Problems With Extracting $m_s$ from Flavor Breaking in Hadronic $\tau$ Decays

Abstract

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.

8 pages, Latex

References in corpus (3)

• Mass Corrections to the Tau Decay Rate
• Isospin Breaking and the Extraction of $m_s$ from the $\tau$-Decay-Like Vector Current Sum Rule
• Determination of $M_b$ and ${\alpha }_s$ from the Upsilon System

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