Strange-quark mass from combined e~+e~- and #tau#-decay data: test of the isospin symmetry and implications on #epsilon#'/#epsilon# and m_(u,d)

摘要

I extract the strange-quark mass using a #tau#-like decay sum rule for the #phi#-meson, and some other sum rules involving its difference with the vector component of the hadronic #tau#-decay. As a conservative estimate, one obtains to order #alpha#_s~3: m-bar_s(1 GeV) = (178 +- 33) MeV => m-bar_s(2 GeV) = (129 +- 24) MeV, while the positivity of the spectral function leads to the upper bound: m-bar_s(1 GeV) <= (200 +- 28) MeV => m-bar_s(2 GeV) <= (145 +- 20) MeV. These results are in good agreement with the existing sum rule and #tau#-decay results, and, in particular, with the result from the the sum rule involving the difference of the isoscalar and isovector components of the e~+e~- -> hadrons data. This signals small effects of the SU(2) isospin violation due to the #omega#-#rho# mixing parameters, and questions the reliability of the existing sum rule estimates of these parameters. Combining our results with the recent data on implied by'/implied by, we can estimate, within the standard model, the four-quark weak matrix elements B_6~(1/2) - 0.54B_8~(3/2) to be about (2.8 +- 1.3). This result may suggest a large violation of the vacuum saturation estimate similarly to the case of the four-quark condensates obtained from the sum rules analysis, and can serve as a guide for a future accurate non-perturbative extraction of such matrix elements. Combining our result with the sum rule estimate of m_u + m_d and with the Dashen formula for the mass ratio, one can deduce the update values: m-bar_d(2 GeV) = (6.4 +- 1.1) MeV and m-bar_u(2 GeV) = (2.3 +- 0.4) MeV.