164 research outputs found
Dispersion relations and the spin polarizabilities of the nucleon
A forward dispersion calculation is implemented for the spin polarizabilities
of the proton and the neutron. These polarizabilities
are related to the spin structure of the nucleon at low energies and are
structure-constants of the Compton scattering amplitude at . In the absence of a direct experimental measurement of these
quantities, a dispersion calculation serves the purpose of constraining the
model building, and of comparing with recent calculations in heavy baryon
chiral perturbation theory.Comment: 14 pages Latex, 1 ps figur
The E2/M1 and C2/M1 ratios and form factors in N -> Delta transitions
A partial wave analysis of pion photoproduction has been obtained in the
framework of fixed-t dispersion relations valid from threshold up to 500 MeV.
In the resonance region we have precisely determined the electromagnetic
properties of the \Delta(1232) resonance, in particular the E2/M1 ratio
R_{EM}=(-2.5 +- 0.1) %. For pion electroproduction recent experimental data
from Mainz, Bates and JLab for Q^2 up to 4.0 (GeV/c)^2 have been analyzed with
two different models, an isobar model (MAID) and a dynamical model. The E2/M1
ratios extracted with these two models show, starting from a small and negative
value at the real photon point, a clear tendency to cross zero, and become
positive with increasing Q^2. This is a possible indication of a very slow
approach toward the pQCD region. The C2/M1 ratio near the photon point is found
as R_{SM}(0)=(-6.5 +- 0.5) %. At high Q^2 the absolute value of the ratio is
strongly increasing, a further indication that pQCD is not yet reached.Comment: 10 pages LaTeX including 3 figures. Talk given at the XVIIth European
conference on Few-Body Problems in Physics, Evora, Portugal, 11 - 16
September 2000; to be published in Nucl.Phys.
A dispersion theoretical approach to the threshold amplitudes of pion photoproduction
We give predictions for the partial wave amplitudes of pion photoproduction
near threshold by means of dispersion relations at fixed t. The free parameters
of this approach are determined by a fit to experimental data in the energy
range 160 MeV 420 MeV. The observables near threshold are
found to be rather sensitive to the amplitudes in the resonance region, in
particular to the (1232) and (1440). We obtain a good agreement
with the existing threshold data for both charged and neutral pion production.
Our predictions also agree well with the results of chiral perturbation theory,
except for neutral pion production off the neutron.Comment: 16 pages LATEX including 4 postscript figure
Radiative pion capture by a nucleon
The differential cross sections for and are computed up to in heavy baryon chiral perturbation
theory (HBChPT). The expressions at and have no free
parameters. There are three unknown parameters at , low energy
constants of the HBChPT Lagrangian, which are determined by fitting to
experimental data. Two acceptable fits are obtained, which can be separated by
comparing with earlier dispersion relation calculations of the inverse process.
Expressions for the multipoles, with emphasis on the p-wave multipoles, are
obtained and evaluated at threshold. Generally the results obtained from the
best of the two fits are in good agreement with the dispersion relation
predictions.Comment: 24 pages, Latex, using RevTe
Multipole analysis of pion photoproduction based on fixed t dispersion relations and unitarity
We have analysed pion photoproduction imposing constraints from fixed t
dispersion relations and unitarity. Coupled integral equations for the S and P
wave multipoles were derived from the dispersion relations and solved by the
method of Omnes and Muskhelishvili. The free parameters were determined by a
fit to the most recent data for \pi^{+} and \pi^{0} production on the proton as
well as \pi^{-} production on the neutron, in the energy We have analysed pion
photoproduction imposing constraints from fixed t dispersion relations and
unitarity. Coupled integral equations for the S and P wave multipoles were
derived from the dispersion relations and solved by the method of Omnes and
Muskhelishvili. The free parameters were determined by a fit to the most recent
data for \pi^{+} and \pi^{0} production on the proton as well as \pi^{-}
production on the neutron, in the energy range 160 MeV \leq E_{\gamma} \leq 420
MeV. The lack of high precision data on the neutron and of polarization
observables leads to some limitations of our results. Especially the multipole
M_{1-} connected with the Roper resonance P_{11}(1440) cannot be determined to
the required precision. Our predictions for the threshold amplitudes are in
good agreement with both the data and chiral perturbation theory. In the region
of the \Delta(1232) we have determined the ratio of electric quadrupole and
magnetic dipole excitation. The position of the resonance pole is obtained in
excellent agreement with pion-nucleon scattering, and the complex residues of
the multipoles are determined with the speed-plot technique.Comment: 46 pages LATEX including 29 postscript figure
A unitary isobar model for pion photo- and electroproduction on the proton up to 1 GeV
A new operator for pion photo- and electroproduction has been developed for
nuclear applications at photon equivalent energies up to 1 GeV. The model
contains Born terms, vector mesons and nucleon resonances (,
, , , , and
). The resonance contributions are included taking into account
unitarity to provide the correct phases of the pion photoproduction multipoles.
