BK-parameter from Nf = 2 twisted mass lattice QCD

TL;DR

This paper reports an unquenched lattice QCD calculation of the $B_K$ parameter using maximally twisted Wilson quarks, achieving a precise non-perturbative renormalization and results consistent with previous studies.

Contribution

It introduces a novel lattice definition of $B_K$ that is multiplicatively renormalizable and O($a$) improved, using a mixed valence quark approach in unquenched $N_f=2$ QCD.

Findings

Calculated $B^{ m RGI}_K=0.729\, ext{±}\,0.030$ at physical pion mass

Results align with existing quenched and unquenched determinations

Employs non-perturbative RI-MOM scheme for renormalization

Abstract

We present an unquenched $N_f=2$ lattice computation of the $B_{K}$ parameter which controls $K^0-\bar K^0$ oscillations. A partially quenched setup is employed with two maximally twisted dynamical (sea) light Wilson quarks, and valence quarks of both the maximally twisted and the Osterwalder--Seiler variety. Suitable combinations of these two kinds of valence quarks lead to a lattice definition of the $B_{K}$ parameter which is both multiplicatively renormalizable and O($a$) improved. Employing the non-perturbative RI-MOM scheme, in the continuum limit and at the physical value of the pion mass we get $B^{\rm RGI}_K=0.729\pm 0.030$, a number well in line with the existing quenched and unquenched determinations.