18,065 research outputs found
(j,0)+(0,j) Covariant spinors and causal propagators based on Weinberg formalism
A pragmatic approach to constructing a covariant phenomenology of the
interactions of composite, high-spin hadrons is proposed. Because there are no
known wave equations without significant problems, we propose to construct the
phenomenology without explicit reference to a wave equation. This is done by
constructing the individual pieces of a perturbation theory and then utilizing
the perturbation theory as the definition of the phenomenology. The covariant
spinors for a particle of spin are constructed directly from Lorentz
invariance and the basic precepts of quantum mechanics following the logic put
forth originally by Wigner and developed by Weinberg. Explicit expressions for
the spinors are derived for j=1, 3/2 and 2. Field operators are constructed
from the spinors and the free-particle propagator is derived from the vacuum
expectation value of the time-order product of the field operators. A few
simple examples of model interactions are given. This provides all the
necessary ingredients to treat at a phenomenological level and in a covariant
manner particles of arbitrary spin.Comment: tex file, 52 page
Microscopic approach to pion-nucleus dynamics
Elastic scattering of pions from finite nuclei is investigated utilizing a
contemporary, momentum--space first--order optical potential combined with
microscopic estimates of second--order corrections. The calculation of the
first--order potential includes:\ \ (1)~full Fermi--averaging integration
including both the delta propagation and the intrinsic nonlocalities in the
- amplitude, (2)~fully covariant kinematics, (3)~use of invariant
amplitudes which do not contain kinematic singularities, and (4)~a
finite--range off--shell pion--nucleon model which contains the nucleon pole
term. The effect of the delta--nucleus interaction is included via the mean
spectral--energy approximation. It is demonstrated that this produces a
convergent perturbation theory in which the Pauli corrections (here treated as
a second--order term) cancel remarkably against the pion true absorption terms.
Parameter--free results, including the delta--nucleus shell--model potential,
Pauli corrections, pion true absorption, and short--range correlations are
presented. (2 figures available from authors)Comment: 13 page
On the degeneracies of the mass-squared differences for three-neutrino oscillations
Using an algebraic formulation, we explore two well-known degeneracies
involving the mass-squared differences for three-neutrino oscillations assuming
CP symmetry is conserved. For vacuum oscillation, we derive the expression for
the mixing angles that permit invariance under the interchange of two
mass-squared differences. This symmetry is most easily expressed in terms of an
ascending mass order. This can be used to reduce the parameter space by one
half in the absence of the MSW effect. For oscillations in matter, we derive
within our formalism the known approximate degeneracy between the standard and
inverted mass hierarchies in the limit of vanishing . This is done
with a mass ordering that permits the map .
Our techniques allow us to translate mixing angles in this mass order
convention into their values for the ascending order convention. Using this
dictionary, we demonstrate that the vacuum symmetry and the approximate
symmetry invoked for oscillations in matter are distinctly different.Comment: 5 pages, revised manuscrip
Extracting forward strong amplitudes from elastic differential cross sections
The feasibility of a model-independent extraction of the forward strong
amplitude from elastic nuclear cross section data in the Coulomb-nuclear
interference region is assessed for and scattering at intermediate
energies. Theoretically-generated "data" are analyzed to provide criteria for
optimally designing experiments to measure these amplitudes, whose energy
dependence (particularly that of the real parts) is needed for disentangling
various sources of medium modifications of the projectile-nucleon interaction.
The issues considered include determining the angular region over which to make
the measurements, the role of the most forward angles measured, and the effects
of statistical and systematic errors. We find that there is a region near the
forward direction where Coulomb-nuclear interference allows reliable extraction
of the strong forward amplitude for both pions and the from .3 to 1
GeV/c.Comment: 16 pages plus 12 separate postscript figure
On detecting CP violation in a single neutrino oscillation channel at very long baselines
We propose a way of detecting CP violation in a single neutrino oscillation
channel at very long baselines (on the order of several thousands of
kilometers), given precise knowledge of the smallest mass-squared difference.
It is shown that CP violation can be characterized by a shift in of the
peak oscillation in the -- appearance channel, both in vacuum
and in matter. In fact, matter effects enhance the shift at a fixed energy. We
consider the case in which sub-GeV neutrinos are measured with varying baseline
and also the case of a fixed baseline. For the varied baseline, accurate
knowledge of the absolute neutrino flux would not be necessary; however,
neutrinos must be distinguishable from antineutrinos. For the fixed baseline,
it is shown that CP violation can be distinguished if the mixing angle
were known.Comment: 8 pages, 9 figures; minor typos correcte
Measuring the mass of a sterile neutrino with a very short baseline reactor experiment
An analysis of the world's neutrino oscillation data, including sterile
neutrinos, (M. Sorel, C. M. Conrad, and M. H. Shaevitz, Phys. Rev. D 70,
073004) found a peak in the allowed region at a mass-squared difference eV. We trace its origin to harmonic oscillations in the
electron survival probability as a function of L/E, the ratio of
baseline to neutrino energy, as measured in the near detector of the Bugey
experiment. We find a second occurrence for eV. We
point out that the phenomenon of harmonic oscillations of as a
function of L/E, as seen in the Bugey experiment, can be used to measure the
mass-squared difference associated with a sterile neutrino in the range from a
fraction of an eV to several eV (compatible with that indicated by the
LSND experiment), as well as measure the amount of electron-sterile neutrino
mixing. We observe that the experiment is independent, to lowest order, of the
size of the reactor and suggest the possibility of a small reactor with a
detector sitting at a very short baseline.Comment: 4 pages, 2 figure
- …