$f_K/f_{\pi}$ in iso-symmetric QCD and the CKM matrix unitarity

TL;DR

This paper reports lattice QCD results for the ratio of decay constants $f_K/f_{}$, examines CKM matrix unitarity, and incorporates isospin-breaking and QED effects for improved precision.

Contribution

It provides new lattice calculations of $f_K/f_{}$ in iso-symmetric QCD and analyzes CKM unitarity with strong isospin-breaking and QED corrections.

Findings

Precise lattice results for $f_K/f_{}$ in isoQCD.

Assessment of CKM matrix unitarity with corrections.

Enhanced continuum-limit control through combined regularizations.

Abstract

We present lattice results for $f_K/f_{\pi}$ in the iso-symmetric limit of pure QCD (isoQCD) with $N_f=2+1$ flavours, along with a determination of $|V_{us}|/|V_{ud}|$ and a study on the unitarity of the first row of the Cabibbo-Kobayashi-Maskawa (CKM) matrix after introducing strong isospin-breaking and QED effects. The results obtained are based on a combination of a Wilson unitary action and the mixed-action setup introduced in arXiv:2309.14154, arXiv:2510.20450. The combination of the two regularisations enables a more precise control over the continuum-limit extrapolation.