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

We present lattice results for $f_K\mathrm{/}{f}_{\pi }$ in the iso-symmetric limit of pure QCD (isoQCD) with $N_f=2+1$ flavours, along with a determination of $\mathrm{\mid }{V}_{us}\mathrm{\mid }\mathrm{/}\mathrm{\mid }{V}_{ud}\mathrm{\mid }$ 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.