Twisted Mass QCD Research Articles

Wilson-like fermions and the static [formula omitted] parameter with no chirality breaking mixings

I consider the recent proposal by R. Frezzotti and G. Rossi to chirally improve Wilson fermions in such a way that mixings among operators of different chirality can be excluded. The method, which is based on the use of twisted mass QCD with several replica of valence quarks, is extended here to static-light systems. The operators relevant for the computation of the B_B parameter (in the static approximation) are discussed. In this case the same renormalization pattern as for Ginsparg-Wilson fermions is obtained by a simple modification of the discretization of the action for valence quarks.

Twisted mass QCD,O(a)improvement, and Wilson chiral perturbation theory

We point out a caveat in the proof for automatic $\mathrm{O}(a)$ improvement in twisted mass lattice QCD at maximal twist angle. With the definition for the twist angle previously given by Frezzotti and Rossi, automatic $\mathrm{O}(a)$ improvement can fail unless the quark mass satisfies ${m}_{q}\ensuremath{\gg}{a}^{2}{\ensuremath{\Lambda}}_{\mathrm{Q}\mathrm{C}\mathrm{D}}^{3}$. We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic $\mathrm{O}(a)$ improvement. In order to illustrate explicitly automatic $\mathrm{O}(a)$ improvement we compute the pion mass in the corresponding chiral effective theory. We consider different definitions for maximal twist and show explicitly the absence or presence of the leading $\mathrm{O}(a)$ effect, depending on the size of the quark mass.

Twisted mass QCD and lattice approaches to the I= 1/2 rule

Twisted mass lattice QCD (tmQCD), generalised to four Wilson quark flavours, can be used for the computation of some weak matrix elements related toI = 1/2 transitions. Besides eliminating unphysical zero modes, tmQCD may alleviate the four-quark oper- ator renormalisation problems encountered in the calculation of CP-conserving K → � matrix elements with traditional Wilson fermion regularisation. With an active charm quark, the renormalisation of the K → � matrix elements requires at most the sub- traction of a linearly divergent counterterm. Furthermore, in the (partially) quenched approximation the twist angles can be chosen so that only a finite counterterm needs to be subtracted.

Pion mass splitting and phase structure in twisted mass QCD

In the framework of Wilson Chiral Perturbation Theory, we study the effect induced by a twisted Wilson term, as it appears in Twisted Mass QCD (with 2 degenerate quarks). In particular we consider the vacuum orientation and the pion masses. The computations are done to NLO both in the mass and in the lattice spacing (i.e. to O(a^2)). There are no restrictions on the relative size of lattice artifacts with respect to the physical mass, thus allowing, in principle, to bridge between the physical regime and the unphysical one, where lattice artifacts tend to dominate. The inclusion of O(a^2) lattice artifacts can account for the splitting of degeneracy of the three pion masses. Moreover O(a^2) terms are necessary to model non trivial behaviors of the vacuum orientation such as possible Aoki phases. It turns out that these last two phenomena are determined by the same constant.

Scaling test for Wilson twisted mass QCD

We present a first scaling test of twisted mass QCD with pure Wilson quarks for a twisting angle of π/2. We have computed the vector meson mass mV and the pseudoscalar decay constant FPS for different values of β at fixed value of r0mPS. The results obtained in the quenched approximation are compared with data for pure Wilson and non-perturbatively O(a) improved Wilson computations. We show that our results from Wilson twisted mass QCD show clearly reduced lattice spacing errors, consistent with O(a) improvement and without the need of any improvement terms added. These results thus provide numerical evidence of the prediction of Frezzotti and Rossi [hep-lat/0306014].

Towards a determination of g8 and g27 from twisted mass lattice QCD

A first step towards solving the δI = 12 puzzle consists in a determination of the lowest order coupling constants g8 and g27 in the effective chiral theory. Using twisted mass QCD with an active charm, it can be shown that the renormalization of K → π matrix elements requires at most the subtraction of a linear divergence. In the (partially) quenched approximation one may eliminate the linear divergence by a suitable choice of the twist angles and the interpolating meson fields.

BK from twisted mass QCD

We present some preliminary results for $B_K$ at $\beta=6.0$, using the twisted mass QCD formalism for the computation of bare matrix elements of the $\Delta S=2$ operator. The main advantage of the method is that mixing with other $d=6$ operators under renormalisation is avoided. Moreover the operator renormalisation is performed in the Schr\"odinger functional (SF) framework, using earlier results of our collaboration for the corresponding step scaling function.

Twisted mass QCD and theΔ I =½ 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 toΔ I =½ transitions has important advantages: the renormalisation of K → π 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 → ππ matrix elements, which, as far as renormalisation and power subtractions axe concerned, has properties analogous to the standard Wilson case.

K0- [formula omitted]0 mixing from the Schrödinger functional and twisted mass QCD

We describe how the Schrödinger functional and twisted mass QCD can be used to compute the kaon B-parameter B K on the lattice with Wilson fermions. This new approach is expected to reduce the systematic uncertainties on B K through a better control of its (nonperturbative) renormalisation. Preliminary results for the bare matrix element in a physical volume of 1.5 3 × 4.5 fm 4 are presented. The renormalisation of the matrix element in a Schrödinger functional scheme is also discussed.

Some remarks on O( a) improved twisted mass QCD

Twisted mass QCD (tmQCD) has been introduced as a solution to the problem of unphysical fermion zero modes in lattice QCD with quarks of the Wilson type. We here argue that O( a) improvement of the tmQCD action and simple quark bilinear operators can be more economical than in the standard framework. In particular, an improved and renormalized estimator of the pion decay constant in two-flavour QCD is available, given only the Sheikholeslami-Wohlert coefficient c sw and an estimate of the critical mass m c.

Quenched twisted mass QCD at small quark masses and in large volume

As a test of quenched lattice twisted mass QCD, we compute the non-perturbatively O( a) improved pseudoscalar and vector meson masses and the pseudoscalar decay constant down to M PS/ M V = 0.467(13) at β = 6 in large volume. We check the absence of exceptional configurations and — by further data at β = 6.2 — the size of scaling violations. The CPU time cost for reaching a given accuracy is close to that with ordinary Wilson quarks at M PS/ M V ⋍ 0.6 and grows smoothly as M PS/ M V decreases.

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 Schrödinger 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.