Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD

We simulate two variants of quenched twisted mass QCD (tmQCD), with degenerate Wilson quarks of masses equal to or heavier than half the strange quark mass. We use Ward identities in order to measure the twist angles of the theory and thus check the quality of the tuning of mass parameters to a physics condition which stays constant as the lattice spacing is varied. Flavour symmetry breaking in tmQCD is studied in a framework of two fully twisted and two standard Wilson quark flavours, tuned to be degenerate in the continuum. Comparing pseudoscalar masses, obtained from connected quark diagrams made of tmQCD and/or standard Wilson quark propagators, we confirm that flavour symmetry breaking effects, which are at most 5%, decrease as we approach the continuum limit. We also compute the pseudoscalar decay constant in the continuum limit, with reduced systematics. As a consequence of improved tuning of the mass parameters at $\beta =6.1$, we reanalyse our previous $B_K$ results. Our main phenomenological findings are $r_0{f}_K=0.421(7)$ and $\hat B_K = 0.735(71)$.