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

We point out a caveat in the proof for automatic 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 O(a) improvement can fail unless the quark mass satisfies m_q >> a^2 Lambda_QCD^3. We propose a different definition for the twist angle which does not require a restriction on the quark mass for automatic O(a) improvement. In order to illustrate explicitly automatic 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 O(a) effect, depending on the size of the quark mass.Comment: 27 pages, no figure

Twisted mass QCD for the pion electromagnetic form factor

The pion form factor is computed using quenched twisted mass QCD and the GMRES-DR matrix inverter. The momentum averaging procedure of Frezzotti and Rossi is used to remove leading lattice spacing artifacts, and numerical results for the form factor show the expected improvement with respect to the standard Wilson action. Although some matrix inverters are known to fail when applied to twisted mass QCD, GMRES-DR is found to be a viable and powerful option. Results obtained for the pion form factor are consistent with the published results from other O(a) improved actions and are also consistent with the available experimental data.Comment: 19 pages, 12 figure

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 $M_{\rm PS}/M_{\rm V} = 0.467(13)$ at $\beta=6$ in large volume. We check the absence of exceptional configurations and -- by further data at $\beta=6.2$ -- the size of scaling violations. The CPU time cost for reaching a given accuracy is close to that with ordinary Wilson quarks at $M_{\rm PS}/M_{\rm V} \simeq 0.6$ and grows smoothly as $M_{\rm PS}/M_{\rm V}$ decreases.Comment: 4 pages, 3 figures, to appear in Nucl. Phys. B (Proc. Suppl.

Observations on discretization errors in twisted-mass lattice QCD

I make a number of observations concerning discretization errors in twisted-mass lattice QCD that can be deduced by applying chiral perturbation theory including lattice artifacts. (1) The line along which the PCAC quark mass vanishes in the twisted mass-twisted mass plane makes an angle to the untwisted mass axis which is a direct measure of O(a) terms in the chiral Lagrangian, and is found numerically to be large; (2) Numerical results for pionic quantities in the mass plane show the qualitative properties predicted by chiral perturbation theory, in particular an asymmetry in slopes between positive and negative untwisted quark masses; (3) By extending the description of the ``Aoki regime'' (where m_q is of size a^2 Lambda_QCD^3) to next-to-leading order in chiral perturbation theory I show how the phase transition lines and lines of maximal twist (using different definitions) extend into this region, and give predictions for the functional form of pionic quantities; (4) I argue that the recent claim that lattice artifacts at maximal twist have apparent infrared singularities in the chiral limit results from expanding about the incorrect vacuum state. Shifting to the correct vacuum (as can be done using chiral perturbation theory) the apparent singularities are summed into non-singular, and furthermore predicted, forms. I further argue that there is no breakdown in the Symanzik expansion in powers of lattice spacing, and no barrier to simulating at maximal twist in the Aoki regime.Comment: 20 pages, 6 figures. Published version. More typos corrected, and summary paragraph added to sections II and I

Chiral perturbation theory for partially quenched twisted mass lattice QCD

Partially quenched Quantum Chromodynamics with Wilson fermions on a lattice is considered in the framework of chiral perturbation theory. Two degenerate quark flavours are associated with a chirally twisted mass term. The pion masses and decay constants are calculated in next-to-leading order including terms linear in the lattice spacing $a$.Comment: 7 pages, LaTeX2e, final published versio

How the PHMC algorithm samples configuration space

We show that in practical simulations of lattice QCD with two dynamical light fermion species the PHMC algorithm samples configuration space differently from the commonly used HMC algorithm.Comment: 3 pages, 2 figures, LATTICE98 (Algorithms

Twisted-mass lattice QCD with mass non-degenerate quarks

The maximally twisted lattice QCD action of an $SU_f(2)$ doublet of mass degenerate Wilson quarks gives rise to a real positive fermion determinant and it is invariant under the product of standard parity times the change of sign of the coefficient of the Wilson term. The existence of this spurionic symmetry implies that O($a$) improvement is either automatic or achieved through simple linear combinations of quantities taken with opposite external three-momenta. We show that in the case of maximal twist all these nice results can be extended to the more interesting case of a mass non-degenerate quark pair.Comment: 10 pages (due to different LateX style), Latex file, based on a talk presented by G.C. Rossi at LHP2003 - Cairns. Reasons for replacement: Correction of the transformation properties of energies under r --> -r. Minor changes in Appendix

Twisted mass chiral perturbation theory for 2+1+1 quark flavours

We present results for the masses of pseudoscalar mesons in twisted mass lattice QCD with a degenerate doublet of u and d quarks and a non-degenerate doublet of s and c quarks in the framework of next-to-leading order chiral perturbation theory, including lattice effects up to O(a^2). The masses depend on the two twist angles for the light and heavy sectors. For maximal twist in both sectors, O(a)-improvement is explicitly exhibited. The mixing of flavour-neutral mesons is also discussed, and results in the literature for the case of degenerate s and c quarks are corrected.Comment: LaTeX2e, 12 pages, corrected typo

Nucleon and Delta masses in twisted mass chiral perturbation theory

We calculate the masses of the nucleons and deltas in twisted mass heavy baryon chiral perturbation theory. We work to quadratic order in a power counting scheme in which we treat the lattice spacing and the quark masses to be of the same order. We give expressions for the mass and the mass splitting of the nucleons and deltas both in and away from the isospin limit. We give an argument using the chiral Lagrangian treatment that, in the strong isospin limit, the nucleons remain degenerate and the delta multiplet breaks into two degenerate pairs to all orders in chiral perturbation theory. We show that the mass splitting between the degenerate pairs of the deltas first appears at quadratic order in in the lattice spacing. We discuss the subtleties in the effective chiral theory that arise from the inclusion of isospin breaking.Comment: 21 pages, 4 figures, version published in PR

The PHMC algorithm for simulations of dynamical fermions: II - Performance analysis

We compare the performance of the PHMC algorithm with the one of the HMC algorithm in practical simulations of lattice QCD. We show that the PHMC algorithm can lead to an acceleration of numerical simulations. It is demonstrated that the PHMC algorithm generates configurations carrying small isolated eigenvalues of the lattice Dirac operator and hence leads to a sampling of configuration space that is different from that of the HMC algorithm.Comment: Latex2e file, 6 figures, 31 page