167 research outputs found
Flavor Twisted Boundary Conditions, Pion Momentum, and the Pion Electromagnetic Form Factor
We investigate the utility of partially twisted boundary conditions in
lattice calculations of meson observables. For dynamical simulations, we show
that the pion dispersion relation is modified by volume effects. In the isospin
limit, we demonstrate that the pion electromagnetic form factor can be computed
on the lattice at continuous values of the momentum transfer. Furthermore, the
finite volume effects are under theoretical control for extraction of the pion
charge radius.Comment: 15 pages, 8 figures, revisions to text, refs adde
Kaon thresholds and two-flavor chiral expansions for hyperons
Two-flavor chiral expansions provide a useful perturbative framework to study hadron properties. Such expansions should exhibit marked improvement over the conventional three-flavor chiral expansion. Although one can theoretically formulate two-flavor theories for the various hyperon multiplets, the nearness of kaon thresholds can seriously undermine the effectiveness of the perturbative expansion in practice. We investigate the importance of virtual kaon thresholds on hyperon properties, specifically their masses and isovector axial charges. Using a three-flavor expansion that includes SU(3) breaking effects, we uncover the underlying expansion parameter governing the description of virtual kaon thresholds. For spin-half hyperons, this expansion parameter is quite small. Consequently virtual kaon contributions are well described in the two-flavor theory by terms analytic in the pion mass-squared. For spin three-half hyperons, however, one is closer to the kaon production threshold, and the expansion parameter is not as small. Breakdown of SU(2) chiral perturbation theory is shown to arise from a pole in the expansion parameter associated with the kaon threshold. Estimating higher-order corrections to the expansion parameter is necessary to ascertain whether the two-flavor theory of spin three-half hyperons remains perturbative. We find that, despite higher-order corrections, there is a useful perturbative expansion for the masses and isovector axial charges of both spin-half and spin three-half hyperons. (C) 2010 Elsevier B.V. All rights reserved
Pion Polarizabilities and Volume Effects in Lattice QCD
We use chiral perturbation theory to study the extraction of pion
electromagnetic polarizabilities from lattice QCD. Chiral extrapolation
formulae are derived for partially quenched QCD, and quenched QCD simulations.
On a torus, volume dependence of electromagnetic observables is complicated by
SO(4) breaking, as well as photon zero-mode interactions. We determine finite
volume corrections to the Compton scattering tensor of pions. We argue,
however, that such results cannot be used to ascertain volume corrections to
polarizabilities determined in lattice QCD with background field methods.
Connection is lacking because momentum expansions are not permitted in finite
volume. Our argument also applies to form factors. Volume effects for
electromagnetic moments cannot be deduced from finite volume form factors.Comment: 5 figs., 19p
Extrapolations of Lattice Meson Form Factors
We use chiral perturbation theory to study the extrapolations necessary to
make physical predictions from lattice QCD data for the electromagnetic form
factors of pseudoscalar mesons. We focus on the quark mass, momentum, lattice
spacing, and volume dependence and apply our results to simulations employing
mixed actions of Ginsparg-Wilson valence quarks and staggered sea quarks. To
determine charge radii at quark masses on the lattices currently used, we find
that all extrapolations except the one to infinite volume make significant
contributions to the systematic error.Comment: 14pp, discussion and Ref. added for disconnected diagram
Current in the light-front Bethe-Salpeter formalism II: Applications
We pursue applications of the light-front reduction of current matrix
elements in the Bethe-Salpeter formalism. The normalization of the reduced wave
function is derived from the covariant framework and related to non-valence
probabilities using familiar Fock space projection operators. Using a simple
model, we obtain expressions for generalized parton distributions that are
continuous. The non-vanishing of these distributions at the crossover between
kinematic regimes (where the plus component of the struck quark's momentum is
equal to the plus component of the momentum transfer) is tied to higher Fock
components. Moreover continuity holds due to relations between Fock components
at vanishing plus momentum. Lastly we apply the light-front reduction to
time-like form factors and derive expressions for the generalized distribution
amplitudes in this model.Comment: 12 pages, 6 figures, RevTex
Gauge invariant reduction to the light-front
The problem of constructing gauge invariant currents in terms of light-cone
bound-state wave functions is solved by utilising the gauging of equations
method. In particular, it is shown how to construct perturbative expansions of
the electromagnetic current in the light-cone formalism, such that current
conservation is satisfied at each order of the perturbation theory.Comment: 12 pages, revtex
Restless pions: orbifold boundary conditions and noise suppression in lattice QCD
The study of one or more baryons in lattice QCD is severely hindered by the
exponential decay in time of the signal-to-noise ratio. The rate at which the
signal-to-noise decreases is a function of the the pion mass. More precisely,
it depends on the minimum allowed pion energy in the box, which, for periodic
boundary conditions, is equal to its mass. We propose a set of boundary
conditions, given by a "parity orbifold'' construction, which eliminates the
zero momentum pion modes, raising the minimum pion energy without altering the
QCD ground state, and thereby improving the signal-to-noise ratio of
(multi)-baryon correlation functions at long Euclidean times. We discuss
variations of these "restless pions" boundary conditions and focus on their
impact on the study of nuclear forces.Comment: 15 pages, 4 figure
Search for Fermion Actions on Hyperdiamond Lattices
Fermions moving in a two-dimensional honeycomb lattice (graphene) have, at
low energies, chiral symmetry. Generalizing this construction to four
dimensions potentially provides fermions with chiral symmetry and only the
minimal fermion doubling demanded by the Nielsen-Ninomiya no-go theorem. The
practical usefulness of such fermions hinges on whether the action has a
necessary set of discrete symmetries of the lattice. If this is the case, one
avoids the generation of dimension three and four operators which require fine
tuning. We construct hyperdiamond lattice actions with enough symmetries to
exclude fine tuning; however, they produce multiple doublings. The limit where
the actions exhibit minimal doubling does not possess the requisite symmetry.Comment: 4 pages, 1 figur
Exploring skewed parton distributions with two body models on the light front II: covariant Bethe-Salpeter approach
We explore skewed parton distributions for two-body, light-front wave
functions. In order to access all kinematical regimes, we adopt a covariant
Bethe-Salpeter approach, which makes use of the underlying equation of motion
(here the Weinberg equation) and its Green's function. Such an approach allows
for the consistent treatment of the non-wave function vertex (but rules out the
case of phenomenological wave functions derived from ad hoc potentials). Our
investigation centers around checking internal consistency by demonstrating
time-reversal invariance and continuity between valence and non-valence
regimes. We derive our expressions by assuming the effective qq potential is
independent of the mass squared, and verify the sum rule in a non-relativistic
approximation in which the potential is energy independent. We consider
bare-coupling as well as interacting skewed parton distributions and develop
approximations for the Green's function which preserve the general properties
of these distributions. Lastly we apply our approach to time-like form factors
and find similar expressions for the related generalized distribution
amplitudes.Comment: 25 pages, 12 figures, revised (minor changes but essential to
consistency
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