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

Recently, the first ever lattice computation of the γ W -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 γ W -box correction on the neutron also led to a significant reduction of the theory uncertainty, but shifted the value of V u d 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 γ W -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 Δ V R = 0.02477 ( 24 ) , in excellent agreement with the dispersion theory result Δ V R = 0.02467 ( 22 ) . Combining with other relevant information, the top-row CKM unitarity deficit persists.