Sum Rules for Magnetic Moments and Polarizabilities in QED and Chiral Effective-Field Theory

We elaborate on a recently proposed extension of the Gerasimov-Drell-Hearn (GDH) sum rule which is achieved by taking derivatives with respect to the anomalous magnetic moment. The new sum rule features a {\it linear} relation between the anomalous magnetic moment and the dispersion integral over a cross-section quantity. We find some analogy of the linearized form of the GDH sum rule with the `sideways dispersion relations'. As an example, we apply the linear sum rule to reproduce the famous Schwinger's correction to the magnetic moment in QED from a tree-level cross-section calculation and outline the procedure for computing the two-loop correction from a one-loop cross-section calculation. The polarizabilities of the electron in QED are considered as well by using the other forward-Compton-scattering sum rules. We also employ the sum rules to study the magnetic moment and polarizabilities of the nucleon in a relativistic chiral EFT framework. In particular we investigate the chiral extrapolation of these quantities.Comment: 24 pages, 7 figures; several additions, published versio

Q^2 Evolution of Generalized Baldin Sum Rule for the Proton

The generalized Baldin sum rule for virtual photon scattering, the unpolarized analogy of the generalized Gerasimov-Drell-Hearn integral, provides an important way to investigate the transition between perturbative QCD and hadronic descriptions of nucleon structure. This sum rule requires integration of the nucleon structure function F_1, which until recently had not been measured at low Q^2 and large x, i.e. in the nucleon resonance region. This work uses new data from inclusive electron-proton scattering in the resonance region obtained at Jefferson Lab, in combination with SLAC deep inelastic scattering data, to present first precision measurements of the generalized Baldin integral for the proton in the Q^2 range of 0.3 to 4.0 GeV^2.Comment: 4 pages, 3 figures, one table; text added, one figure replace

Survey of charge symmetry breaking operators for dd -> alpha pi0

The charge-symmetry-breaking amplitudes for the recently observed d d -> alpha pi0 reaction are investigated. Chiral perturbation theory is used to classify and identify the leading-order terms. Specific forms of the related one- and two-body tree level diagrams are derived. As a first step toward a full calculation, a few tree-level two-body diagrams are evaluated at each considered order, using a simplified set of d and alpha wave functions and a plane-wave approximation for the initial dd state. The leading-order pion-exchange term is shown to be suppressed in this model because of poor overlap of the initial and final states. The higher-order one-body and short-range (heavy-meson-exchange) amplitudes provide better matching between the initial and final states and therefore contribute significantly and coherently to the cross section. The consequences this might have for a full calculation, with realistic wave functions and a more complete set of amplitudes, are discussed.Comment: REVTeX 4, 35 pages, 8 eps figures, submitted to PR

Impact of saturation on spin effects in proton-proton scattering

For pomerons described by a sum of two simple-pole terms, a soft and a hard pomeron, the unitarity bounds from saturation in impact-parameter space are examined. We consider the effect of these bounds on observables linked with polarisation, such as the analyzing power in elastic proton-proton scattering, for LHC energies. We obtain the s and t dependence of the Coulomb-nuclear interference at small momentum transfer, and show that the effect of the hard pomeron may be observed at the LHC.Comment: 8 pages, 2 figures, presented by O.V.S. at the Advanced Studies Institute "Symetries and Spin" (SPIN-Praha-2004), Prague, July 5 - July 10, 200

Coulomb-hadron phase factor and spin phenomena in a wide region of transfer momenta

The Coulomb-hadron interference effects are examined at small and large $t$. The methods for the definition of spin-dependent parts of hadron scattering amplitude are presented. The additional contributions to analyzing power $A_N$ and the double spin correlation parameter $A_{NN}$ owing to the electromagnetic-hadron interference are determined in the diffraction dip domain of high-energy elastic hadron scattering.Comment: 9 pages, LaTeX, 4 figure

Individual and joint trajectories of change in bone, lean mass and physical performance in older men.

BackgroundDeclines in bone, muscle and physical performance are associated with adverse health outcomes in older adults. However, few studies have described concurrent age-related patterns of change in these factors. The purpose of this study was to characterize change in four properties of muscle, physical performance, and bone in a prospective cohort study of older men.MethodsUsing repeated longitudinal data from up to four visits across 6.9 years from up to 4681 men (mean age at baseline 72.7 yrs. ±5.3) participating in the Osteoporotic Fractures in Men (MrOS) Study, we used group-based trajectory models (PROC TRAJ in SAS) to identify age-related patterns of change in four properties of muscle, physical performance, and bone: total hip bone mineral (BMD) density (g/m2) and appendicular lean mass/ht2 (kg/m2), by DXA; grip strength (kg), by hand dynamometry; and walking speed (m/s), by usual walking pace over 6 m. We also described joint trajectories in all pair-wise combinations of these measures. Mean posterior probabilities of placement in each trajectory (or joint membership in latent groups) were used to assess internal reliability of the model. The number of trajectories for each individual factor was limited to three, to ensure that the pair-wise determination of joint trajectories would yield a tractable number of groups as well as model fit considerations.ResultsThe patterns of change identified were generally similar for all measures, with three district groups declining over time at roughly similar rates; joint trajectories revealed similar patterns with no cross-over or convergence between groups. Mean posterior probabilities for all trajectories were similar and consistently above 0.8 indicating reasonable model fit to the data.ConclusionsOur description of trajectories of change with age in bone mineral density, grip strength, walking speed and appendicular lean mass found that groups identified by these methods appeared to have little crossover or convergence of change with age, even when considering joint trajectories of change in these factors

Updated resonance photo-decay amplitudes to 2 GeV

We present the results of an energy-dependent and set of single-energy partial-wave analyses of single-pion photoproduction data. These analyses extend from threshold to 2 GeV in the laboratory photon energy, and update our previous analyses to 1.8 GeV. Photo-decay amplitudes are extracted for the baryon resonances within this energy range. We consider two photoproduction sum rules and the contributions of two additional resonance candidates found in our most recent analysis of $\pi N$ elastic scattering data. Comparisons are made with previous analyses.Comment: Revtex, 26 pages, 3 figures. Postscript figures available from ftp://clsaid.phys.vt.edu/pub/pr or indirectly from http://clsaid.phys.vt.edu/~CAPS

Curvature-direction measures of self-similar sets

We obtain fractal Lipschitz-Killing curvature-direction measures for a large class of self-similar sets F in R^d. Such measures jointly describe the distribution of normal vectors and localize curvature by analogues of the higher order mean curvatures of differentiable submanifolds. They decouple as independent products of the unit Hausdorff measure on F and a self-similar fibre measure on the sphere, which can be computed by an integral formula. The corresponding local density approach uses an ergodic dynamical system formed by extending the code space shift by a subgroup of the orthogonal group. We then give a remarkably simple proof for the resulting measure version under minimal assumptions.Comment: 17 pages, 2 figures. Update for author's name chang