Compton-scattering Amplitude Research Articles

Towards fully nonperturbative computations of inelastic ℓN scattering cross sections from lattice QCD

We propose a fully nonperturbative method to compute inelastic lepton-nucleon ($\ensuremath{\ell}N$) scattering cross sections using lattice quantum chromodynamics (QCD). The method is applicable even at low energies, such as the energy region relevant for the recent and future neutrino-nucleon scattering experiments, for which perturbative analysis is invalidated. The basic building block is the forward Compton-scattering amplitude, or the hadronic tensor, computed on a Euclidean lattice. A total cross section is constructed from the hadronic tensor by multiplying a phase space factor and integrating over the energy and momentum of final hadronic states. The energy integral that induces a sum over all possible final states is performed implicitly by promoting the phase space factor to an operator written in terms of the transfer matrix on the lattice. The formalism is imported from that of the inclusive semileptonic $B$ meson decay [P. Gambino and S. Hashimoto, Phys. Rev. Lett. 125, 032001 (2020)] and generalized to compute the $\ensuremath{\ell}N$ scattering cross sections and their moments, as well as the virtual correction to the nuclear $\ensuremath{\beta}$ decay.

A Study of Compton Form Factors in Scalar QED

Deeply virtual Compton scattering has been proposed as a tool to study the structure of hadrons in an exclusive process. The Compton-scattering amplitude can be expressed in terms of scalar quantities, the Compton form factors. Their number depends on the spin of the target as well as the virtuality of the incoming and outgoing photons. For high values of the virtuality Q 2 of the incoming photon, these form factors are expected to scale with inverse powers of Q 2. In this paper these features are studied for a scalar target hadron.

Model-independent determination of K-matrix poles and residues in the Delta (1232) region from the multipole data for pion photoproduction.

Using only the analytic structure of the $K$ matrix and the assumption that the Compton-scattering amplitude is small compared to strong and electrostrong amplitudes, we extract the pole position and the residues for the resonant multipoles, in a model-independent and background-free fashion, directly from the experimentally obtained multipole data base in the $\ensuremath{\Delta}(1232)$ region, posing a challenge for QCD-inspired hadron models.

Pion polarizabilities from backward and fixed-usum rules

Various contributions to the pion polarizabilities are estimated using sum rules obtained from backward and fixed-u = ..mu../sup 2/ (..mu.. = pion mass) dispersion relations for the relevant pion Compton-scattering amplitude. While the s-channel part can be quite reliably computed in terms of the strong and radiative widths of known meson resonances, the evaluation of the t-channel piece remains highly model dependent despite important clarifications provided recently by measurements of the ..gamma gamma --> pi pi.. reaction.

Dispersive approach to the nuclear compton amplitude and exchange effects

We discuss the limitation of the standard approach to exchange current effects from photonuclear sum rules. We propose to look for an energy-independent contribution to the real part of the forward Compton-scattering amplitude below pion threshold. Experimental data on photonuclear cross-sections are used to calculate the real part of the amplitude, by means of an once-subtracted dispersion relation. The analysis is made for2H,7Li and9Be at energies varying between 50 and 150 MeV. A remarkably stable value ofK=0.60 is extracted for deuterium. For 1p shell nuclei, the main uncertainty is due to the lack of data above 300 MeV.

Low-energy theorems for nuclei

A generalization of low-energy theorems is given to obtain the Compton-scattering amplitude on nuclei up to energies smaller than the excitation of nucleons. By means of this technique the presence of seagull terms coming from exchange forces is predicted and the consistency of their contribution is demonstrated in the framework of subtracted dispersion relations.

High-energy photoproduction in a dual relativistic quark Model

The high-energy photoproduction and scaling limits of a previously constructed model for pion electroproduction off nucleons are studied. The amplitude has a satisfactory quark model mass spectrum, spin structure and factorization properties on the leading trajectory. Reasonable values are obtained for forward and backward photoproduction peaks. These results and their significance are discussed and backward pion-nucleon scattering is also examined in the same scheme. Lastly the possibility of our fixed final multiplicity amplitude contributing to the scaling limit of the imaginary part of a Comptonscattering amplitude is examined.

Does Duality Hold in Current Interactions?

Deep-inelastic electron-proton scattering is shown to be naturally interpreted in a field theory where the current is given by a bilinear form in some fields. It is proved that in such a theory the Compton-scattering amplitude is not saturated with the vector-dominance model and that the term which scales in the Bjorken limit does not obey Freund-Harari duality.

Forward Compton Scattering Amplitude as a Simultaneous Analytic Function of Complex Photon Mass and Energy

The analytic structure of the virtual forward Compton scattering amplitude as a function of one and two complex variables is investigated for various combinations of variables which involve the virtual photon mass. This is done both by using the Deser-Gilbert-Sudarshan representation and by using the Feynman perturbation theory. The role and significance of complex Landau singularities is discussed. In general these are branch points, but it is found that at $t=0$ some of these become poles. The effect of these complex singularities and of overlapping cuts on the ordinary single-variable dispersion relations and the mass extrapolations in the vector-meson-dominance model is explained. Using the Cutkosky discontinuity formula for Feynman graphs, the analytic structure of the discontinuities across various normal threshold cuts of the non-Born-term part of this amplitude is deduced. One finds that the two-variable analyticity of the amplitude implies a single-variable analyticity for these discontinuities. It is shown that in general the inelastic structure functions $W$ and $\overline{W}$ cannot be expected to have a simply determinable analytic structure. But under certain conditions $W$ and $\overline{W}$ can be identified with boundary values of the discontinuities across the $s$-and $u$-channel normal threshold cuts in the virtual forward Compton scattering amplitude, respectively. This is used to show that the contribution to $W$ and $\overline{W}$ from certain types of Feynman graphs under certain conditions are analytic functions of one complex variable, and only for such cases can one use crossing symmetry to relate the inelastic-electron-scattering structure functions and the annihilation structure functions. The motion of the Landau singularities of $\ensuremath{\nu}{W}_{2}$ is shown to provide a possible explanation for its observed rapid approach to "scaling" for finite but large final-state masses.

High-energy assumption and subtraction constants in compton-scattering sum rules

Under the assumption that in high-energy limit the forward Compton-scattering amplitude is given by the Born amplitude determined by the interaction of the photon field with the Dirac current of the proton, possible subtraction constants in the sum rules of the Compton scattering are discussed.