Electroweak box diagram contribution for pion and kaon decay from lattice QCD

Abstract

One of the sensitive probes of physics beyond the standard model is the test of the unitarity of the Cabbibo-Kobyashi-Maskawa matrix. Current analysis of the first row is based on $|{V}_{ud}|$ from fifteen superallowed ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ nuclear $\ensuremath{\beta}$ decays and $|{V}_{us}|$ from the kaon semileptonic decay, $K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$. Modeling the nuclear effects in the ${0}^{+}\ensuremath{\rightarrow}{0}^{+}$ decays is a major source of uncertainty, which would be absent in neutron decays. To make neutron decay competitive requires improving the measurement of neutron lifetime and the axial charge, as well as the calculation of the radiative corrections (RC) to the decay. The largest uncertainty in these RCs comes from the nonperturbative part of the $\ensuremath{\gamma}W$-box diagram, and lattice QCD provides a first principle method for its evaluation. Our calculations, using lattice configurations generated with highly improved staggered quarks by the MILC Collaboration, show that the analogous calculations for the pion and kaon decays are robust and give ${\ensuremath{\square}}_{\ensuremath{\gamma}W}^{VA}{|}_{\ensuremath{\pi}}=2.810(26)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and ${\ensuremath{\square}}_{\ensuremath{\gamma}W}^{VA}{|}_{{K}^{0,SU(3)}}=2.389(17)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ in agreement with the previous analysis carried out by Feng et al. using a different discretization of the fermion action.

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