Virtual Photon Structure Functions

We discuss the perturbatively calculable virtual photon structure functions. First we present the framework for analyzing the structure functions of the virtual photon and derive a first moment of $g_1^\gamma$ of the virtual photon. We then investigate the three positivity constraints satisfied by the eight structure functions of the virtual photon.Comment: 5 pages, LaTeX, 5 eps figures, npb.sty file included Talk given at RADCOR/Loops and Legs 2002, Kloster Banz, Germany, September 8-13, 2002, to appear in the Proceeding

Parton distribution functions of proton in a light-front quark-diquark model

We present the parton distribution functions (PDFs) for un- polarised, longitudinally polarized and transversely polarized quarks in a proton using the light-front quark diquark model. We also present the scale evolution of PDFs and calculate axial charge and tecsor charge for $u$ and $d$ quarks at a scale of experimental findings.Comment: XXII DAE-BRNS High Energy Physics Symposium, December 12-16, 2016, University of Delhi, India; 4 pages, 1 figur

Polarized Quarks, Gluons and Sea in Nucleon Structure Functions

We perform a NLO analysis of polarized deep inelastic scattering data to test two different solutions to the so called spin crisis: one of them based on the axial gluon anomaly and consistent with the Bjorken sum rule and another one, where the defects in the spin sum rules and in the Gottfried sum rule are related. In this case a defect is also expected for the Bjorken sum rule. The first solution is slightly favoured by the SLAC E154 results, but both options seem to be consistent with the CERN SMC data.Comment: 19 pages, LateX, 6 figures. Figures included in the tex

Stable directions for small nonlinear Dirac standing waves

We prove that for a Dirac operator with no resonance at thresholds nor eigenvalue at thresholds the propagator satisfies propagation and dispersive estimates. When this linear operator has only two simple eigenvalues close enough, we study an associated class of nonlinear Dirac equations which have stationary solutions. As an application of our decay estimates, we show that these solutions have stable directions which are tangent to the subspaces associated with the continuous spectrum of the Dirac operator. This result is the analogue, in the Dirac case, of a theorem by Tsai and Yau about the Schr\"{o}dinger equation. To our knowledge, the present work is the first mathematical study of the stability problem for a nonlinear Dirac equation.Comment: 62 page

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

Equivariant wave maps exterior to a ball

We consider the exterior Cauchy-Dirichlet problem for equivariant wave maps from 3+1 dimensional Minkowski spacetime into the three-sphere. Using mixed analytical and numerical methods we show that, for a given topological degree of the map, all solutions starting from smooth finite energy initial data converge to the unique static solution (harmonic map). The asymptotics of this relaxation process is described in detail. We hope that our model will provide an attractive mathematical setting for gaining insight into dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture.Comment: 16 pages, 9 figure

Long time dynamics and coherent states in nonlinear wave equations

We discuss recent progress in finding all coherent states supported by nonlinear wave equations, their stability and the long time behavior of nearby solutions.Comment: bases on the authors presentation at 2015 AMMCS-CAIMS Congress, to appear in Fields Institute Communications: Advances in Applied Mathematics, Modeling, and Computational Science 201

MC-Simulation of the Transverse Double Spin Asymmetry for RHIC

Using {\sc Sphinx tt}, a new MC simulation program for transverse polarized nucleon--nucleon scattering based on {\sc Pythia~5.6}, we calculate the transverse double spin asymmetry $A^{TT}$ in the Drell-Yan process. If one assumes (quite arbitrarily) that the transversity parton distribution $\delta q(x,Q^2)$ equals the helicity distribution $\Delta q(x,Q^2)$ at some low $Q_0^2$ scale, the resulting asymmetry is of order 1\%. In this case is $A^{TT}$ would hardly be be measurable with PHENIX at RHIC.Comment: 17 pages, 5 figure

Asymptotic stability of breathers in some Hamiltonian networks of weakly coupled oscillators

We consider a Hamiltonian chain of weakly coupled anharmonic oscillators. It is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space (breathers). In this paper we prove asymptotic stability in energy space of such solutions. The proof is based on two steps: first we use canonical perturbation theory to put the system in a suitable normal form in a neighborhood of the breather, second we use dispersion in order to prove asymptotic stability. The main limitation of the result rests in the fact that the nonlinear part of the on site potential is required to have a zero of order 8 at the origin. From a technical point of view the theory differs from that developed for Hamiltonian PDEs due to the fact that the breather is not a relative equilibrium of the system

Impact of D0-D0bar mixing on the experimental determination of gamma

Several methods have been devised to measure the weak phase gamma using decays of the type B+- --> D K+-, where it is assumed that there is no mixing in the D0-D0bar system. However, when using these methods to uncover new physics, one must entertain the real possibility that the measurements are affected by new physics effects in the D0-D0bar system. We show that even values of x_D and/or y_D around 10^{-2} can have a significant impact in the measurement of sin^2{gamma}. We discuss the errors incurred in neglecting this effect, how the effect can be checked, and how to include it in the analysis.Comment: 18 pages, Latex with epsfig, 8 figure