Light Quark Masses 99

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.