Quenched $B_K$-parameter from Osterwalder-Seiler tmQCD quarks and mass-splitting discretization effects

TL;DR

This paper investigates a modified twisted mass QCD approach to compute the $B_K$ parameter, demonstrating improved scaling behavior and reduced mass splitting effects in the quenched approximation.

Contribution

It introduces an Osterwalder-Seiler twisted mass QCD setup that improves $B_K$ calculations and reduces systematic errors compared to standard methods.

Findings

Significant improvement in $B_K$ scaling behavior with Clover term.

Reduced $K^0$-$ar{K}^0$ mass splitting in maximally twisted theory.

Systematic errors are better controlled in the proposed approach.

Abstract

We apply an Osterwalder-Seiler version of twisted mass QCD to a study of the $B_K$ parameter, in which three of the four quark fields making up the relevant $\Delta S =2$ operator are maximally twisted with the same twist angle, while the fourth one has a twist angle of opposite sign. It is known that this setup ensures automatic improvement of the bare $K^0$-$\overline K^0$ operator matrix element and multiplicative renormalization of the $\Delta S =2$ operator, at the price of breaking the $K^0$-$\overline K^0$ mass degeneracy by discretization effects. As a result, two dominant systematic errors of the $B_ K$ determination with Wilson fermions are kept under control. With the Clover term included in the fermion action, we perform a feasibility study and find, in the quenched approximation, a significant improvement of the scaling behaviour of $B_K$, compared to earlier standard tmQCD determinations. Moreover, we study in detail the $K^0$-$\overline K^0$ mass splitting that characterizes this approach and confirm that, in the presence of the Clover term, it is greatly reduced in a maximally twisted theory.