A precise determination of $B_K$ in quenched QCD

Abstract

The $B_K$ parameter is computed in quenched lattice QCD with Wilson twisted mass fermions. Two variants of tmQCD are used; in both of them the relevant $\Delta S=2$ four-fermion operator is renormalised multiplicatively. The renormalisation adopted is non-perturbative, with a Schroedinger functional renormalisation condition. Renormalisation group running is also non-perturbative, up to very high energy scales. In one of the two tmQCD frameworks the computations have been performed at the physical $K$-meson mass, thus eliminating the need of mass extrapolations. Simulations have been performed at several lattice spacings and the continuum limit was reached by combining results from both tmQCD regularisations. Finite volume effects have been partially checked and turned out to be small. Exploratory studies have also been performed with non-degenerate valence flavours. The final result for the RGI bag parameter, with all sources of uncertainty (except quenching) under control, is ${\hat{B}}_K=0.789\pm 0.046$.

54 pages, 11 figures

References in corpus (8)

• Chirally improving Wilson fermions II. Four-quark operators
• Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
• Flavour Breaking Effects of Wilson twisted mass fermions
• Non-perturbative renormalization of left-left four-fermion operators in quenched lattice QCD
• A perturbative study of two four-quark operators in finite volume renormalization schemes
• BK from the lattice with Wilson quarks
• Scaling behavior of discretization errors in renormalization and improvement constants
• Wilson-like fermions and the static B_B parameter with no chirality breaking mixings

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• BK-parameter from Nf = 2 twisted mass lattice QCD
• Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD
• Exploring twisted mass Lattice QCD with the Clover term
• Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD
• Non-perturbative renormalisation of Delta F=2 four-fermion operators in two-flavour QCD
• K-->pipi amplitudes from lattice QCD with a light charm quark
• Non-leptonic kaon decays at large $N_c$
• Non-perturbative renormalisation of left-left four-fermion operators with Neuberger fermions
• Quenched $B_K$-parameter from Osterwalder-Seiler tmQCD quarks and mass-splitting discretization effects
• Precise determination of $B_K$ and light quark masses in quenched domain-wall QCD
• A strategy for implementing non-perturbative renormalisation of heavy-light four-quark operators in the static approximation
• Probing the chiral weak Hamiltonian at finite volumes
• Twisted mass QCD for weak matrix elements
• Progress in kaon physics on the lattice