Problems With Extracting $m_s$ from Flavor Breaking in Hadronic $τ$ Decays

Details Problems With Extracting $m_s$ from Flavor Breaking in Hadronic $τ$ Decays Problems With Extracting $m_s$ from Flavor Breaking in Hadronic $τ$ Decays

1998-04-15

arxiv.org/abs/hep-ph/9804298v1

Phys.Rev. D58 (1998) 093015

Physics

High Energy Physics

High Energy Physics - Phenomenology

8 pages, Latex

Scientific paper

10.1103/PhysRevD.58.093015

A numerical error is pointed out in the existing expression for the order $\alpha_s^2$ longitudinal component of the squared-mass (D=2) contribution to the hadronic $\tau$ decay rate. The corrected version is found to be such that, to order $\alpha_s^2$, each term in the resulting series is larger than the previous one, ruling out the direct use of flavor breaking in hadronic $\tau$ decays as a means of extracting the strange quark mass. An alternate approach, using model spectral functions previously developed for the strangeness-changing scalar channel (and employed in alternate sum rule analyses of $m_s$) as input to the $\tau$ decay analysis, is shown to provide mutual consistency checks for the two different methods. The results for $m_s$ implied by $\tau$ decay data, and the existing model spectral function are also presented.

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