Long distance part of $\epsilon_K$ from lattice QCD

TL;DR

This paper presents a lattice QCD calculation of the long-distance contribution to the CP-violation parameter epsilon_K, including all diagrams and a perturbative subtraction at NLO.

Contribution

It provides a complete lattice QCD computation of epsilon_K's long-distance part, incorporating both connected and disconnected diagrams with NLO perturbative subtraction.

Findings

Successful calculation of long-distance epsilon_K contribution.

Inclusion of all connected and disconnected diagrams.

Implementation of NLO perturbative subtraction.

Abstract

We demonstrate the lattice QCD calculation of the long distance contribution to $\epsilon_K$. Due to the singular, short-distance structure of $\epsilon_K$, we must perform a short-distance subtraction and introduce a corresponding low-energy constant determined from perturbation theory, which we calculate at Next Leading Order (NLO). We perform the calculation on a $24^3 \times 64$ lattice with a pion mass of 329 MeV. This work is a complete calculation, which includes all connected and disconnected diagrams.