Compton Amplitude Research Articles

Tree-level unitarity constraints on the gravitational couplings of higher-spin massive fields.

We analyze the high-energy behavior of tree-level graviton Compton amplitudes for particles of mass m and arbitrary spin, concentrating on a combination of forward amplitudes that will be unaffected by eventual cross couplings to other, higher spins. We first show that for any spin >2, tree-level unitarity is already violated at energies \ensuremath{\sim} \ensuremath{\surd}${\mathit{mM}}_{\mathrm{Pl}}$ , rather than at the Planck scale ${\mathit{M}}_{\mathrm{Pl}}$, even for m\ensuremath{\ll}${\mathit{M}}_{\mathrm{Pl}}$. We then restore unitarity to this amplitude up to ${\mathit{M}}_{\mathrm{Pl}}$ by adding nonminimal couplings that depend on the curvature and its derivatives, and modify the minimal description, including particle gravitational quadrupole moments, at \ensuremath{\sim}${\mathit{m}}^{\mathrm{\ensuremath{-}}1}$ scales.

Incompatibility of multipole predictions for the nucleon spin-polarizability and Drell-Hearn-Gerasimov sum rules.

Energy-weighted integrals of the difference in helicity-dependent photoreaction cross sections (${\mathrm{\ensuremath{\sigma}}}_{1/2}$-${\mathrm{\ensuremath{\sigma}}}_{3/2}$) provide information on the nucleon's spin-dependent polarizability (\ensuremath{\gamma}), and on the spin-dependent part of the asymptotic forward Compton amplitude through the Drell-Hearn-Gerasimov (DHG) sum rule. Estimates from current \ensuremath{\pi}-photoproduction multipole analyses, particularly for the proton-neutron difference, are in good agreement with relativistic-one-loop chiral calculations for \ensuremath{\gamma} but predict large deviations from the DHG sum rule. Either (a) both the two-loop corrections to the spin-polarizability are large and the existing multipoles are wrong, or (b) modifications to the Drell-Hearn-Gerasimov sum rule are required to fully describe the isospin structure of the nucleon.

Small momentum evolution of the extended Drell-Hearn-Gerasimov sum rule.

We investigate the momentum dependence of the extended Drell-Hearn-Gerasimov sum rule. An economical formalism is developed which allows to express the extended DHG sum rule in terms of a single virtual Compton amplitude in forward direction. Rigorous results for the small momentum evolution are derived from chiral perturbation theory within the one-loop approximation. Furthermore, we evaluate some higher order contributions arising from $\Delta(1232)$ intermediate states and relativistic corrections. (2 figures available upon request).

Chiral structure of the nucleon

We analyze the structure of QCD Green functions with one external nucleon, treated as a very massive field. We discuss the matching conditions and relations of various nucleon matrix elements of quark currents to the relativistic approach. Particular emphasis is put on the forward Compton amplitudes. Besides the nucleon electromagnetic polarizabilities we consider the spin-flip amplitude ƒ 2(ω 2) to one-loop order. We predict the slope parameter of ƒ 2(ω 2) which can be determined from the absorption cross sections of circularly polarized photons on polarized nucleons.

Gauge invariance and the nonrelativistic Ward-Takahashi identity.

A simple derivation is given of the nonrelativistic Ward-Takahashi identity, which has been used in nearly every derivation of low-energy theorems for electromagnetic processes in nuclei. The low-energy theorem for Compton scattering is derived without assuming that identity. It is shown that gauge invariance alone leads to the correct form for the Compton amplitude, except that the magnetic recoil term does not have its conventional form. Use of Siegert's theorem, however, leads to that form.

Model-independent connections between pion photoproduction and Compton scattering in the Delta (1232) region.

