Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Precision Test of First Row CKM Unitarity from Lattice QCD

Ramón Merino

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.

A Precision Test of First Row CKM Unitarity from Lattice QCD

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 and . 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 MILC configurations along with Staggered Chiral Perturbation Theory (SChPT) as a functional form for the chiral-continuum limit.

Paper Structure

This paper contains 5 sections, 3 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Current status
  3. Analysis strategy
  4. Preliminary results
  5. Conclusions and outlook

Figures (2)

  • Figure 1: Determinations of $|V_{ud}|$, $|V_{us}|$ and $|V_{us}|/|V_{ud}|$. The black band represents the unitarity constraint, taking into account the value of $|V_{ub}|$ from the PDG ParticleDataGroup:2024cfk. The green band represents the determination of $|V_{us}|$ coming from kaon decaysFermilabLattice:2018zqv, while the olive band corresponds to the average of the exclusive and inclusive determinations from tau decays HeavyFlavorAveragingGroupHFLAV:2024ctg. Red, orange and pink bands show determinations of $|V_{ud}|$ using superallowed beta, neutron and pion beta decays, respectively. They are taken from Ref. Cirigliano:2022yyo. The blue oblique band is the determination of the ratio $|V_{us}|/|V_{ud}|$ from leptonic kaon and pion decays Bazavov:2017lyh.
  • Figure 2: Correlation matrix for a representative subset of SChPT LECs obtained from the first step of the chiral-continuum analysis. Several pairs exhibit strong correlations, underlining the importance of a correlated treatment. For more information, see Lattice:2026euh.