Strange-quark mass from combined e+e- and tau-decay data:test of the isospin symmetry and implications on epsilon'/εand m_{u,d}

Stephan Narison

doi:10.1016/S0370-2693(99)01093-X

paper

Strange-quark mass from combined e+e- and tau-decay data:test of the isospin symmetry and implications on epsilon'/εand m_{u,d}

arXiv:hep-ph/9905264 · doi:10.1016/S0370-2693(99)01093-X

Abstract

I extract the strange-quark mass using a $τ$ -like decay sum rule for the $ϕ$ -meson, and some other sum rules involving its difference with the vector component of the hadronic $τ$ -decay. As a conservative estimate, one obtains to order $α_{s}^{3}$ : $m ˉ_{s}$ (1 GeV) = $(178 \pm 33)$ MeV $\lrar \~\bar{m}_s$(2 GeV) = $(129 \pm 24)$ MeV, while the positivity of the spectral function leads to the upper bound: $m ˉ_{s} (1 GeV) \leq (200 \pm 28) M e V ⟹ m ˉ_{s} (2 GeV) \leq (145 \pm 20) M e V$ . These results are in good agreement with the existing sum rule and $τ$ -decay results, and, in particular, with the result from the the sum rule involving the difference of the isoscalar and isovector components of the $e^+e^-\rar$ hadrons data. This signals small effects of the SU(2) isospin violation due to the $ω$ - $ρ$ mixing parameters, and questions the reliability of the existing sum rule estimates of these parameters. Combining our result with the recent data on $ε^{'} / ε$ , we can estimate, within the standard model, the four-quark weak matrix elements $B_{6}^{1/2} - 0.54 B_{8}^{3/2}$ to be about $(2.8 \pm 1.3)$ . 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: $m ˉ_{d} (2 GeV) = (6.4 \pm 1.1) MeV$ and $m ˉ_{u} (2 GeV) = (2.3 \pm 0.4) MeV$ .

Latex2e sources 11 pages + 1 table. Revised version written on July 99 to appear in Phys. Lett. B

Strange-quark mass from combined e+e- and tau-decay data:test of the isospin symmetry and implications on epsilon'/εand m_{u,d}

Abstract

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