A precise determination of 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 S = 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, isB K = 0.789 ± 0.046.

Exploring twisted mass lattice QCD with the Clover term

“…Indeed, this is the quantity that renormalizes with the same renormalization constant Z µ = 1/Z P of the bare twisted mass aµ in the twisted formulation of LQCD. 3 From the plots in Figs. 1 and 2 we observe that:…”

Progress in kaon physics on the lattice

“…4.2. An interesting demonstration of the progress in B K calculations is that the value of B K calculated using the TM Wilson fermions ends up being in agreement with other B K calculations using different fermion formulations [17]. The calculation of B K with TM Wilson fermions has been discussed in great detail in the plenary talk by Pena [22] so we skip all the details here.…”

Non-perturbative renormalisation of ΔF= 2 four-fermion operators in two-flavour QCD

“…given an operator O ∈ {Q ± 1 , Q ′ + k } the corresponding operator insertion in any on-shell renormalised correlation function is given by 6) where g 0 , a are the bare coupling and lattice spacing, respectively and µ is the renormalisation scale. The RG-running of the operator is controlled by the anomalous dimension γ, defined by the Callan-Symanzik equation…”