Generalized polarizabilities of the nucleon studied in the linear sigma model (II)

In a previous paper virtual Compton scattering off the nucleon has been investigated in the one-loop approximation of the linear sigma model in order to determine the 3 scalar generalized polarizabilities. We have now extended this work and calculated the 7 vector polarizabilities showing up in the spin-dependent amplitude of virtual Compton scattering. The results fulfill 3 model-independent constraints recently derived. Compared to the constituent quark model there exist enormous differences for some of the vector polarizabilities. At vanishing three-momentum of the virtual photon, the analytical results of the sigma model and of chiral perturbation theory can be related. The influence of the π⁰ exchange in the t channel has been discussed in some detail. Besides, the vector polarizabilities determine 2 linear combinations of the third order spin-polarizabilities appearing in real Compton scattering.     

Low-energy theorem for virtual compton scattering and generalized sum rules of the nucleon

We formulate the low-energy theorem for virtual Compton scattering off a nucleon and examine its consequences for generalized nucleon polarizabilites. As a result of a new, model-independent definition of the low-energy limit for doubly virtual Compton scattering, all generalized sum rules of the nucleon have a continuous limit for real photons and obtain contributions from the t channel that were not included previously.     

Twist-4 photon helicity-flip amplitude in DVCS on a nucleon in the Wandzura-Wilczek approximation

We computed the twist-4 part of the photon spin-flip amplitude in deeply virtual Compton scattering on a nucleon in the Wandzura–Wilczek approximation. We found a factorizable contribution, which arises from photon scattering on quarks with non-zero angular momentum along the collision axis. As the genuine twist-2 amplitude arises at the NLO, for moderate virtualities of the hard photon, GeV, a kinematical twist-4 correction can give a numerically important contribution to the photon helicity-flip amplitude. Received: 2 July 2001 / Revised version: 17 July 2001 / Published online: 31 August 2001     

The accelerated scaling attractor solution of the interacting agegraphic dark energy in Brans–Dicke theory

We study the deeply virtual Compton scattering off a spin-one particle, as the case for the coherent scattering off a deuteron target. We extend our approach, formulated initially for a spinless case, and discuss the role of twist three contributions for restoring the gauge invariance of the amplitude. Using twist three contributions and relations, which emanate from the QCD equations of motion, we derive the gauge invariant amplitude for the deeply virtual Compton scattering (DVCS) off hadrons with spin 1. Using the derived gauge invariant amplitude, the single spin asymmetry is discussed.     

DVCS on the nucleon to the twist-3 accuracy

The amplitude of the deeply virtual Compton scattering off nucleon is computed to the twist-3 accuracy in the Wandzura–Wilczek (WW) approximation. The result is presented in the form which can be easily used for analysis of DVCS observables.     

Deeply virtual Compton scattering off nuclei

We consider the hard leptoproduction of a photon off nuclei up to spin-1. As a new result we present here the general azimuthal angular dependence of the differential cross section for a spin-1 target. Its twist-two Fourier coefficients of the interference and squared deeply virtual Compton scattering amplitude are evaluated in leading order approximation of perturbation theory in terms of generalized parton distributions, while the pure Bethe-Heitler cross section is exactly calculated in terms of electromagnetic form factors. Relying on a simple model for the nucleon generalized parton distribution H, which describes the existing DVCS data for a proton target, we estimate the size of unpolarized cross sections, beam and longitudinal target spin as well as unpolarized charge asymmetries for the present fixed target experiments with nuclei. These estimates are confronted with preliminary HERMES data for deuterium and neon.Received: 1 October 2003, Published online: 3 December 2003     

Electromagnetic energies of nuclei and the nuclear compton amplitude

The electromagnetic energy of a nucleus is derived in perturbation theory, which relates this quantity to the amplitude for the forward scattering of virtual photons on a nucleus (nuclear Compton amplitude). Using the gauge invariance of this amplitude, the energy is separated into Coulomb and transverse components. Our formalism, although basically nonrelativistic, admits corrections of order ($\text{v}\text{c}$)² to the nuclear charge operator. The energy is further separated into one-body terms, related to the n-p mass difference, and two-body terms which lead to the Breit interaction and the nuclear Lamb shift. These results are then related to electron scattering sum rules in the manner of Cottingham. Mesonic contributions to the electromagnetic energy are also discussed.     

Compton scattering on208Pb

In this paper we briefly review the formalism of the nuclear Compton scattering in the frame of the low-energy theorems (LET). We treat the resonant terms of the amplitude, having collective intermediate nuclear states, as a superposition of Lorentz lines with energy, width and strength fixed by the photo-absorption experiments. The gauge terms are evaluated starting from a simple, but realistic, nuclear Hamiltonian. Dynamical nucleon-nucleon correlations are consistently taken into account, beyond those imposed by the Pauli principle. The comparison of the theoretical predictions with the data of elastic diffusion of photons from²⁰⁸Pb shows that LET are insufficient to account for the experiment.     

