A precise determination of BKBK in quenched QCD

The BKBK parameter is computed in quenched lattice QCD with Wilson twisted mass fermions. Two variants of tmQCD are used; in both of them the relevant ΔS=2ΔS=2 four-fermion operator is renormalised multiplicatively. The renormalisation adopted is non-perturbative, with a Schrödinger 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 BˆK=0.789±0.046.