of the next millennium. QCD spectral sum rules combined with ChPT give, to order $\alpha_s^3$, the world average for the running masses: $\bar{m}_s$(2 GeV)= $(118.9\pm 12.2)$ MeV, $\bar{m}_d(2~{GeV})=(6.3\pm 0.8)$ MeV, $\bar{m}_u(2~{GeV})=(3.5\pm 0.4)$ MeV and the corresponding values of the invariant masses given in Eq. 24. Lower and upper bounds derived from the positivity of spectral moments are presented in Tables 2 and 3. For a comparison, we critically review the recent lattice results (section 8 and Table 5) and attempt to deduce the present {\it QCD grand average} determination (Table 6): $\bar{m}_s$(2 GeV)= $(110.9\pm 8.8)$ MeV, to be used with a great care. Then, we deduce the value: $B_6^{1/2}-0.45(\rm resp.~0.32)B_8^{3/2}\simeq 1.6\pm 0.4~(\rm resp.~1.1\pm 0.3)$ and the lower bound $1.1\pm 0.2$ (resp. $0.7\pm 0.1$), for the combination of the penguin operators, governing the CP-violating parameters $\epsilon'/\epsilon$ without (resp. with) the inclusion of the final state interaction effects. The result signals a possible deviation from the leading 1/N prediction by about $1\sim 3\sigma$, which should be tested using accurate non-perturbative calculations.