Abstract
We propose and apply a new approach to determining |V_{us}| using dispersion relations with weight functions having poles at Euclidean (spacelike) momentum which relate strange hadronic τ decay distributions to hadronic vacuum polarization (HVP) functions obtained from lattice quantum chromodynamics. We show examples where spectral integral contributions from the region where experimental data have large errors or do not exist are strongly suppressed but accurate determinations of the relevant lattice HVP combinations remain possible. The resulting |V_{us}| agrees well with determinations from K physics and three-family Cabibbo-Kobayashi-Maskawa unitarity. Advantages of this new approach over the conventional hadronic τ decay determination employing flavor-breaking sum rules are also discussed.
Highlights
Peter Boyle,1 Renwick James Hudspith,2 Taku Izubuchi,3,4 Andreas Jüttner,5 Christoph Lehner,3 Randy Lewis,2 Kim Maltman,2,6 Hiroshi Ohki,4,7 Antonin Portelli,8 and Matthew Spraggs8
We propose and apply a new approach to determining jVusj using dispersion relations with weight functions having poles at Euclidean momentum which relate strange hadronic τ decay distributions to hadronic vacuum polarization (HVP) functions obtained from lattice quantum chromodynamics
We show examples where spectral integral contributions from the region where experimental data have large errors or do not exist are strongly suppressed but accurate determinations of the relevant lattice HVP combinations remain possible
Summary
The low jVusj noted above results from a conventional implementation [17] of Eq (1) which employs fixed s0 1⁄4 m2τ and ω 1⁄4 ωτ and assumptions for experimentally unknown D 1⁄4 6 and 8 condensates. Us spectral integral uncertainties dominate the error, with current ∼25% residual mode contribution errors precluding a competitive determination [9]. Motivated by this limitation, we switch to generalized dispersion relations involving the experimental us. With large enough N, and all Q2k below ∼1 GeV2, spectral integral contributions from s > m2τ and the higher-s, larger-error part of the experimental distribution can be strongly suppressed. Estimated LHS continuum Að0Þ contributions, obtained using sum-rule Kð1460Þ and Kð1830Þ relative lattice residue contributions (N=4) 1. The lower panel, shows the relative sizes of different contributions to the weighted us spectral
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