Strange quark mass from e{sup +}e{sup -} revisited and present status of light quark masses
- Laboratoire de Physique Theorique et Astrophysiques, CNRS and Universite de Montpellier II, Place Eugene Bataillon 34095-Montpellier Cedex 05 (France)
We reconsider the determinations of the strange quark mass m{sub s} from e{sup +}e{sup -} into hadrons data using a new combination of finite energy sum rules (FESR) and revisiting the existing {tau}-like sum rules by including nonresonant contributions to the spectral functions. To order {alpha}{sub s}{sup 3} and including the tachyonic gluon mass {lambda}{sup 2} contribution, which phenomenologically parametrizes the UV renormalon effect into the perturbative series, we obtain the invariant mass m-circumflex{sub s}=(119{+-}17) MeV leading to m{sub s}(2 GeV)=(104{+-}15) MeV. Combining this value with the recent and independent phenomenological determinations from some other channels, to order {alpha}{sub s}{sup 3} and including {lambda}{sup 2}, we deduce the weighted average m{sub s}(2 GeV)=(96.1{+-}4.8) MeV. The positivity of the spectral functions in the (pseudo)scalar (resp. vector) channels leads to the lower (resp. upper) bounds of m{sub s}(2 GeV): (71{+-}4) MeV{<=}m{sub s}(2 GeV){<=}(151{+-}14) MeV, to order {alpha}{sub s}{sup 3}. Using the chiral perturbation theory (ChPT) mass ratio r{sub 3}{identical_to}2m{sub s}/(m{sub u}+m{sub d})=24.2{+-}1.5, and the average value of m{sub s}, we deduce (m{sub u}+m{sub d})(2 GeV)=(7.9{+-}0.6) MeV, consistent with the pion sum rule result, which, combined with the ChPT value for m{sub u}/m{sub d}, gives m{sub d}(2 GeV)=(5.1{+-}0.4) MeV and m{sub u}(2 GeV)=(2.8{+-}0.2) MeV. Finally, using (m{sub u}+m{sub d}) from the pion sum rule and the average value of m{sub s} (without the pion sum rule), the method gives r{sub 3}=23.5{+-}5.8, in perfect agreement with the ChPT ratio, indicating the self-consistency of the sum rule results. Using the value m{sub b}(m{sub b})=(4.23{+-}0.06) GeV, we also obtain the scale-independent mass ratio m{sub b}/m{sub s}=50{+-}3, which is useful for model-buildings. Absolute values of the light quark masses from QCD spectral sum rules reported in this paper are the most accurate determinations to date.
- OSTI ID:
- 20869245
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 74, Issue 3; Other Information: DOI: 10.1103/PhysRevD.74.034013; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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