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

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

2009-02-06

arxiv.org/abs/0902.1074v1

JHEP 0907:007,2009

Physics

High Energy Physics

High Energy Physics - Lattice

18 pages, 4 figures

Scientific paper

10.1088/1126-6708/2009/07/007

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.

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