Pion beta decay and Cabibbo-Kobayashi-Maskawa unitarity

Pion beta decay, π⁺→π⁰e⁺ν(γ), provides a theoretically clean ±0.3% determination of the Cabibbo-Kobayashi-Maskawa matrix element Vud. Although impressive, that result falls short of super-allowed nuclear beta decays where an order of magnitude better precision already exists. Here, we advocate a new strategy for utilizing pion beta decay, based on its utility in determining Vᵤₛ/Vud via the ratio ${R}V={{Γ}}(K{→}{π}l{ν}({γ}))/{{Γ}}({{π}}⁺{→}{{π}}⁰{e}⁺{ν}({γ}))$ which provides a measure of ${f}₊K(0)|{V}ᵤₛ|/{f}₊^{{π}}(0)|{V}ud|$ independent of the Fermi constant and short-distance radiative corrections. Its dependence on the ratio of two hadronic vector current form factors provides an interesting computational goal for lattice gauge theory studies. Employing a recent lattice based value f₊K(0)/f₊^π(0)=0.970(2), we find Vᵤₛ/Vud=0.22910(91) compared to Vᵤₛ/Vud=0.23131(45) obtained from ${R}A={{Γ}}(K{→}{μ}{ν}({γ}))/{{Γ}}({π}{→}{μ}{ν}({γ}))$. Those independent ${V}ᵤₛ/{V}ud$ determinations exhibit a $2.2{σ}$ discrepancy. That tension suggests a needed shift in the lattice ${f}₊K(0)/{f}₊^{{π}}(0)$ value towards the consistency range 0.961(4), experimental/theory input changes or ``new physics'' effects. Other features and implications of ${R}V$ and ${R}A$ are also discussed.