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

Abstract

We present lattice results for $f_K/f_{\ddot{I}}€$ 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.

20 pages, 6 figures, 4 tables; v2: minor clarifications added to the text; conclusions and results unchanged; accepted for publication