Twisted mass QCD and the ΔI=1/2\Delta I=1/2 rule

We show that the application of twisted mass QCD (tmQCD) with four (Wilson) quark flavours to the computation of lattice weak matrix elements relevant to $\Delta I=1/2$ transitions has important advantages: the renormalisation of $K \to \pi$ matrix elements does not require the subtraction of other dimension six operators, the divergence arising from the subtraction of lower dimensional operators is softened by one power of the lattice spacing and quenched simulations do not suffer from exceptional configurations at small pion mass. This last feature is also retained in the tmQCD computation of $K \to \pi\pi$ matrix elements, which, as far as renormalisation and power subtractions are concerned, has properties analogous to the standard Wilson case.Comment: Lattice2002(matrixel). Eq.(11) correcte

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Cutoff effects in twisted mass lattice QCD

We present a first numerical study of lattice QCD with O(a) improved Wilson quarks and a chirally twisted mass term. Renormalized correlation functions are derived from the Schroedinger functional and evaluated in an intermediate space-time volume of size 0.75^3 x 1.5 fm^4. In the quenched approximation precise results are then obtained with a moderate computational effort, allowing for a detailed study of the continuum approach. The latter is discussed in terms of observables which converge to meson masses and decay constants in the limit of large space-time volume. In the O(a) improved theory we find residual cutoff effects to be at the level of a few percent for lattice spacings of about 0.1 fm.Comment: 20 pages, 5 figures. Comments about the uncertainties on improvement coefficients adde

A perturbative study of two four-quark operators in finite volume renormalization schemes

Starting from the QCD Schroedinger functional (SF), we define a family of renormalization schemes for two four-quark operators, which are, in the chiral limit, protected against mixing with other operators. With the appropriate flavour assignments these operators can be interpreted as part of either the $\Delta F=1$ or $\Delta F=2$ effective weak Hamiltonians. In view of lattice QCD with Wilson-type quarks, we focus on the parity odd components of the operators, since these are multiplicatively renormalized both on the lattice and in continuum schemes. We consider 9 different SF schemes and relate them to commonly used continuum schemes at one-loop order of perturbation theory. In this way the two-loop anomalous dimensions in the SF schemes can be inferred. As a by-product of our calculation we also obtain the one-loop cutoff effects in the step-scaling functions of the respective renormalization constants, for both O(a) improved and unimproved Wilson quarks. Our results will be needed in a separate study of the non-perturbative scale evolution of these operators.Comment: 22 pages, 4 figure

Non-perturbative scaling tests of twisted mass QCD

We present a scaling study of lattice QCD with O(a) improved Wilson fermions and a chirally twisted mass term. In order to get precise results with a moderate computational effort, we have considered a system of physical size of 0.75^3 * 1.5 fm^4 with Schroedinger functional boundary conditions in the quenched approximation. Looking at meson observables in the pseudoscalar and vector channels, we find that O(a) improvement is effective and residual cutoff effects are fairly small.Comment: 5 pages, 4 figures, Lattice 2000 (Improvement and Renormalization), two misprints correcte