Virtual photon structure functions and positivity constraints

We study the three positivity constraints among the eight virtual photon structure functions, derived from the Cauchy-Schwarz inequality and which are hence model-independent. The photon structure functions obtained from the simple parton model show quite different behaviors in a massive quark or a massless quark case, but they satisfy, in both cases, the three positivity constraints. We then discuss an inequality which holds among the unpolarized and polarized photon structure functions $F_1^\gamma$, $g_1^\gamma$ and $W_{TT}^\tau$, in the kinematic region $\Lambda^2\ll P^2 \ll Q^2$, where $-Q^2 (-P^2)$ is the mass squared of the probe (target) photon, and we examine whether this inequality is satisfied by the perturbative QCD results.Comment: 24 pages, 13 eps figure

Features of elastic scattering at small t at the LHC

The problems linked with the extraction of the basic parameters of the hadron elastic scattering amplitude at the LHC are explored. It is shown that one should take into account the saturation regime which will lead to new effects at the LHC.Comment: 3. pages, 6 figures, talk on the International workshop on "Diffraction in High Energy Physics", La Londe-les-Maures, France (2008

Status of Spin Physics - Experimental Summary

The current status of spin physics experiments, based on talks presented at the Third Circum-Pan-Pacific Symposium on High Energy Spin Physics held in Beijing, 2001, is summarized in this article. Highlights of recent experimental results at SLAC, JLab, and DESY, as well as future plans at these facilities and at RHIC-spin are discussed.Comment: 18 pages, 7 figures, Invited talk presented at the Third Circum-Pan-Pacific Symposium on High Energy Spin Physics held in Beijing, October, 200

Positivity Constraints for Spin-Dependent Parton Distributions

We derive new positivity constraints on the spin-dependent structure functions of the nucleon. These model independent results reduce conside\-rably their domain of allowed values, in particular for the chiral-odd parton distribution $h_1 (x)$.Comment: 8 pages,CPT-94/P.3059,LaTex,3 fig available on cpt.univ-mrs.fr directory pub/preprints/94/fundamental-interactions/94-P.305

Representation of Quantum Mechanical Resonances in the Lax-Phillips Hilbert Space

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips $S$-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips $S$-matrix is unitarily related to the $S$-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable $\sigma$ of the Lax-Phillips theory. Analytic continuation in $\sigma$ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.Comment: Plain TeX, 26 pages. Minor revision

Transverse Double-Spin Asymmetries for Muon Pair Production in pp-Collisions

We calculate the rapidity dependence of the transverse double-spin asymmetry for the Drell-Yan process to next-to-leading order in the strong coupling. Input transversity distributions are obtained by saturating the Soffer inequality at a low hadronic mass scale. Results for the polarized BNL-RHIC proton-proton collider and the proposed HERA-N fixed-target experiment are presented, and the influence of the limited muon acceptance of the detectors on measurements of the asymmetry is studied in detail.Comment: 7 pages including 5 figures; significantly shortened, to be published in Phys. Rev.

Theory of Nonlinear Dispersive Waves and Selection of the Ground State

A theory of time dependent nonlinear dispersive equations of the Schroedinger / Gross-Pitaevskii and Hartree type is developed. The short, intermediate and large time behavior is found, by deriving nonlinear Master equations (NLME), governing the evolution of the mode powers, and by a novel multi-time scale analysis of these equations. The scattering theory is developed and coherent resonance phenomena and associated lifetimes are derived. Applications include BEC large time dynamics and nonlinear optical systems. The theory reveals a nonlinear transition phenomenon, ``selection of the ground state'', and NLME predicts the decay of excited state, with half its energy transferred to the ground state and half to radiation modes. Our results predict the recent experimental observations of Mandelik et. al. in nonlinear optical waveguides

Exclusive quasielastic production of dijets at hadronic colliders

We critically re-examine the calculation of central production of dijets in quasi-elastic hadronic collisions. We find that the process is not dominated by the perturbative contribution, and discuss several sources of uncertainties in the calculation.Comment: 4 pages, talk given at Diffraction-2008, La Londe-les-Maures, France, 9-14 Sept 200

Carleman estimates and absence of embedded eigenvalues

Let L be a Schroedinger operator with potential W in L^{(n+1)/2}. We prove that there is no embedded eigenvalue. The main tool is an Lp Carleman type estimate, which builds on delicate dispersive estimates established in a previous paper. The arguments extend to variable coefficient operators with long range potentials and with gradient potentials.Comment: 26 page

Double-Spin Transverse Asymmetries in Drell-Yan Processes

We calculate the double-spin transverse asymmetries for the Drell-Yan lepton pair production in p-p and p-anti p collisions. We assume the transverse and the longitudinal polarization densities to be equal at a very small scale, as it is suggested by confinement model results. Using a global fit for the longitudinal distributions, we find transverse asymmetries of order of 10^-2 at most, in the accessible kinematic regions.Comment: 8 pages, REVTeX, 6 figures included as file figures.tar.g