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

The relevance of positivity in spin physics

Positivity reduces substantially the allowed domain for spin observables. We briefly recall some methods used to determine these domains and give some typical examples for exclusive and inclusive spin-dependent reactions.Comment: 7 pages, 3 figures, Talk presented at CIPANP 2009, San Diego California, USA, May 26-31, 2009 To be published in AIP Conference Proceeding

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

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

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.

A remark on asymptotic completeness for the critical nonlinear Klein-Gordon equation

We give a short proof of asymptotic completeness and global existence for the cubic Nonlinear Klein-Gordon equation in one dimension. Our approach to dealing with the long range behavior of the asymptotic solution is by reducing it, in hyperbolic coordinates to the study of an ODE. Similar arguments extend to higher dimensions and other long range type nonlinear problems.Comment: To appear in Lett. Math. Phy

QCD radiative and power corrections and Generalized GDH sum rules

We extend the earlier suggested QCD-motivated model for the $Q^2$-dependence of the generalized Gerasimov-Drell-Hearn (GDH) sum rule which assumes the smooth dependence of the structure function $g_T$, while the sharp dependence is due to the $g_2$ contribution and is described by the elastic part of the Burkhardt-Cottingham sum rule. The model successfully predicts the low crossing point for the proton GDH integral, but is at variance with the recent very accurate JLAB data. We show that, at this level of accuracy, one should include the previously neglected radiative and power QCD corrections, as boundary values for the model. We stress that the GDH integral, when measured with such a high accuracy achieved by the recent JLAB data, is very sensitive to QCD power corrections. We estimate the value of these power corrections from the JLAB data at $Q^2 \sim 1 {GeV}^2$. The inclusion of all QCD corrections leads to a good description of proton, neutron and deuteron data at all $Q^2$.Comment: 10 pages, 4 figures (to be published in Physical Review D

The GDH Sum Rule and Related Integrals

The spin structure of the nucleon resonance region is analyzed on the basis of our phenomenological model MAID. Predictions are given for the Gerasimov-Drell-Hearn sum rule as well as generalized integrals over spin structure functions. The dependence of these integrals on momentum transfer is studied and rigorous relationships between various definitions of generalized Gerasimov-Drell-Hearn integrals and spin polarizabilities are derived. These results are compared to the predictions of chiral perturbation theory and phenomenological models.Comment: 15 pages LaTeX including 5 figure

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

Investigating the trade-off between the effectiveness and efficiency of process modeling

Despite recent efforts to improve the quality of process models, we still observe a significant dissimilarity in quality between models. This paper focuses on the syntactic condition of process models, and how it is achieved. To this end, a dataset of 121 modeling sessions was investigated. By going through each of these sessions step by step, a separate ‘revision’ phase was identified for 81 of them. Next, by cutting the modeling process off at the start of the revision phase, a partial process model was exported for these modeling sessions. Finally, each partial model was compared with its corresponding final model, in terms of time, effort, and the number of syntactic errors made or solved, in search for a possible trade-off between the effectiveness and efficiency of process modeling. Based on the findings, we give a provisional explanation for the difference in syntactic quality of process models