The CKM matrix and flavor physics from lattice QCD

TL;DR

This paper reviews how lattice QCD calculations are crucial for testing the Standard Model's flavor sector, constraining the CKM matrix, and exploring potential signs of new physics through weak matrix elements and rare decay processes.

Contribution

It provides an updated overview of lattice QCD's role in CKM matrix determinations, highlights current tensions suggesting new physics, and discusses future prospects for rare decay calculations.

Findings

Current CKM matrix element determinations rely on lattice QCD.

Hints of new physics include a 2-3 sigma tension in the unitarity triangle.

Lattice QCD calculations of rare decays are essential for future beyond Standard Model searches.

Abstract

I discuss the role of lattice QCD in testing the Standard Model and searching for physics beyond the Standard Model in the quark flavor sector. I first review the Standard Model CKM framework. I then present the current status of the CKM matrix, focusing on determinations of CKM matrix elements and constraints on the CKM unitarity triangle that rely on lattice QCD calculations of weak matrix elements. I also show the potential impact of improved lattice QCD calculations on the global CKM unitarity triangle fit. I then describe several hints of new physics in the quark flavor sector that rely on lattice QCD calculations of weak matrix elements, such as evidence of a ~2-3 sigma tension in the CKM unitarity triangle and the "f_{D_s} puzzle". I finish with a discussion of lattice QCD calculations of rare B- and K-decays needed to probe physics beyond the Standard Model at future experiments.