$K_L-K_S$ mass difference from lattice QCD

TL;DR

This paper presents the first complete lattice QCD calculation of the $K_L-K_S$ mass difference, demonstrating the significance of disconnected diagrams and achieving results close to experimental values.

Contribution

It provides the first full lattice QCD computation of $ riangle M_K$ including disconnected diagrams and GIM cancellation effects.

Findings

Calculated $ riangle M_K$ close to experimental value

Disconnected diagrams are crucial, indicating OZI rule failure

Quantified systematic and statistical errors in the calculation

Abstract

We report on the first complete calculation of the $K_L-K_S$ mass difference, $\Delta M_K$, using lattice QCD. The calculation is performed on a 2+1 flavor, domain wall fermion ensemble with a 330MeV pion mass and a 575 MeV kaon mass. We use a quenched charm quark with a 949 MeV mass to implement Glashow-Iliopoulos-Maiani cancellation. For these heavier-than-physical particle masses, we obtain $\Delta M_K =3.19(41)(96)\times 10^{-12}$ MeV, quite similar to the experimental value. Here the first error is statistical and the second is an estimate of the systematic discretization error. An interesting aspect of this calculation is the importance of the disconnected diagrams, a dramatic failure of the OZI rule.