Comments on Exclusive Electroproduction of Transversely Polarized Vector Mesons

We discuss the electroproduction of light vector mesons from transversely polarized photons. Here QCD factorization cannot be applied as shown explicitly in a leading order calculation of corresponding Feynman diagrams. It is emphasized that present infrared singular contributions cannot be regularized through phenomenological meson distribution amplitudes with suppressed endpoint configurations. We point out that infrared divergencies arise also from integrals over skewed parton distributions of the nucleons. In a phenomenological analysis of transverse vector meson production model dependent regularizations have to be applied. If this procedure preserves the analytic structure suggested by a leading order calculation of Feynman diagrams, one obtains contributions from nucleon parton distributions and their derivatives. In particular polarized gluons enter only through their derivative

Quantum Information Encoding, Protection, and Correction from Trace-Norm Isometries

We introduce the notion of trace-norm isometric encoding and explore its implications for passive and active methods to protect quantum information against errors. Beside providing an operational foundations to the "subsystems principle" [E. Knill, Phys. Rev. A 74, 042301 (2006)] for faithfully realizing quantum information in physical systems, our approach allows additional explicit connections between noiseless, protectable, and correctable quantum codes to be identified. Robustness properties of isometric encodings against imperfect initialization and/or deviations from the intended error models are also analyzed.Comment: 10 pages, 1 figur

Surfaces Meeting Porous Sets in Positive Measure

Let n>2 and X be a Banach space of dimension strictly greater than n. We show there exists a directionally porous set P in X for which the set of C^1 surfaces of dimension n meeting P in positive measure is not meager. If X is separable this leads to a decomposition of X into a countable union of directionally porous sets and a set which is null on residually many C^1 surfaces of dimension n. This is of interest in the study of certain classes of null sets used to investigate differentiability of Lipschitz functions on Banach spaces

Deeply Virtual Neutrino Scattering (DVNS)

We introduce the study of neutrino scattering off protons in the deeply virtual kinematics, which describes under a unified formalism elastic and deep inelastic neutrino scattering. A real final state photon and a recoiling nucleon are detected in the few GeV ($|t|\sim 0.2-5$ GeV) region of momentum transfer. This is performed via an extension of the notion of deeply virtual Compton scattering, or DVCS, to the case of a neutral current exchange. The relevance of this process and of other similar exclusive processes for the study of neutrino interactions in neutrino factories for GeV neutrinos is pointed out.Comment: 28 pages, 12 figures, revised final version, to appear in JHE

Off-Forward Parton Distributions

Recently, there have been some interesting developments involving off-forward parton distributions of the nucleon, deeply virtual Compton scattering, and hard diffractive vector-meson production. These developments are triggered by the realization that the off-forward distributions contain information about the internal spin structure of the nucleon and that diffractive electroproduction of vector mesons depends on these unconventional distributions. This paper gives a brief overview of the recent developments

On the number of Mather measures of Lagrangian systems

In 1996, Ricardo Ricardo Ma\~n\'e discovered that Mather measures are in fact the minimizers of a "universal" infinite dimensional linear programming problem. This fundamental result has many applications, one of the most important is to the estimates of the generic number of Mather measures. Ma\~n\'e obtained the first estimation of that sort by using finite dimensional approximations. Recently, we were able with Gonzalo Contreras to use this method of finite dimensional approximation in order to solve a conjecture of John Mather concerning the generic number of Mather measures for families of Lagrangian systems. In the present paper we obtain finer results in that direction by applying directly some classical tools of convex analysis to the infinite dimensional problem. We use a notion of countably rectifiable sets of finite codimension in Banach (and Frechet) spaces which may deserve independent interest

The Status of Lattice Calculations of the Nucleon Structure Functions

We review our progress on the lattice calculation of low moments of both the unpolarised and polarised nucleon structure functions.Comment: 6 pages, contribution to 29th International Symposium on the Theory of Elementary Particles, Buckow, Germany, (29 August - 2 September 1995). 6 pages, Latex, requires espcrc2.sty, epsf.st

Generalized parton distributions of the pion in chiral quark models and their QCD evolution

We evaluate Generalized Parton Distributions of the pion in two chiral quark models: the Spectral Quark Model and the Nambu-Jona-Lasinio model with a Pauli-Villars regularization. We proceed by the evaluation of double distributions through the use of a manifestly covariant calculation based on the alpha representation of propagators. As a result polynomiality is incorporated automatically and calculations become simple. In addition, positivity and normalization constraints, sum rules and soft pion theorems are fulfilled. We obtain explicit formulas, holding at the low-energy quark-model scale. The expressions exhibit no factorization in the t-dependence. The QCD evolution of those parton distributions is carried out to experimentally or lattice accessible scales. We argue for the need of evolution by comparing the Parton Distribution Function and the Parton Distribution Amplitude of the pion to the available experimental and lattice data, and confirm that the quark-model scale is low, about 320 MeV.Comment: 25 pages, 15 figures, added discussion of the end-point behavio