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

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.

18 pages, 4 figures

References in corpus (10)

• Chirally improving Wilson fermions II. Four-quark operators
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• Quenched Scaling of Wilson twisted mass fermions
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• Exploring twisted mass Lattice QCD with the Clover term
• Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD
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• Precise determination of $B_K$ and light quark masses in quenched domain-wall QCD

Cited by in corpus (9)

• Review of lattice results concerning low energy particle physics
• Simulating twisted mass fermions at physical light, strange and charm quark masses
• ΔS=2 and ΔC=2 bag parameters in the SM and beyond from Nf=2+1+1 twisted-mass LQCD
• First Physics Results at the Physical Pion Mass from $N_f=2$ Wilson Twisted Mass Fermions at Maximal Twist
• D-Dbar Mixing in the Standard Model and Beyond from Nf=2 Twisted Mass QCD
• BK-parameter from Nf = 2 twisted mass lattice QCD
• Power corrections from decoupling of the charm quark
• How perturbative are heavy sea quarks?
• K* vector and tensor couplings from Nf = 2 tmQCD