Pion Beta Decay and CKM Unitarity

Pion beta decay, ${\pi }^{+}\to {\pi }^0{e}^{+}\nu (\gamma )$, provides a theoretically clean $\pm 0.3\mathrm{\%}$ determination of the CKM matrix element $V_{\text{ud}}$. That value falls short of super-allowed nuclear beta decays where an order of magnitude better precision already exists. We advocate a new strategy for utilizing pion beta decay, based on its role in determining ${V_{$\text{us}$} / V_{$\text{ud}$}}$viatheratio$R_V=\Gamma\left(K\to \pi l \nu(\gamma)\right)/\Gamma\left(\pi^+\to \pi^0 e^+\nu(\gamma)\right)$\mathrm{.}$R_V$measures$ { f_+^K(0) |V_{$\text{us}$}| / f_+^\pi(0) |V_{$\text{ud}$}| }$ and is insensitive to the Fermi constant and some radiative corrections. Its dependence on the ratio of form factors may also prove useful for lattice gauge theory calculations. Employing a lattice based value ${ f_+^K(0) / f_+^\pi(0) } = 0.970(2)$,wefind$V_{$\text{us}$}/V_{$\text{ud}$}=0.22918(88)$comparedto$V_{$\text{us}$}/V_{$\text{ud}$}=0.23131(45)$obtainedfrom$R_A=\Gamma(K\to \mu\nu(\gamma))/\Gamma(\pi\to \mu\nu(\gamma))$. Those vector and axial-vector based $V_{\text{us}}\mathrm{/}{V}_{\text{ud}}$ values exhibit a 2.2$\sigma$ discrepancy. That tension may be relieved by a shift in the lattice $ { f_+^K(0) / f_+^\pi(0) } $ towards the consistency range 0.961(4), changes in experimental input or new physics. Other implications of $R_V$ and $R_A$ are also discussed.