Dispersion Theory in Electromagnetic Interactions

We review various applications of dispersion relations (DRs) to the electromagnetic structure of hadrons. We discuss the way DRs allow one to extract information on hadron structure constants by connecting information from complementary scattering processes. We consider the real and virtual Compton scattering processes off the proton, and summarize recent advances in the DR analysis of experimental data to extract the proton polarizabilities, in comparison with alternative studies based on chiral effective field theories. We discuss a multipole analysis of real Compton scattering data, along with a DR fit of the energy-dependent dynamical polarizabilities. Furthermore, we review new sum rules for the double-virtual Compton scattering process off the proton, which allow for model independent relations between polarizabilities in real and virtual Compton scattering, and moments of nucleon structure functions. The information on the double-virtual Compton scattering is used to predict and constrain the polarizability corrections to muonic hydrogen spectroscopy.Comment: preprint version of a review to appear in Ann. Rev. Nucl. Part. Sci. 68 (2018

Constrained annealing for spin glasses

The quenched free energy of spin glasses is estimated by means of annealed averages where the frustration is constrained to its average value. We discuss the case of d-dimensional Ising models with random nearest neighbour coupling, and we introduce a new method to obtain constrained annealed averages without recurring to Lagrange multipliers. It requires to perform quenched averages either on small volumes in an analytic way, or on finite size strips via products of random transfer matrices. We thus give a sequence of converging lower bounds for the quenched free energy of 2d spin glasses.Comment: plane TeX file,24 pages. 6 figures may be requested to Paladin at vxscaq.aquila.infn.i

Dispersive evaluation of the D-term form factor in deeply virtual Compton scattering

We present a dispersive representation of the D-term form factor for hard exclusive reactions, using unsubtracted $t$-channel dispersion relations. The $t$-channel unitarity relation is saturated with the contribution of two-pion intermediate states, using the two-pion distributions amplitude for the $\gamma^*\gamma\rightarrow \pi\pi$ subprocess and reconstructing the $\pi\pi\rightarrow N\bar N$ subprocess from available information on pion-nucleon partial-wave helicity amplitudes. Results for the D-term form factor as function of $t$ as well as at $t=0$ are discussed in comparison with available model predictions and phenomenological parametrizations.Comment: 8 pages, 3 figures; improved presentation of the results; version to appear in Phys. Lett.

Estimating Residual Faults from Code Coverage

Many reliability prediction techniques require an estimate for the number of residual faults. In this paper, a new theory is developed for using test coverage to estimate the number of residual faults. This theory is applied to a specific example with known faults and the results agree well with the theory. The theory is used to justify the use of linear extrapolation to estimate residual faults. It is also shown that it is important to establish the amount of unreachable code in order to make a realistic residual fault estimate

Chiral-odd generalized parton distributions in constituent quark models

We derive the overlap representation of chiral-odd generalized parton distributions using the Fock-state decomposition in the transverse-spin basis. This formalism is applied to the case of light-cone wave functions in a constituent quark model. Numerical results for the four chiral-odd generalized parton distributions at the hadronic scale are shown in different kinematics. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon.Comment: 23 pages, 7 figures; one reference added and one formula corrected; conclusions and discussions unchange

Chiral-Odd Generalized Parton Distributions, Transversity and Double Transverse-Spin Asymmetry in Drell-Yan Dilepton Production

Within the framework of light-cone quantization we derive the overlap representation of generalized parton distributions for transversely polarized quarks using the Fock-state decomposition in the transverse-spin basis. We apply this formalism to the case of light-cone wave functions in a constituent quark model giving numerical results for the four chiral-odd generalized parton distributions in a region where they describe the emission and reabsorption of a quark by the nucleon. With the transversity distribution obtained in the forward limit of the generalized distribution, we provide some predictions for the double transverse-spin asymmetry in Drell-Yan dilepton production in the kinematics of the PAX experiment.Comment: 8 pages, 4 figures. To appear in the Proceedings of the "XI Conference on Problems in Theoretical Nuclear Physics", Cortona, Italy, 11-14 October 200

Light-Front Densities for Transversely Polarized Hadrons

We discuss the recent interpretation of quark distribution functions in the plane transverse to the light-cone direction. Such a mapping is model independent and allows one to build multidimensional pictures of the hadron and to develop a semi-classical intuition of the quark dynamics. We comment briefly the results obtained from the Form Factors of the nucleon. A generalization to a target with arbitrary spin led to a set of preferred values for the electromagnetic coupling characterizing structureless particles. Generalized polarizabilities can also be interpreted in that frame as the distortion of the charge densities due to an external electromagnetic field. Finally, we present preliminary results for the Generalized Transverse-Momentum dependent Distributions which encode in principle the most complete information about quark distributions.Comment: 8 pages, 2 figures, 1 table; contribution to the proceedings of "The 4th Workshop on Exclusive Reactions at High Momentum Transfer", Jefferson Lab., May 18-21, 201

Chiral-Odd Generalized Parton Distributions and Transversity in Light-Front Constituent Quark Models

We present the general framework to calculate chiral-odd generalized parton distributions in the overlap representation using the Fock-state decomposition in the transverse spin basis. In the forward limit we derive the transversity distribution, the tensor charge and the angular momentum sum rule for quarks with transverse polarization in an unpolarized nucleon. Numerical results are obtained by applying the formalism to the case of light-cone wavefunctions of constituent quark models.Comment: 8 pages, 3 figures. Invited talk at the "Advanced Studies Institute on SYMMETRIES AND SPIN" (SPIN-Praha-2006), 19-26 July, 2006, Prague. To be pubblished in Czechoslovak Journal of Physics. Some references adde

Two-photon exchange contribution to elastic e−e^--proton scattering: Full dispersive treatment of πN\pi N states and comparison with data

We evaluate the two-photon exchange correction to the elastic electron-proton scattering cross section within a dispersive framework. Besides the elastic contribution, we account for all $\pi N$ intermediate state contributions using the phenomenological MAID fit as an input. We develop a novel method for the analytical continuation of the two-photon exchange amplitudes into the unphysical region and generalize our previous work to the momentum transfer region $0.064~\mathrm{GeV}^2 \lesssim Q^2 \lesssim 1~\mathrm{GeV}^2$. We compare our results with recent OLYMPUS, CLAS and VEPP-3 data as well as with empirical fits and estimates in the forward angular region.Comment: 43 pages, 21 figures, version published in Phys. Rev. D 96, 096001 (2017