The dependence of electromagnetic resonance vertices is described with
appropriate form factors in the electromagnetic helicity amplitudes. Within
this model we have obtained good agreement with the experimental data for pion
photo- and electroproduction on the nucleon for both differential cross
sections and polarization observables. The model can be used as a starting
point to predict and analyze forthcoming data.Comment: 32 pages LaTeX including 23 postscript figures (a few misprints have
been corrected
Radiative decays of decuplet hyperons
We calculate the radiative decay widths of decuplet hyperons in a chiral
constituent quark model including electromagnetic exchange currents between
quarks. Exchange currents contribute significantly to the E2 transition
amplitude, while they largely cancel for the M1 transition amplitude.
Strangeness suppression of the radiative hyperon decays is found to be weakened
by exchange currents. Differences and similarities between our results and
other recent model predictions are discussed.Comment: 11 pages, 1 eps figure, revtex, accepted for publication in Phys.
Rev.
Compton scattering in a unitary approach with causality constraints
Pion-loop corrections for Compton scattering are calculated in a novel
approach based on the use of dispersion relations in a formalism obeying
unitarity. The basic framework is presented, including an application to
Compton scattering. In the approach the effects of the non-pole contribution
arising from pion dressing are expressed in terms of (half-off-shell) form
factors and the nucleon self-energy. These quantities are constructed through
the application of dispersion integrals to the pole contribution of loop
diagrams, the same as those included in the calculation of the amplitudes
through a K-matrix formalism. The prescription of minimal substitution is used
to restore gauge invariance. The resulting relativistic-covariant model
combines constraints from unitarity, causality, and crossing symmetry.Comment: 25 pages, 9 ps-figure
Non-linear doublon production in a Mott insulator --- Landau-Dykhne method applied to an integrable model
Doublon-hole pair production which takes place during dielectric breakdown in
a Mott insulator subject to a strong laser or a static electric field is
studied in the one-dimensional Hubbard model. Two nonlinear effects cause the
excitation, i.e., multi-photon absorption and quantum tunneling. Keldysh
crossover between the two mechanisms occurs as the field strength and photon
energy is changed. The calculation is done analytically by the Landau-Dykhne
method in combination with the Bethe ansatz solution and the results are
compared with those of the time dependent density matrix renormalization group.
Using this method, we calculate distribution function of the generated
doublon-hole pairs and show that it drastically changes as we cross the Keldysh
crossover line. After calculating the tunneling threshold for several
representative one-dimensional Mott insulators, possible experimental tests of
the theory is proposed such as angle resolved photoemission spectroscopy of the
upper Hubbard band in the quantum tunneling regime. We also discuss the
relation of the present theory with a many-body extension of electron-positron
pair production in nonlinear quantum electrodynamics known as the Schwinger
mechanism.Comment: 15 page
Low-Energy Compton Scattering of Polarized Photons on Polarized Nucleons
The general structure of the cross section of scattering with
polarized photon and/or nucleon in initial and/or final state is systematically
described and exposed through invariant amplitudes. A low-energy expansion of
the cross section up to and including terms of order is given which
involves ten structure parameters of the nucleon (dipole, quadrupole,
dispersion, and spin polarizabilities). Their physical meaning is discussed in
detail. Using fixed-t dispersion relations, predictions for these parameters
are obtained and compared with results of chiral perturbation theory. It is
emphasized that Compton scattering experiments at large angles can fix the most
uncertain of these structure parameters. Predictions for the cross section and
double-polarization asymmetries are given and the convergence of the expansion
is investigated. The feasibility of the experimental determination of some of
the struture parameters is discussed.Comment: 41 pages of text, 9 figures; minor revisions prior to publication in
Phys. Rev.
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