# Lattice QCD Impact on Determination of the CKM Matrix

## TL;DR

This paper reviews lattice QCD calculations of meson decay constants and form factors, highlighting their role in precisely determining the CKM matrix and addressing discrepancies in $|V_{ub}|$ and $|V_{cb}|$ from different decay methods.

## Contribution

It provides a comprehensive review of lattice QCD results impacting CKM matrix determination and discusses the longstanding $|V_{ub}|$ and $|V_{cb}|$ discrepancy.

## Key findings

- Lattice QCD calculations constrain the first two rows of the CKM matrix.
- Implications of $ ext{Lambda}_b$ form factors are analyzed.
- The review discusses the $|V_{ub}|$ and $|V_{cb}|$ discrepancy from exclusive and inclusive decays.

## Abstract

We review many lattice QCD calculations that impact the precise determination of the CKM matrix. We focus on decay constants and semileptonic form factors of both light ($\pi$ and K) and heavy-light ($D_{(s)}$ and $B_{(s)}$) mesons. Implication of $\Lambda_b$ form factors will be shown. When combined with experimental results for branching fractions and differential decay rates, the above calculations strongly constrain the first two rows of the CKM matrix. We discuss a long standing difference between $|V_{ub}|$ and $|V_{cb}|$ as determined from exclusive or inclusive decays.