Joint lattice QCD-dispersion theory analysis confirms the quark-mixing top-row unitarity deficit

Abstract

Recently, the first ever lattice computation of the γW-box radiative correction to the rate of the semileptonic pion decay allowed for a reduction of the theory uncertainty of that rate by a factor of ∼3. A recent dispersion evaluation of the γW-box correction on the neutron also led to a significant reduction of the theory uncertainty, but shifted the value of Vud extracted from the neutron and superallowed nuclear β decay, resulting in a deficit of the Cabibbo-Kobayashi-Maskawa (CKM) unitarity in the top row. A direct lattice computation of the γW-box correction for the neutron decay would provide an independent cross-check for this result but is very challenging. Before those challenges are overcome, we propose a hybrid analysis, converting the lattice calculation on the pion to that on the neutron by a combination of dispersion theory and phenomenological input. The new prediction for the universal radiative correction to free and bound neutron β-decay reads ΔRV=0.02477(24), in excellent agreement with the dispersion theory result ΔRV=0.02467(22). Combining with other relevant information, the top-row CKM unitarity deficit persists.