Chirally improving Wilson fermions II. Four-quark operators

Abstract

In this paper we discuss how the peculiar properties of twisted mass lattice QCD at maximal twist can be employed to set up a consistent computational scheme in which, despite the explicit breaking of chiral symmetry induced by the presence of the Wilson and mass terms in the action, it is possible to completely bypass the problem of wrong chirality and parity mixings in the computation of the CP-conserving matrix elements of the ∆S = 1, 2 effective weak hamiltonian, and at the same time have a positive determinant for pairs of non-degenerate quarks, as well as absence of O(a) discretization effects in on-shell quantities with no need of improving lattice action and operators. JHEP10(2004)070 C. Absence of the mixing of Q ± V A+AV with operators of dimension six 37 C.1 The operator Q ± [0] V A+AV 37 C.2 The operator Q ± [1] V A+AV 38

Kaon mixing beyond the SM from Nf = 2 tmQCD and model independent constraints from the UTA

“…A proof of the latter point is given in appendix A and its validity is numerically verified in appendix B, while O(a) improvement of physical quantities is a genuine property of the setup of ref. [12]. As a consequence unitarity violations due to different sea and valence quark regularization yield only O(a 2 ) artifacts, provided renormalized sea and valence quark masses are matched.…”

“…This strategy has been suggested in ref. [12] as a way of setting up a computational framework allowing for a calculation of ∆S = 2 four-fermion matrix elements that is both automatically O(a) improved and free of wrong chirality mixing effects. A proof of the latter point is given in appendix A and its validity is numerically verified in appendix B, while O(a) improvement of physical quantities is a genuine property of the setup of ref.…”

“…In section 6 we give our estimates of the various B-parameters and matrix elements ratios and compare the present results with the previous determinations existing in the literature. In five appendices we discuss a number of technicalities: i) the renormalization properties of the four-fermion operators in our "mixed action" setup [12]; ii-iii) the RI-MOM computation of renormalization constants (RCs) and corresponding results respectively; iv) tables of lattice data on pseudoscalar meson masses, decay constants and bare four-fermion matrix elements; v) complete results on renormalized four-fermion matrix elements obtained by using various formulae for the chiral extrapolation and two alternative procedures for the RI-MOM determination of RCs.…”

Lattice QCD determination of m b , f B and f Bs with twisted mass Wilson fermions

“…The calculation is based on the N f = 2 gauge field configurations generated by the European Twisted Mass (ETM) Collaboration with the tree-level improved Symanzik gauge action [9] and the twisted mass quark action [10] at maximal twist, discussed in detail in [11][12][13][14][15][16][17]. We simulated N f = 2 mass-degenerate dynamical quarks, whose mass is eventually extrapolated to the physical isospin averaged mass of the up and down quarks, m u/d .…”

“…The strange and charm quarks are quenched in the present calculation. In our lattice setup all physical quantities are O(a) improved [16,17], in particular cutoff effects related to the heavy quark mass µ h are of order a 2 µ 2 h . For further details of our simulations we refer to [18], where the same ensembles of gauge configurations were used.…”