18,706 research outputs found
Quenched Chiral Perturbation Theory for Baryons
We develop quenched chiral perturbation theory for baryons using the
graded-symmetry formalism of Bernard and Golterman and calculate non-analytic
contributions to the baryon masses coming from quenched chiral loops. The usual
term proportional to is substantially altered due to the
cancellation of diagrams with internal quark loops. In addition, the
``hairpin'' vertex leads to a new correction, proportional to . We
compare our results to numerical lattice data and use them to estimate the size
of the quenching error in the octet baryon masses.Comment: 7 pages (An abridged version of this note will appear in the
proceedings of Lattice'93. Latex + 14 postscript files, bundled using
uufiles. Needs psfig.) UW/PT-93-0
Chiral 3-exchange NN-potentials: Results for dominant next-to-leading order contributions
We calculate in (two-loop) chiral perturbation theory the local NN-potentials
generated by the three-pion exchange diagrams with one insertion from the
second order chiral effective pion-nucleon Lagrangian proportional to the
low-energy constants . The resulting isoscalar central potential
vanishes identically. In most cases these -exchange potentials are larger
than the ones generated by the diagrams involving only leading order vertices
due to the large values of (which mainly represent virtual
-excitation). A similar feature has been observed for the chiral
-exchange. We also give suitable (double-integral) representations for
the spin-spin and tensor potentials generated by the leading-order diagrams
proportional to involving four nucleon propagators. In these cases the
Cutkosky rule cannot be used to calculate the spectral-functions in the
infinite nucleon mass limit since the corresponding mass-spectra start with a
non-vanishing value at the -threshold. Altogether, one finds that chiral
-exchange leads to small corrections in the region fm where
- and chiral -exchange alone provide a very good strong NN-force as
shown in a recent analysis of the low-energy pp-scattering data-base.Comment: 11 pages, 7 figures, to be published in The Physical Review
Electric quadrupole and magnetic dipole moments of odd nuclei near the magic ones in a self-consistent approach
We present a model which describes the properties of odd-even nuclei with one
nucleon more, or less, with respect to the magic number. In addition to the
effects related to the unpaired nucleon, we consider those produced by the
excitation of the closed shell core. By using a single particle basis generated
with Hartree-Fock calculations, we describe the polarization of the doubly
magic-core with Random Phase Approximation collective wave functions. In every
step of the calculation, and for all the nuclei considered, we use the same
finite-range nucleon-nucleon interaction. We apply our model to the evaluation
of electric quadrupole and magnetic dipole moments of odd-even nuclei around
oxygen, calcium, zirconium, tin and lead isotopes. Our Random Phase
Approximation description of the polarization of the core improves the
agreement with experimental data with respect to the predictions of the
independent particle model. We compare our results with those obtained in
first-order perturbation theory, with those produced by
Hartree-Fock-Bogolioubov calculations and with those generated within the
Landau-Migdal theory of finite Fermi systems. The results of our universal,
self-consistent, and parameter free approach have the same quality of those
obtained with phenomenological approaches where the various terms of the
nucleon-nucleon interaction are adapted to reproduce some specific experimental
data. A critical discussion on the validity of the model is presented.Comment: 18 pages, 7 figures, 7 table
Applications of Partially Quenched Chiral Perturbation Theory
Partially quenched theories are theories in which the valence- and sea-quark
masses are different. In this paper we calculate the nonanalytic one-loop
corrections of some physical quantities: the chiral condensate, weak decay
constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude,
using partially quenched chiral perturbation theory. Our results for weak decay
constants and masses agree with, and generalize, results of previous work by
Sharpe. We compare B_K and the K+ decay amplitude with their real-world values
in some examples. For the latter quantity, two other systematic effects that
plague lattice computations, namely, finite-volume effects and unphysical
values of the quark masses and pion external momenta are also considered. We
find that typical one-loop corrections can be substantial.Comment: 22 pages, TeX, refs. added, minor other changes, version to appear in
Phys. Rev.
On the Existence of Radiation Gauges in Petrov type II spacetimes
The radiation gauges used by Chrzanowski (his IRG/ORG) for metric
reconstruction in the Kerr spacetime seem to be over-specified. Their
specification consists of five conditions: four, which we treat here as valid
gauge conditions, plus an additional condition on the trace of the metric
perturbation. In this work, we utilize a newly developed form of the perturbed
Einstein equations to establish a condition -- on a particular tetrad component
of the stress-energy tensor -- under which the full IRG/ORG can be imposed.
Using gauge freedom, we are able to impose the full IRG for Petrov type II and
type D backgrounds, using a different tetrad for each case. As a specific
example, we work through the process of imposing the IRG in a Schwarzschild
background, using a more traditional approach. Implications for metric
reconstruction using the Teukolsky curvature perturbations in type D spacetimes
are briefly discussed.Comment: 21 pages, uses iop style files. v2: proved a stronger result for type
II backgrounds, added a subsection on remaining gauge freedom in the full IRG
and improved calrity and readability throughout due to insightful referee
comments; published as Class. Quantum Grav. 24 (2007) 2367-238
On the number of Mather measures of Lagrangian systems
In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact
the minimizers of a "universal" infinite dimensional linear programming
problem. This fundamental result has many applications, one of the most
important is to the estimates of the generic number of Mather measures.
Ma\~n\'e obtained the first estimation of that sort by using finite dimensional
approximations. Recently, we were able with Gonzalo Contreras to use this
method of finite dimensional approximation in order to solve a conjecture of
John Mather concerning the generic number of Mather measures for families of
Lagrangian systems. In the present paper we obtain finer results in that
direction by applying directly some classical tools of convex analysis to the
infinite dimensional problem. We use a notion of countably rectifiable sets of
finite codimension in Banach (and Frechet) spaces which may deserve independent
interest
Towards an understanding of isospin violation in pion-nucleon scattering
We investigate isospin breaking in low-energy pion-nucleon scattering in the
framework of chiral perturbation theory. This work extends the systematic
analysis of [1] to the energy range above threshold. Various relations, which
identically vanish in the limit of isospin symmetry, are used to quantify
isospin breaking effects. We study the energy dependence of the S- and P-wave
projections of these ratios and find dramatic effects in the S-waves of those
two relations which are given in terms of isoscalar quantities only. This
effect drops rather quickly with growing center-of-mass energy.Comment: 12 pp, REVTeX, 8 figs, FZJ-IKP(TH)-2000-2
Light Hadron Spectrum in Quenched Lattice QCD with Staggered Quarks
Without chiral extrapolation, we achieved a realistic nucleon to (\rho)-meson
mass ratio of (m_N/m_\rho = 1.23 \pm 0.04 ({\rm statistical}) \pm 0.02 ({\rm
systematic})) in our quenched lattice QCD numerical calculation with staggered
quarks. The systematic error is mostly from finite-volume effect and the
finite-spacing effect is negligible. The flavor symmetry breaking in the pion
and (\rho) meson is no longer visible. The lattice cutoff is set at 3.63 (\pm)
0.06 GeV, the spatial lattice volume is (2.59 (\pm) 0.05 fm)(^3), and bare
quarks mass as low as 4.5 MeV are used. Possible quenched chiral effects in
hadron mass are discussed.Comment: 5 pages and 5 figures, use revtex
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