Within a conventional Hamiltonian description, we find accurate closed-form expressions for the oscillation probabilities of three coupled neutrinos propagating in matter. Subtle cancelations that occur in coefficients of our formulation are avoided for all transitions $\nu_a \to \nu_b$ by transforming to a different set of coefficients presented in an appendix of this paper. The neutrino mass eigenvalues are easily obtained numerically as the solution of a cubic equation. Our methods are illustrated for flavor-changing transitions in the $(\nu_e,\nu_\mu)$ sector. The resulting analytic expressions oscillation probabilities, which are particularly simple, are also accurate to a few percent over all regions of interest at present and the envisioned future neutrino facilities. While somewhat less accurate than numerical simulations, our approximate expressions are sufficiently accuracy to obviate the need for exact computer simulations in many circumstances.

We develop an exact analytical formulation of neutrino oscillations in matter within the framework of the standard neutrino model assuming three Dirac neutrinos. Our Hamiltonian formulation, which includes CP violation, leads to expressions for the partial oscillation probabilities that are linear combinations of spherical Bessel functions in the eigenvalue differences. The coefficients of these Bessel functions are polynomials in the neutrino CKM matrix elements, the neutrino mass differences squared, the strength of the neutrino interaction with matter, and the neutrino mass eigenvalues in matter. We give exact closedform expressions for all partial oscillation probabilities in terms of these basic quantities. Adopting the standard neutrino model, we then examine how the exact expressions for the partial oscillation probabilities might simplify by expanding in one of the small parameters a and sin. 13 of this model. We show explicitly that for small a and sin. 13, there are branch points in the analytic structure of the eigenvalues that lead to singular behavior of expansions near the solar and atmospheric resonances. We present numerical calculations that indicate how to use the small-parameter expansions in practice.

We examine the reliability of the theoretical methods presently used for analysis and prediction of neutrino oscillation phenomena. Of particular interest are the limitations imposed by branch points when expansions in one of the small parameters of the Standard Neutrino Model (SNM) are made to obtain tractable results. Our evaluation compares the approximate oscillation probabilities for flavor-changing transitions in the $(ν_e , ν_μ)$ sector to exact results obtained from of a recently-developed exact analytical representation of neutrino oscillations in matter within the SNM. From our numerical comparisons, we are able to identify regions where the existing approaches can be improved to take full advantage of the higher quality data expected at future neutrino facilities.

We estimate the dependence of νμ to νe conversion on parameters θ13 and δ CP for several experimental facilities studying neutrino oscillations. We use the S-Matrix theory to estimate νe disappearance and compare estimates based on an older theory being used to extract θ13 from the Double Chooz, Daya Bay, and RENO data, to assist in extracting an accurate value for θ13 from these projects. We use values of θ13 within known limits, and estimate the dependence of νμ-νe CP violation (CPV) probability on δ CP in order to suggest new experiments to measure CPV for neutrinos moving in matter.

We calculate the momentum given to a proto neutron star during the first 10 seconds after temperature equilibrium is reached, using recent evidence of sterile neutrinos and a measurement of the mixing angle. This is a continuation of an earlier estimate with a wide range of possible mixing angles. Using the new mixing angle we find that sterile neutrinos can account for the observed pulsar velocities.

We present a theory of the generation of magnetic fields in bubble collisions during the electroweak phase transition, which may be first order in various extensions of the standard model, for example, the minimal supersymmetric standard model. Using the equations of motion determined from an effective minimal supersymmetric standard model Lagrangian, we derive the magnetic field using a model of gentle collisions of the electroweak phase transition bubbles, discussed in our earlier work. Solutions of the relevant equations of motion for the magnetic field are examined in O(1,2) space-time symmetry with boundary conditions applied at the time of collision. These solutions indicate that the magnetic fields evolving from our equations of motion are somewhat larger in magnitude and extend more uniformly through the available volume of the bubble than those found in the Abelian Higgs model. The magnetic fields so produced might possibly seed galactic and extragalactic magnetic fields observed today.

We estimate CP violation for several experimental facilities studying neutrino oscillations. We also estimate the probability of �µ to �e conversion in order to suggest new experiments to measure CP violation for neutrinos moving in matter.

This is an extension of the L-2L experiment for measurement of time reversal violation (TRV) proposed in a recent publication. The main new aspects are taking into account the curvature of the earth's surface for long baseline neutrino beams, and recognizing that the matter effects disappear when the baseline is extended. A slight modification of the MINOS project, with a new detector at 2L, is proposed.

We estimate the time reversal violations for neutrino oscillations in matter for typical experimental energies and baselines. We examine the present status of experiments on neutrino oscillations, propose experiments for TRV, and discuss the future.

We present a theory of the generation of magnetic seed fields in bubble collisions during a first-order electroweak phase transition (EWPT) possible for some choices of parameters in the minimal supersymmetric Standard Model. The theory extends earlier work and is formulated to assess the importance of surface dynamics in such collisions. We are led to linearized equations of motion with O(3) symmetry appropriate for examining collisions in which the Higgs field is relatively unperturbed from its mean value in the collision volume. Coherent evolution of the charged $W$ fields within the bubbles is the main source of the electromagnetic current for generating the seed fields, with fermions also contributing through the conductivity terms. We present numerical simulations within this formulation to quantify the role of the surface of the colliding bubbles, particularly the thickness of the surface, and to show how conclusions drawn from earlier work are modified. The main sensitivity arises such that the steeper the bubble surface the more enhanced the seed fields become. Consequently, the magnetic seed fields may be several times larger and smoother over the collision volume than found in earlier studies. Our work thus provides additional support to the supposition that magnetic fields produced during the EWPT in the early universe seed the galactic and extra-galactic magnetic fields observed today.

