792 research outputs found

### 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

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