**$V_{us}$ 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.