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 $\pi$-$N$ 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 $\theta_{13}$. This is done with a mass ordering that permits the map $\Delta_{31} \mapsto -\Delta_{31}$. 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

Charging axisymmetric space-times with cosmological constant

Ernst's solution generating technique for adding electromagnetic charge to axisymmetric space-times in general relativity is generalised in presence of the cosmological constant. Ernst equations for complex potentials are found and they are traced back to an affective dual complex dynamical system, whose symmetries are studied. In particular this method is able to generate charged, asymptotically (A)dS black holes from their uncharged version: as an example, it is shown explicitly how to pass from the Kerr-(A)dS to the Kerr-Newman-(A)dS metric. A new solution describing a magnetic universe in presence of the cosmological constant is also generated.Comment: 15 pages, v2: typos correcte

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 $\pi$ and $K^+$ 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 $K^+$ 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 $L/E$ of the peak oscillation in the $\nu_e$--$\nu_\mu$ 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 $\theta_{13}$ were known.Comment: 8 pages, 9 figures; minor typos correcte