Update on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo>/</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>u</mml:mi><mml:mi>d</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math> from semileptonic kaon and pion decays
Chien-Yeah Seng, Daniel Galviz, William J. Marciano, Ulf-G. Meißner
Abstract
Implications for Cabibbo universality based on progress in the study of semileptonic kaon and pion decays are discussed. Included are recent updates of experimental input along with improved radiative corrections, form factors, and isospin-breaking effects. As a result, we obtain for the Cabibbo-Kobayashi-Maskawa (CKM) quark mixing matrix element $|{V}_{us}|=0.22309(56)$ from semileptonic ${K}_{\ensuremath{\ell}3}$ $(K\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu})$ decays and $|{V}_{us}/{V}_{ud}|=0.22908(87)$ from the ratio between the kaon and pion (${\ensuremath{\pi}}_{e3}$) semileptonic decay rates. In both, a lattice QCD value of the form factor $|{f}_{+}^{K}(0)|=0.9698(17)$ is employed. The ${V}_{us}$ from ${K}_{\ensuremath{\ell}3}$ decays together with ${V}_{ud}=0.97373(31)$ found from superallowed nuclear beta decays implies an apparent $3.2\ensuremath{\sigma}$ violation of the first-row CKM unitarity condition. The $|{V}_{us}|/|{V}_{ud}|$ obtained from the ratio of weak vector current induced meson decays is consistent with the observed unitarity violation but found to differ by $2.2\ensuremath{\sigma}$ from its extraction using the ratio of weak axial-vector leptonic decay rates $\mathrm{\ensuremath{\Gamma}}(K\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu})/\mathrm{\ensuremath{\Gamma}}(\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\mu}\ensuremath{\nu})$. The situation suggests a difference between vector and axial-vector derived CKM matrix elements or a problem with the lattice QCD form factor input. Prospects for future improvements in comparative precision tests involving $|{V}_{ud}|$, $|{V}_{us}|$, and their ratios are briefly described.