A note on isospin violation in Pl2(gamma) decays

TL;DR

This paper analyzes the impact of electromagnetic and strong isospin-violating effects on P_{l2(γ)} decays, highlighting their significance for accurately extracting CKM matrix element ratios from experimental data.

Contribution

It provides a detailed assessment of both electromagnetic and strong isospin-breaking effects, including corrections previously neglected, to improve the precision of |V_{us}/V_{ud}| determination.

Findings

Strong isospin-breaking corrections are as significant as electromagnetic effects.

Updated ratio of CKM elements: |V_{us}/V_{ud}| = 0.2316(12).

Highlights the importance of including strong isospin violation in decay analyses.

Abstract

We discuss the size of isospin violating effects of both electromagnetic (e \neq 0) and strong (m_u \neq m_d) origin in P_{\ell 2 (\gamma)} decays. Our results are relevant for the extraction of |V_{us}/V_{ud}| from the measured ratio of the K_{\mu 2 (\gamma)} and \pi_{\mu 2 (\gamma)} decay widths combined with F_K/F_\pi obtained in lattice calculations in the isospin limit. We point out that strong isospin-breaking corrections, neglected in previous studies, enter at the same level as the electromagnetic effects. The updated value for the ratio of CKM elements reads |V_{us}/V_{ud}| = 0.2316(12).