Approximate Zero Modes for the Pauli Operator on a Region

Let $\mathcal{P}_{\Omega,tA}$ denoted the Pauli operator on a bounded open region $\Omega\subset\mathbb{R}^2$ with Dirichlet boundary conditions and magnetic potential $A$ scaled by some $t>0$. Assume that the corresponding magnetic field $B=\mathrm{curl}\,A$ satisfies $B\in L\log L(\Omega)\cap C^\alpha(\Omega_0)$ where $\alpha>0$ and $\Omega_0$ is an open subset of $\Omega$ of full measure (note that, the Orlicz space $L\log L(\Omega)$ contains $L^p(\Omega)$ for any $p>1$). Let $\mathsf{N}_{\Omega,tA}(\lambda)$ denote the corresponding eigenvalue counting function. We establish the strong field asymptotic formula $$\mathsf{N}_{\Omega,tA}(\lambda(t))=\frac{t}{2\pi}\int_{\Omega}\lvert B(x)\rvert\,dx\;+o(t)$$ as $t\to+\infty$, whenever $\lambda(t)=Ce^{-ct^\sigma}$ for some $\sigma\in(0,1)$ and $c,C>0$. The corresponding eigenfunctions can be viewed as a localised version of the Aharonov-Casher zero modes for the Pauli operator on $\mathbb{R}^2$.Comment: 28 pages; for the sake of clarity the main results have been reformulated and some minor presentational changes have been mad

DVCS with CLAS

Generalized parton distributions provide a unifying framework for the interpretation of exclusive reactions at high $Q^2$. The most promising reaction for the investigation of these distributions is the hard production of photons using Deeply Virtual Compton Scattering (DVCS). This reaction can be accessed experimentally by determining the production asymmetry using polarized electrons on a proton target. Pioneering experiments with CLAS and HERMES have produced the first measurements of this asymmetry. We will review the current experimental program to study DVCS at Jefferson Lab. Recent high statistics data taken with CLAS at 5.75 GeV allows us to determine this asymmetry at low -$t$ in the valence region ($x_{B}$=0.1-0.5) up to a $Q^2$ of 4 GeV$^2/c^2$.Comment: 5 pages, 3 figures, Conference on the Intersections of Particle and Nuclear Physics, New York City, May 19-24, 200

Review of Recent Jlab Results

High quality polarized electron beams at Jefferson Lab make possible precision measurements of hadronic properties in the regime of strongly interacting QCD. We will describe a few programs at Jefferson Lab that are making measurements that link the basic static properties of hadrons to their quark sub-structure. For example, parity-violating electron proton elastic scattering probes the spatial distribution of strange quarks in the nucleon. The nucleon-Delta transition form factors give us information about the deformation of nucleons and Deltas. Finally, new high statistics measurements of photons scattering off proton and deuteron targets are used to set upper limits on the production of exotic baryons with strangeness S=+1. These examples will be used to illustrate the capabilities and focus of the experimental program at JLab.Comment: Contribution to XI International Conference on Hadron Spectroscopy, 4 figure

JLab: Probing Hadronic Physics with Electrons and Photons

Precision measurements of the structure of nucleons and nuclei in the regime of strong interaction QCD are now possible with the availability of high current polarized electron beams, polarized targets, and recoil polarimeters, in conjunction with modern spectrometers and detector instrumentation. The physics at JLab will be highlighted using two recent measurements of general interest. The ratio of the proton electric to magnetic form factors indicates the importance of the role of angular momentum in the structure of the nucleon. The existence of 5-quark configurations in the ground state wavefunctions of hadrons is confirmed by a narrow peak attributed to an exotic baryon with strangeness S=+1. These and other examples will be used to illustrate the capabilities and focus of the experimental program at JLab.Comment: V Latinamerican Symposium on Nuclear Physics, Santos, Brazil (Sept 1-5, 2003) 4 pages, 4 figure