# Light Quark Masses and the CP violation parameter $\epsilon'/\epsilon$

## TL;DR

This paper estimates light quark masses using lattice QCD data, providing updated values that influence the understanding of CP violation parameter $rac{ ext{epsilon}'}{ ext{epsilon}}$ within the Standard Model.

## Contribution

It offers the first comprehensive lattice-based estimates of light quark masses in the MSbar scheme, including both quenched and dynamical flavor scenarios.

## Key findings

- Quark masses are smaller than previous sum rule estimates.
- Results agree between Wilson and Staggered fermions after continuum extrapolation.
- Lower quark masses impact the extraction of $rac{ ext{epsilon}'}{ ext{epsilon}}$.

## Abstract

We present estimates of light quarks masses using lattice data. Our main results are based on a global analysis of all the published data for Wilson and Staggered fermions, both in the quenched approximation and with $n_f=2$ dynamical flavors. The Wilson and Staggered results agree after extrapolation to the continuum limit for both the $n_f=0,2$ theories. Our best estimates, in the MSbar scheme at scale $2 GeV$, are $mbar=3.2(4) MeV$ and $m_s = 90(20) MeV$ in the quenched approximation, and $mbar ~ 2.7 MeV$ and $m_s ~ 70 MeV$ for the $n_f=2$ theory. These estimates are significantly smaller than phenomenological estimates based on sum rules, but maintain the ratios predicted by chiral perturbation theory. Along with the new estimates of 4-fermion operators, lower quark masses have a significant impact on the extraction of $\epsilon'/\epsilon$ from the Standard Model.