BK-parameter from Nf = 2 twisted mass lattice QCD

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 $B_K^{\mathrm{RGI}}=0.729\pm 0.030$, a number well in line with the existing quenched and unquenched determinations.

Accepted for publication in Phys. Rev. D; systematic error discussion slightly modified; total uncertainty estimate on the BK result unchanged; 42 pages, 25 figures