Post Big Bang Processing of the Primordial Elements

We explore the Gnedin-Ostriker suggestion that a post-Big-Bang photodissociation process may modify the primordial abundances of the light elements. We consider several specific models and discuss the general features that are necessary (but not necessarily sufficient) to make the model work. We find that with any significant processing, the final D and $^3$He abundances, which are independent of their initial standard big bang nucleosynthesis (SBBN) values, rise quickly to a level several orders of magnitude above the observationally inferred primordial values. Solutions for specific models show that the only initial abundances that can be photoprocessed into agreement with observations are those that undergo virtually no processing and are already in agreement with observation. Thus it is unlikely that this model can work for any non-trivial case unless an artificial density and/or photon distribution is invoked.Comment: 12 page Latex file (AASTEX style). Tarred, gzipped, and uuencoded postscript files of seven figures. Also available (with ps file of paper) at ftp://www-physics.mps.ohio-state.edu/pub/nucex/phot

Model-Independent Semileptonic Form Factors Using Dispersion Relations

We present a method for parametrizing heavy meson semileptonic form factors using dispersion relations, and from it produce a two-parameter description of the B -> B elastic form factor. We use heavy quark symmetry to relate this function to B -> D* l nu form factors, and extract |V_cb|=0.0355^{+0.0029}_{-0.0025} from experimental data with a least squares fit. Our method eliminates model-dependent uncertainties inherent in choosing a parametrization for the extrapolation of the differential decay rate to threshold.Comment: uses lanlmac(harvmac) and epsf, 12 pages, 1 eps figure included (Talk by BG at the 6-th International Symposium on Heavy Flavour Physics, Pisa, Italy, 6--10 June, 1995

Bounds on Heavy-to-Heavy Mesonic Form Factors

We provide upper and lower bounds on the form factors for B -> D, D^* by utilizing inclusive heavy quark effective theory sum rules. These bounds are calculated to leading order in Lambda_QCD/m_Q and alpha_s. The O(alpha_s^2 beta_0) corrections to the bounds at zero recoil are also presented. We compare our bounds with some of the form factor models used in the literature. All the models we investigated failed to fall within the bounds for the combination of form factors (omega^2 - 1)/(4 omega)|omega h_{A2}+h_{A3}|^2.Comment: 27 pages, 10 figure

Parametric down-conversion from a wave-equations approach: geometry and absolute brightness

Using the approach of coupled wave equations, we consider spontaneous parametric down-conversion (SPDC) in the narrow-band regime and its relationship to classical nonlinear processes such as sum-frequency generation. We find simple expressions in terms of mode overlap integrals for the absolute pair production rate into single spatial modes, and simple relationships between the efficiencies of the classical and quantum processes. The results, obtained with Green function techniques, are not specific to any geometry or nonlinear crystal. The theory is applied to both degenerate and non-degenerate SPDC. We also find a time-domain expression for the correlation function between filtered signal and idler fields.Comment: 10 pages, no figure

Neutrino-Nucleus Cross Section Measurements using Stopped Pions and Low Energy Beta Beams

Two new facilities have recently been proposed to measure low energy neutrino-nucleus cross sections, the nu-SNS (Spallation Neutron Source) and low energy beta beams. The former produces neutrinos by pion decay at rest, while the latter produces neutrinos from the beta decays of accelerated ions. One of the uses of neutrino-nucleus cross section measurements is for supernova studies, where typical neutrino energies are 10s of MeV. In this energy range there are many different components to the nuclear response and this makes the theoretical interpretation of the results of such an experiment complex. Although even one measurement on a heavy nucleus such as lead is much anticipated, more than one data set would be still better. We suggest that this can be done by breaking the electron spectrum down into the parts produced in coincidence with one or two neutrons, running a beta beam at more than one energy, comparing the spectra produced with pions and a beta beam or any combination of these.Comment: 6 pages, 6 figure

New Constraints on Dispersive Form Factor Parameterizations from the Timelike Region

We generalize a recent model-independent form factor parameterization derived from rigorous dispersion relations to include constraints from data in the timelike region. These constraints dictate the convergence properties of the parameterization and appear as sum rules on the parameters. We further develop a new parameterization that takes into account finiteness and asymptotic conditions on the form factor, and use it to fit to the elastic \pi electromagnetic form factor. We find that the existing world sample of timelike data gives only loose bounds on the form factor in the spacelike region, but explain how the acquisition of additional timelike data or fits to other form factors are expected to give much better results. The same parameterization is seen to fit spacelike data extremely well.Comment: 24 pages, latex (revtex), 3 eps figure

Breaking the Symmetry of a Circular System of Coupled Harmonic Oscillators

First we compute the natural frequencies of vibration of four identical particles coupled by ideal, massless harmonic springs. The four particles are constrained to move on a fixed circle. The initial computations are simplified by a transformation to symmetry coordinates. Then the symmetry of the vibrating system is broken by changing the mass of a single particle by a very small amount. We observe the effect of applying the symmetry transformation to the now slightly nonsymmetric system. We compute the new frequencies and compare them with the frequencies of the original symmetric system of oscillators. Results of similar calculations for 2,3,5, and 6particles are given

Four Anharmonic Oscillators on a Circle

Four identical, uniformly separated particles interconnected by ideal anharmonic springs are constrained to move on a fixed, frictionless circular track. The Lagrangian for the system is written and then transformed by matrix operations suggested by the symmetry of the arrangement of springs and particles. The equations of motion derived from the transformed Lagrangian yield four natural frequencies of motion

Breaking of the overall permutation symmetry in nonlinear optical susceptibilities of one-dimensional periodic dimerized Huckel model

Based on infinite one-dimensional single-electron periodic models of trans-polyacetylene, we show analytically that the overall permutation symmetry of nonlinear optical susceptibilities is, albeit preserved in the molecular systems with only bound states, no longer generally held for the periodic systems. The overall permutation symmetry breakdown provides a fairly natural explanation to the widely observed large deviations of Kleinman symmetry for periodic systems in off-resonant regions. Physical conditions to experimentally test the overall permutation symmetry break are discussed.Comment: 7 pages, 1 figur