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PoS(LATTICE2016)279

$V_{us}$ from inclusive determinations based on hadronic tau data

K. Maltman, R. Hudspith, T. Izubuchi, R. Lewis, H. Ohki, J. Zanotti

in 34th annual International Symposium on Lattice Field Theory

Contribution: pdf

Abstract

The conventional implementation of the inclusive
hadronic $\tau$ decay data based, flavor-breaking (FB) finite-energy
sum rule (FESR) determination of $V_{us}$ is know to produce
results $>3\sigma$ low compared to kaon physics based results
and 3-family-unitarity expectations. We revisit this implementation,
showing that it fails a number of self-consistency tests, and that
the problems originate from a breakdown of assumptions employed
for treating higher dimension OPE contributions. A recently proposed
alternate implementation, which cures these problems, and uses lattice
data to more reliably quantify leading $D=2$ OPE uncertainties,
is then briefly reviewed. Employing this new implementation, using
also preliminary BaBar results for the $\tau\rightarrow K^-\pi^0\nu_\tau$
exclusive branching fraction, yields a result,
$V_{us}=0.2228(23)_{exp}(6)_{th}$, in excellent agreement with that
from $K_{\ell 3}$, and, within errors, with three-family-unitarity
expectations. Limitations in the near-term possibilities for
reducing the experimental error by the desired factor of $\sim 2$
reduction are then highlighted. These serve to motivate a new proposal
for determining $V_{us}$ via a dispersive analysis employing
strange hadronic $\tau$ data and lattice data in place of the OPE.