A Precision Test of First Row CKM Unitarity from Lattice QCD

TL;DR

This paper discusses high-precision lattice QCD calculations of CKM matrix elements, focusing on the first row unitarity test, and reviews collaborative efforts to improve theoretical inputs for this fundamental physics test.

Contribution

It presents a detailed review of ongoing lattice QCD efforts to refine CKM matrix element calculations using HISQ and SChPT, aiming to address unitarity deficits.

Findings

Current lattice calculations contribute to CKM unitarity tests.

Collaborative efforts improve decay constant and form factor determinations.

Results impact the search for physics beyond the Standard Model.

Abstract

High-precision determinations of 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 $|V_{ud}|$ and $|V_{us}|$. Without resorting to nuclear inputs, they can be extracted from the combination of the experimental decay width of kaon and pion leptonic decays, along with the theoretical calculation of their decay constants; combined with the decay width of semileptonic kaon decays, with the computation of the corresponding 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 $N_f=2+1+1$ MILC configurations along with Staggered Chiral Perturbation Theory (SChPT) as a functional form for the chiral-continuum limit.