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 α s 3, the world average for the running masses: m s (2 GeV) = (118.9 ± 12.2) MeV, m d (2 GeV = 6.3 ± 0.8) MeV, m u (2 GeV) = (3.5 ± 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 QCD grand average determination (Table 6): m s(2 GeV) = (110.9 ± 8.8) MeV , to be used with a great care. Then, we deduce the value: B 6 1 2 −0.45( resp.0.32) B 8 3 2 ⋍ 1.6±0.4 (resp. 1.1±0.3) and the lower bound 1.1±0.2 (resp. 0.7±0.1), for the combination of the penguin operators, governing the CP-violating parameters ϵ ′ ϵ 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 ∼ 3σ, which should be tested using accurate non-perturbative calculations.