103 research outputs found
The Effective Field Theory of Dark Matter Direct Detection
We extend and explore the general non-relativistic effective theory of dark
matter (DM) direct detection. We describe the basic non-relativistic building
blocks of operators and discuss their symmetry properties, writing down all
Galilean-invariant operators up to quadratic order in momentum transfer arising
from exchange of particles of spin 1 or less. Any DM particle theory can be
translated into the coefficients of an effective operator and any effective
operator can be simply related to most general description of the nuclear
response. We find several operators which lead to novel nuclear responses.
These responses differ significantly from the standard minimal WIMP cases in
their relative coupling strengths to various elements, changing how the results
from different experiments should be compared against each other. Response
functions are evaluated for common DM targets - F, Na, Ge, I, and Xe - using
standard shell model techniques. We point out that each of the nuclear
responses is familiar from past studies of semi-leptonic electroweak
interactions, and thus potentially testable in weak interaction studies. We
provide tables of the full set of required matrix elements at finite momentum
transfer for a range of common elements, making a careful and fully
model-independent analysis possible. Finally, we discuss embedding
non-relativistic effective theory operators into UV models of dark matter.Comment: 32+23 pages, 5 figures; v2: some typos corrected and definitions
clarified; v3: some factors of 4pi correcte
Isospin breaking corrections to nucleon form factors in the constituent quark model
We examine isospin breaking in the nucleon wave functions due to the
quark mass difference and the Coulomb interaction among the quarks, and their
consequences on the nucleon electroweak form factors in a nonrelativistic
constituent quark model. The mechanically induced isospin breaking in the
nucleon wave functions and electroweak form factors are exactly evaluated in
this model. We calculate the electromagnetically induced isospin admixtures by
using first-order perturbation theory, including the lowest-lying resonance
with nucleon quantum numbers but isospin 3/2. We find a small (), but
finite correction to the anomalous magnetic moments of the nucleon stemming
almost entirely from the quark mass difference, while the static nucleon axial
coupling remains uncorrected. Corrections of the same order of magnitude appear
in charge, magnetic, and axial radii of the nucleon. The correction to the
charge radius in this model is primarily isoscalar, and may be of some
significance for the extraction of the strangeness radius from e.g. elastic
forward angle parity violating electron-proton asymmetries, or elastic
experiments.Comment: 15 pp(22 as preprint), revtex, 3 uuencoded figs at end of this fil
Levinson's Theorem for Dirac Particles
Levinson's theorem for Dirac particles constraints the sum of the phase
shifts at threshold by the total number of bound states of the Dirac equation.
Recently, a stronger version of Levinson's theorem has been proven in which the
value of the positive- and negative-energy phase shifts are separately
constrained by the number of bound states of an appropriate set of
Schr\"odinger-like equations. In this work we elaborate on these ideas and show
that the stronger form of Levinson's theorem relates the individual phase
shifts directly to the number of bound states of the Dirac equation having an
even or odd number of nodes. We use a mean-field approximation to Walecka's
scalar-vector model to illustrate this stronger form of Levinson's theorem. We
show that the assignment of bound states to a particular phase shift should be
done, not on the basis of the sign of the bound-state energy, but rather, in
terms of the nodal structure (even/odd number of nodes) of the bound state.Comment: Latex with Revtex, 7 postscript figures (available from the author),
SCRI-06109
Nuclear dependence of the coherent eta photoproduction reaction in a relativistic approach
We study the nuclear (or A) dependence of the coherent eta photoproduction
reaction in a relativistic impulse approximation approach. We use a standard
relativistic parameterization of the elementary amplitude, based on a set of
four Lorentz- and gauge-invariant amplitudes, to calculate the coherent
production cross section from He-4, C-12, and Ca-40. In contrast to
nonrelativistic treatments, our approach maintains the full relativistic
structure of the process. The nuclear structure affects the process through the
ground-state tensor density. This density is sensitive to relativistic effects
and depends on A in a different manner than the vector density used in
nonrelativistic approaches. This peculiar dependence results in He-4 having a
cross section significantly smaller than that of C-12---in contrast to existent
nonrelativistic calculations. Distortion effects are incorporated through an
eta-nucleus optical potential that is computed in a simple ``t rho''
approximation.Comment: 4 pages, 3 postscript figures. The replace is due to a misspelling in
the Authors' lis
-mass Modification in - a Signal of Restoration of Chiral Symmetry or Test for Nuclear Matter Models ?
