Full CKM matrix with lattice QCD

TL;DR

This paper demonstrates that it is now possible to determine the entire CKM matrix using lattice QCD, providing a comprehensive set of matrix elements with high accuracy and minimal theoretical assumptions.

Contribution

First complete determination of all CKM matrix elements and Wolfenstein parameters solely from lattice QCD calculations.

Findings

All nine CKM matrix elements are obtained with accuracy comparable to experimental averages.

The entire Wolfenstein parameter set is derived using lattice QCD for the first time.

The use of unquenched lattice configurations reduces theoretical uncertainties.

Abstract

We show that it is now possible to fully determine the CKM matrix, for the first time, using lattice QCD. |V_{cd}|, |V_{cs}|, |V_{ub}|, |V_{cb}| and |V_{us}| are, respectively, directly determined with our lattice results for form factors of semileptonic D->pi l nu, D->K l nu, B->pi l nu, B->D l nu, and K->pi l nu decays. The error from the quenched approximation is removed by using the MILC unquenched lattice gauge configurations, where the effect of u,d and s quarks is included. The error from the ``chiral'' extrapolation (m_l->m_{ud}) is greatly reduced by using improved staggered quarks. The accuracy is comparable to that of the Particle Data Group averages. In addition, |V_{ud}|, |V_{tb}|, |V_{ts}| and |V_{td}| are determined by using unitarity of the CKM matrix and the experimental result for sin{(2beta)}. In this way, we obtain all 9 CKM matrix elements, where the only theoretical input is lattice QCD. We also obtain all the Wolfenstein parameters, for the first time, using lattice QCD.