A Precision Test of First-row CKM Unitarity from Lattice QCD

High-precision determinations of the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements are essential probes of physics beyond the Standard Model (BSM). Current precision tests show a deficit in the first-row unitarity relation. At the current level of precision, the only relevant CKM matrix elements that contribute to this test are \ (|Vₔ₃|\) and \ (|Vₔₒ|\). Without resorting to nuclear inputs, these elements can be determined by analyzing pion and kaon leptonic decays together with kaon semileptonic decays. This determination combines the experimentally measured decay widths for these processes with the theoretical computation of the ratio between the pion and kaon decay constants, as well as the semileptonic form factor at zero momentum transfer. We review current efforts by the Fermilab Lattice and MILC collaborations towards a correlated analysis of the lattice inputs needed for this test using Highly Improved Staggered Quarks (HISQ) on the \ (Nf=2+1+1\) MILC configurations along with Staggered Chiral Perturbation Theory (SChPT) as a functional form for the chiral-continuum limit. Abstract Published by the Jagiellonian University 2026 authors