Two recent experiments have demonstrated that the effective -mass in
nuclear medium, as extracted from the reaction, is
substantially reduced. This has been advocated as an indication of partial
restoration of chiral symmetry in nuclear matter. We show that even in the
absence of chiral symmetry, effective mean field nuclear matter models can
explain these findings quantitatively.Comment: ReVTeX file with 2 postscript figures include
Neutrino capture by r-process waiting-point nuclei
We use the Quasiparticle Random Phase Approximation to include the effects of
low-lying Gamow-Teller and first forbidden strength in neutrino capture by very
neutron-rich nuclei with N = 50, 82, or 126. For electron neutrinos in what is
currently considered the most likely r-process site the capture cross sections
are two or more times previous estimates. We briefly discuss the reliability of
our calculations and their implications for nucleosynthesis.Comment: 9 pages, 4 figure
Friedel Oscillations in Relativistic Nuclear Matter
We calculate the low-momentum N-N effective potential obtained in the OBE
approximation, inside a nuclear plasma at finite temperature, as described by
the relativistic - model. We analyze the screening effects
on the attractive part of the potential in the intermediate range as density or
temperature increase. In the long range the potential shows Friedel-like
oscillations instead of the usual exponential damping. These oscillations arise
from the sharp edge of the Fermi surface and should be encountered in any
realistic model of nuclear matter.Comment: 11 pages in preprint format, typeset using REVTEX, 3 included figures
in tar, compressed, uuencoded forma
Density Dependent Hadron Field Theory
A fully covariant approach to a density dependent hadron field theory is
presented. The relation between in--medium NN interactions and
field--theoretical meson--nucleon vertices is discussed. The medium dependence
of nuclear interactions is described by a functional dependence of the
meson--nucleon vertices on the baryon field operators. As a consequence, the
Euler--Lagrange equations lead to baryon rearrangement self--energies which are
not obtained when only a parametric dependence of the vertices on the density
is assumed. It is shown that the approach is energy--momentum conserving and
thermodynamically consistent. Solutions of the field equations are studied in
the mean--field approximation. Descriptions of the medium dependence in terms
of the baryon scalar and vector density are investigated. Applications to
infinite nuclear matter and finite nuclei are discussed. Density dependent
coupling constants obtained from Dirac--Brueckner calculations with the Bonn
NN-potentials are used. Results from Hartree calculations for energy spectra,
binding energies and charge density distributions of , and
are presented. Comparisons to data strongly support the importance
of rearrangement in a relativistic density dependent field theory. Most
striking is the simultanuous improvement of charge radii, charge densities and
binding energies. The results indicate the appearance of a new "Coester line"
in the nuclear matter equation of state.Comment: 48 LateX pages, 12 Figures, figures and full paper are available as
postscript files by anonymous ftp at ftp://theorie.physik.uni-giessen.de/dd
Excluded Volume Effects in the Quark Meson Coupling Model
Excluded volume effects are incorporated in the quark meson coupling model to
take into account in a phenomenological way the hard core repulsion of the
nuclear force. The formalism employed is thermodynamically consistent and does
not violate causality. The effects of the excluded volume on in-medium nucleon
properties and the nuclear matter equation of state are investigated as a
function of the size of the hard core. It is found that in-medium nucleon
properties are not altered significantly by the excluded volume, even for large
hard core radii, and the equation of state becomes stiffer as the size of the
hard core increases.Comment: 14 pages, revtex, 6 figure
Quasifree kaon-photoproduction from nuclei in a relativistic approach
We compute the recoil polarization of the lambda-hyperon and the photon
asymmetry for the quasifree photoproduction of kaons in a relativistic
impulse-approximation approach. Our motivation for studying polarization
observables is threefold. First, polarization observables are more effective
discriminators of subtle dynamics than the unpolarized cross section. Second,
earlier nonrelativistic calculations suggest an almost complete insensitivity
of polarization observables to distortions effects. Finally, this insensitivity
entails an enormous simplification in the theoretical treatment. Indeed, by
introducing the notion of a ``bound-nucleon propagator'' we exploit Feynman's
trace techniques to develop closed-form, analytic expressions for all
photoproduction observables. Moreover, our results indicate that polarization
observables are also insensitive to relativistic effects and to the nuclear
target. Yet, they are sensitive to the model parameters, making them ideal
tools for the study of modifications to the elementary amplitude --- such as in
the production, propagation, and decay of nucleon resonances --- in the nuclear
medium.Comment: 15 pages and 6 figures - submitted to PR
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