Timelike Compton scattering: exclusive photoproduction of lepton pairs

We investigate the exclusive photoproduction of a heavy timelike photon which decays into a lepton pair, . This can be seen as the analog of deeply virtual Compton scattering, and we argue that the two processes are complementary for studying generalized parton distributions in the nucleon. In an unpolarized experiment the angular distribution of the leptons readily provides access to the real part of the Compton amplitude. We estimate the possible size of this effect in kinematics where the Compton process should be dominated by quark exchange. Received: 9 October 2001 / Published online: 5 April 2002     

Inclusive and Deep-Inelastic Scattering from a Dressed Structureless Nucleon

Nonperturbative polaron variational methods are used to study inclusive scattering in the context of the scalar Wick-Cutkosky model. We derive the structure functions for a scalar point-like nucleon surrounded by a cloud of strongly interacting mesons from the Compton amplitude that is obtained in a recent variational calculation based on the particle (or worldline) representation. In zeroth variational order, a covariant exponentiated form is obtained, which is identical to the one suggested by Vineyard for scattering of slow neutrons from quantum liquids. In first order, the much richer dependence of the structure function on momentum and energy transfer, which emerges, is evaluated numerically. We study the -evolution and the perturbative as well as the scaling limit of our variational structure functions. Finally, the momentum sum rule is derived and evaluated in order to determine the momentum fraction carried by the neutral mesons inside the dressed nucleon. Received May 30, 1997; revised December 19, 1997; accepted for publication January 30, 1998     

New Asymptotic Formulae for the Point Coulomb Phase Shift

We investigate the Coulomb phase shift, and derive and analyze new and more precise analytical formulae. We consider next to leading order terms to the Stirling’s approximation, and show that they are important at small values of the angular momentum l and other regimes. We employ the uniform approximation. The use of our expressions in low-energy scattering of charged particles is discussed and some comparisons are made with other approximation methods. Potential use of our results in the search for deviations from pure Mott scattering of sub-barrier scattering of very heavy ions is pointed out.     

Virtual Compton scattering off the pseudoscalar meson octet

We present a calculation of the virtual Compton scattering amplitude for the pseudoscalar meson octet in the framework of chiral perturbation theory at O(p ⁴). We calculate the electromagnetic generalized polarizabilities and compare the results in the real Compton scattering limit to available experimental values. Finally, we give predctions for the differential cross section of electron-meson bremsstrahlung.     

Low-energy theorems for nuclear compton and raman scattering and 0+ → 0+ two-photon decays in nuclei

Low-energy theorems for elastic photon scattering (nuclear Compton scattering) from a nucleus of arbitrary spin are derived in the nonrelativistic approximation through terms quadratic in the photon frequency. The same derivation is made for the special case of 0⁺ → 0⁺ nuclear excitation by inelastic photon scattering (nuclear Raman scattering). Use is made of the general principle of gauge invariance, which bypasses the need to specify the form of the current operator explicitly. A general discussion of the contribution of mesonic exchanges is made and their effect is isolated. The center-of-mass correction to the nuclear diamagnetic susceptibility is calculated. The 0⁺ → 0⁺ two-photon decay amplitude is obtained from the nuclear Raman amplitude and the transition rate is calculated.     

Spin polarizabilities of the nucleon from polarized low-energy Compton scattering

As a guideline for forthcoming experiments, we present predictions from Chiral Effective Field Theory for polarized cross-sections in low-energy Compton scattering for photon energies below 170 MeV, both on the proton and on the neutron. Special interest is put on the role of the nucleon spin polarizabilities which can be examined especially well in polarized Compton scattering. We present a model-independent way to extract their energy dependence and static values from experiment, interpreting our findings also in terms of the low-energy effective degrees of freedom inside the nucleon: The polarizabilities are dominated by chiral dynamics from the pion cloud, except for resonant multipoles, where contributions of the -resonance turn out to be crucial. We therefore include it as an explicit degree of freedom. We also identify some experimental settings which are particularly sensitive to the spin polarizabilities.Received: 19 August 2003, Revised: 30 October 2003, Published online: 27 April 2004PACS: 13.40.-f Electromagnetic processes and properties - 13.60.Fz Elastic and Compton scattering - 14.20.Dh Protons and neutronsH.W. Grießhammer: Permanent address: Technische Universität MünchenT.R. Hemmert: Permanent address: Technische Universität München     

Aspects of nucleon Compton scattering

We consider the spin-averaged nucleon forward Compton scattering amplitude in heavy baryon chiral perturbation theory including all terms to order . The chiral prediction for the spin-averaged forward Compton scattering amplitude is in good agreement with the data for photon energies110 MeV. We also evaluate the nucleon electric and magnetic Compton polarizabilities to this order and discuss the uncertainties of the various counter terms entering the chiral expansion of these quantities.     

Deeply virtual Compton scattering on a virtual pion target

We study deeply virtual Compton scattering on a virtual pion that is emitted by a proton. Using a range of models for the generalized parton distributions of the pion, we evaluate the cross section, as well as the beam spin and beam charge asymmetries in the leading-twist approximation. Studying Compton scattering on the pion in suitable kinematics puts high demands on both beam energy and luminosity, and we find that the corresponding requirements will first be met after the energy upgrade at Jefferson Laboratory. As a by-product of our study, we construct a parameterization of pion generalized parton distributions that has a non-trivial interplay between the x and t dependence and is in good agreement with form factor data and lattice calculations.     

The total virtual photoabsorption cross section,deeply virtual Compton scattering and vector-meson production

Based on the generic two-gluon-exchange dynamical mechanism for deeply inelastic scattering at low , we stress the intimate direct connection between the total virtual photoabsorption cross section, deeply virtual Compton scattering and vector-meson electroproduction. A simple expression for the cross section for deeply virtual Compton scattering is derived. Parameter-free predictions are obtained for deeply virtual Compton forward scattering and vector-meson forward production, once the parameters in the total virtual photoabsorption cross section are determined in a fit to the experimental data on deeply inelastic scattering. Our predictions are compared with the experimental data from HERA. Received: 16 February 2004, Revised: 16 July 2004, Published online: 2 September 2004 Supported by Deutsche Forschungsgemeinschaft, contract number schi 189/6-2. An erratum to this article is available at .     

Issues in the GPD Formulation of DVCS

The kinematics used in computing deeply virtual Compton scattering makes a dramatic difference in terms of the widely used reduced operators that define generalized parton distributions. We analyze this difference at tree-level.