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, ${\bar{m}}_d(2GeV)=(6.3\pm 0.8)$ MeV, ${\bar{m}}_u(2GeV)=(3.5\pm 0.4)$ 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: $B_6^{1/2}-0.45(resp.0.32){\mathrm{B}}_8^{3/2}\simeq 1.6\pm 0.4(resp.1.1\pm 0.3)$ 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 ${\epsilon }^{\prime }/\epsilon$ 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.

Latex2e two-column 13 pages 5 Tables + 1 figure. Review talk given at QCD 99 (Montpellier 7-13th July 1999) and plenary talk at QCD Confinement 2000 (Osaka 7-10th March 2000) Report-n0: Montpellier preprint PM/99-50. Updated version and application to epsilon'/epsilon

References in corpus (3)

• Profiles of the Unitarity Triangle and CP-Violating Phases in the Standard Model and Supersymmetric Theories
• Strange-quark mass from combined e+e- and tau-decay data:test of the isospin symmetry and implications on epsilon'/εand m_{u,d}
• The Strange Quark Mass From Finite Energy Sum Rules

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