K^0-\bar{K}^0 mixing in the Standard Model from Nf=2+1+1 Twisted Mass Lattice QCD

TL;DR

This paper reports the first unquenched N_f=2+1+1 lattice QCD calculation of the B_K parameter, crucial for understanding neutral kaon oscillations, using twisted mass fermions and non-perturbative renormalization.

Contribution

It provides a novel unquenched lattice QCD computation of B_K with N_f=2+1+1 flavors, including non-perturbative renormalization and preliminary continuum extrapolation.

Findings

B_K^{RGI} (a=0.077) = 0.747(18)

Weak dependence of B_K^{RGI} on the number of dynamical flavors

Results consistent with previous unquenched N_f=2 calculations

Abstract

We present preliminary results at {\beta} = 1.95 (a = 0.077 fm) on the first unquenched N_f=2+1+1 lattice computation of the B_K parameter which controls the neutral kaon oscillations in the Standard Model. Using N_f=2+1+1 maximally twisted sea quarks and Osterwalder-Seiler valence quarks we achieve O(a) improvement and a continuum-like renormalization pattern for the four-fermion operator. Our results are extrapolated/interpolated to the physical light/strange quark mass but not yet to the continuum limit. The computation of the relevant renormalization constants is performed non perturbatively in the RI'-MOM scheme using dedicated simulations with N_f=4 degenerate sea quark flavours produced by the ETM collaboration. We get B_K^{RGI} (a = 0.077) = 0.747(18), which when compared to our previous unquenched N_f=2 determination and most of the existing results, suggests a rather weak B_K^{RGI} dependence on the number of dynamical flavours. We are at the moment analysing lattice data at two additional {\beta} values which will allow us to perform an extrapolation to the continuum limit.