Using EW-MSSM field theory, so the electroweak phase transition (EWPT) is first order, we derive the equations of motion (e.o.m.) for the gauge fields. With an isospin ansatz we derive e.o.m. for the electrically charged W fields uncoupled from all other fields. These and the lepton currents serve as the current for the Maxwell-like e.o.m. for the electromagnetic field. The electromagnetic field arising during EWPT bubble nucleation without leptons is found. We then calculate the electron current contribution, which is seen to be quite large. This provides the basis for determining the magnetic field created by EWPT bubble collisions, which could seed galactic and extragalactic magnetic fields.

Building on earlier work, we develop an equation-of-motion method for calculating magnetic seed fields generated from currents arising from charged W-+/- fields in bubble collisions during a first-order primordial electroweak phase transition allowed in some proposed extensions of the standard model. The novel feature of our work is that it takes into account, for the first time, the dynamics of the bubble walls in such collisions. We conclude that for bubbles with sufficiently thin surfaces the magnetic seed fields may be comparable to, or larger than, those found in earlier work. Thus, our results strengthen the conclusions of previous studies that cosmic magnetic fields observed today may originate from seeds created during the electroweak phase transition, and consequently that these fields may offer a clue relevant to extensions of the standard model.

We investigate the momentum given to a protoneutron star, the pulsar kick, during the first ten seconds after temperature equilibrium is reached. Using a model with two sterile neutrinos obtained by fits to the MiniBooNE and LSND experiments, which is consistent with a new global fit, there is a large mixing angle, and the effective volume for emission is calculated. Using formulations with neutrinos created by URCA processes in a strong magnetic field, so the lowest Landau level has a sizable probability, we find that with known parameters, the asymmetric sterile neutrino emissivity might account for large pulsar kicks.

We calculate the magnetic field generated during bubble collisions in a first-order electroweak phase transition that may occur for some choices of parameters in the minimal supersymmetric standard model. We derive equations of motion from the electroweak Lagrangian that couple the Higgs field and the gauge fields of the standard model sector. We show that for sufficiently gentle collisions, where the Higgs field is relatively unperturbed in the bubble overlap region, the equations of motion can be linearized so that in the absence of fermions the charged W-+/- fields are the source of the electromagnetic current for generating the seed fields. Solutions of the equations of motion for the charged gauge fields and Maxwell's equations for the magnetic field in O(1,2) space-time symmetry are expressed in closed form by applying boundary conditions at the time of collision. Our results indicate that the magnetic fields generated by charged W-+/- fields in the collision are comparable to those found in previous work. The magnetic fields so produced could seed galactic and extra-galactic magnetic fields observed today.

We derive the energy asymmetry given the protoneutron star during the time when the neutrino sphere is near the surface of the protoneutron star, using the modified Urca process. The electrons produced with the antineutrinos are in Landau levels due to the strong magnetic field, and this leads to asymmetry in the neutrino momentum, and a pulsar kick. The magnetic field must be strong enough for a large fraction of the electrons to be in the lowest Landau level; however, there is no direct dependence of our pulsar velocity on the strength of the magnetic field. Our main prediction is that the large pulsar kicks start at about 10 s and last for about 10 s, with the corresponding neutrinos correlated with the direction of the magnetic field. We predict a pulsar velocity of $1.03\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}(T/{10}^{10}\text{ }\mathrm{K}{)}^{7}\text{ }\text{ }\mathrm{km}/s$, which reaches $1000\text{ }\text{ }\mathrm{km}/s$ if $T\ensuremath{\simeq}{10}^{11}\text{ }\mathrm{K}$.

We derive the equations of motion for electroweak MSSM with a right-handed Stop, from which we derive the equations for the electromagnetic field that arises from bubble nucleation and collisions during the first order electroweak phase transition that can occur in this MSSM. Introducing an isospin ansatz we derive e.o.m. for the electrically charged W fields uncoupled from all other fields. These serve as the current for the Maxwell-like e.o.m. for the em field. The resulting electromagnetic field arising during EWPT bubble nucleation is found. This electromagnetic structure, along with that arising from bubble collisions, could seed galactic and extra-galactic magnetic fields.

The color dipole approach has been applied in the target rest frame to address the issues of transverse momentum broadening and energy loss of a fast quark propagating in the nuclear medium. A recent application of the theory to the FermiLab E772/E866 experimental data, determining the rate of energy loss of a quark propagating in the medium to be 2 to 3 GeV/fm, will be reviewed. Calculations for the transverse momentum distribution will be presented, and the results will be compared to the E866 data. The theory will be shown to compare favorably to the data, and these results will be shown to suggest that the momentum broadening of a quark is about twice the generally accepted size.

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.

We present an analysis of the existing constraints for the twist-two lightcone pion wave function. We find that existing information on the pion wave function does not exclude the possibility that the pion wave function attains its asymptotic form. New bounds on the parameters of the pion wave function are presented.