Yukawa Bound States of a Large Number of Fermions

We consider the bound state problem for a field theory that contains a Dirac fermion $\chi$ that Yukawa couples to a (light) scalar field $\phi$. We are interested in bound states with a large number $N$ of $\chi$ particles. A Fermi gas model is used to numerically determine the dependence of the radius $R$ of these bound states on $N$ and also the dependence of the binding energy on $N$. Since scalar interactions with relativistic $\chi$'s are suppressed two regimes emerge. For modest values of $N$ the state is composed of non-relativistic $\chi$ particles. In this regime as $N$ increases $R$ decreases. Eventually the core region becomes relativistic and the size of the state starts to increase as $N$ increases. As a result, for fixed Yukawa coupling and $\chi$ mass, there is a minimum sized state that occurs roughly at the value of $N$ where the core region first becomes relativistic. We also compute an elastic scattering form factor that can be relevant for direct detection if the dark matter is composed of such $\chi$ particles.Comment: 14 pages, 7 figure

Effect of a thin optical Kerr medium on a Laguerre-Gaussian beam

Using a generalized Gaussian beam decomposition method we determine the propagation of a Laguerre-Gaussian beam that has passed through a thin nonlinear optical Kerr medium. The orbital angular momentum per photon of the beam is found to be conserved while the component beams change. As an illustration of applications, we propose and demonstrate a z-scan experiment using an $LG_0^1$ beam and a dye-doped polymer film.Comment: 3 pages, 2 figures, corrected typo

Effective Theory and Simple Completions for Neutrino Interactions

We consider all the dimension 6 operators as well as some simple extensions of the standard model that give new contributions to neutrino interactions with matter. Such interactions are usually parametrized by $\epsilon_{\alpha \beta}$, where $\alpha$ and $\beta$ are neutrino flavor indices taking the values $e$, $\mu$ and $\tau$. In the simple models we consider the $\epsilon_{\alpha \beta}$'s are much more constrained than in the operator-based model-independent approach. Typically the $\epsilon_{\alpha \beta}$'s are restricted to be smaller in magnitude than around $10^{-3}$. In some of the leptoquark models, a specific pattern for the leptoquark Yukawa couplings allows the diagonal element $\epsilon_{\tau\tau}$ to be as large as $\sim0.1$, or one of $\epsilon_{ee}$, $\epsilon_{\mu\mu}\sim0.01$. We discuss the interplay between neutrino physics and leptoquark searches at the LHC.Comment: 12 pages, 2 figure

Relationships among Interpolation Bases of Wavelet Spaces and Approximation Spaces

A multiresolution analysis is a nested chain of related approximation spaces.This nesting in turn implies relationships among interpolation bases in the approximation spaces and their derived wavelet spaces. Using these relationships, a necessary and sufficient condition is given for existence of interpolation wavelets, via analysis of the corresponding scaling functions. It is also shown that any interpolation function for an approximation space plays the role of a special type of scaling function (an interpolation scaling function) when the corresponding family of approximation spaces forms a multiresolution analysis. Based on these interpolation scaling functions, a new algorithm is proposed for constructing corresponding interpolation wavelets (when they exist in a multiresolution analysis). In simulations, our theorems are tested for several typical wavelet spaces, demonstrating our theorems for existence of interpolation wavelets and for constructing them in a general multiresolution analysis

Lepton Flavorful Fifth Force and Depth-dependent Neutrino Matter Interactions

We consider a fifth force to be an interaction that couples to matter with a strength that grows with the number of atoms. In addition to competing with the strength of gravity a fifth force can give rise to violations of the equivalence principle. Current long range constraints on the strength and range of fifth forces are very impressive. Amongst possible fifth forces are those that couple to lepton flavorful charges $L_e-L_{\mu}$ or $L_e-L_{\tau}$. They have the property that their range and strength are also constrained by neutrino interactions with matter. In this brief note we review the existing constraints on the allowed parameter space in gauged $U(1)_{L_e-L_{\mu}, L_{\tau}}$. We find two regions where neutrino oscillation experiments are at the frontier of probing such a new force. In particular, there is an allowed range of parameter space where neutrino matter interactions relevant for long baseline oscillation experiments depend on the depth of the neutrino beam below the surface of the earth.Comment: 6 pages, 5 figure

A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)

Representations of the non-semisimple superalgebra $gl(2|2)$ in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of $gl(2|2)$ are constructed explicitly through the explicit construction of all $gl(2)\oplus gl(2)$ particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of $gl(2|2)$ in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.Comment: LaTex file, 23 pages, two references and a comment added, to appear in J. Math. Phy