We exploit Grushin {ital et} {ital al}.'s {ital independent} {ital determinations} of the real and the imaginary parts of the pion photoproduction multipoles in the {Delta}(1232) region, without the use of an approximate form of Watson's theorem, and obtain model-independent estimates for the Compton amplitudes for the resonance excitation off nucleons. We compare these with the results obtained from other analyses of photoproduction multipoles. We find the lower bound for the differential cross section using unitarity, and compare our results with available experiments, both the older-generation experiments, primarily at Bonn, and the preliminary results from the recent studies at the Saskatchewan Accelerator Lab. We explore consistency of photoproduction multipoles with the forward Compton scattering amplitude extracted from the measured total hadronic cross sections of photons in hydrogen, using the optical theorem. Finally, we discuss implications for future precision Compton studies of the {Delta}(1232) excitation, in particular, attempts to measure the {ital E}2 to {ital M}1 amplitude ratio, in the nucleon-to-{Delta} electromagnetic transition, which will be feasible at new photon facilities such as the Brookhaven Laser Electron-Gamma Source, exploring the photon polarization observables. These amplitudes contain valuable information on the structure of nucleon and {Delta} baryons, of great topical interest. Wemore » vividly demonstrate here the inadequacy of the older generation of Compton scattering experiments, as their poor photon energy resolution and counting statistics limit the quality of physics extractable from the data. This urgently calls for newer-generation {ital high}{minus}{ital statistics} experiments with {ital high} photon energy resolution, using the photon polarization as a powerful tool.« less

Higher-twist parton distributions in QCD 2

The higher-twist structure functions are calculated in QCD 1+1 and formal sum rules are derived. It is demonstrated that the sum rule for the first moment of ƒ 4 is violated if one restricts the integration to “experimental data” ( x > 0). However, the sum rule is valid if a δ-function at the origin is taken into account. The physical origin of this δ-function is clarified from the point of view of canonical light-cone quantization (“zero mode” for the “bad” component) as well as using dispersion relations (fixed pole). The coefficient of the δ-function can be calculated by means of these dispersion relations as well as by considering a slightly non-forward Compton amplitude instead of the usual forward amplitude.

Gauge-invariant forms of the nonrelativistic Compton amplitude.

Various forms of the long-wavelength, nonrelativistic nuclear Compton amplitude are discussed. Simple manipulations allow the usual low-energy theorem for the amplitude to be cast into a manifestly gauge-invariant form, which facilitates interpretation.

Perturbative QCD calculation of real and virtual Compton scattering.

We present the predictions of perturbative QCD for Compton scattering as a function of photon virtuality. Individual helicity amplitudes are given, along with formulas to permit calculation of the $\mathrm{eN}\ensuremath{\rightarrow}{e}^{\ensuremath{'}}{N}^{\ensuremath{'}}\ensuremath{\gamma}$ amplitudes. We discover remarkable structure in some of the amplitudes as a function of photon virtuality. Since $\mathrm{eN}\ensuremath{\rightarrow}{e}^{\ensuremath{'}}{N}^{\ensuremath{'}}\ensuremath{\gamma}$ contains a contribution from Bethe-Heitler scattering, whose magnitude and phase are known, the phases of the virtual Compton amplitudes can in principle be measured by interference with it. It has been shown that the leading-twist behavior of high-energy, large-angle Compton scattering is not affected by soft physics; thus at sufficiently high energies these predictions provide a stringent test of QCD.

Deuteron Compton scattering.

The theory of deuteron Compton scattering developed previously (Phys. Rev. C 38, 611 (1988)) is reviewed and corrected in some minor points. Numerical results are presented and compared with other theoretical approaches. In particular, I now find reasonable agreement with a previous dispersion theoretical analysis of this process. I also get good agreement with low-energy parameters calculated elsewhere. I present predictions for angular distribution cross sections at a number of energies. These are of particular interest, since experiments at these energies are presently under way. I also investigate the influence of the spin-orbit correction to the current operator on the Compton amplitude.

Boson exchange phenomenology: A first step from nucleons to nuclei

We investigate medium renormalization effects of strong and weak meson-nucleon vertex functions in the framework of a non-linear chiral meson theory. The density dependence of the nucleon properties is entirely determined by the medium renormalization of the fundamental meson parameters. Our results indicate a mild density dependence of the strong-coupling constants and quenching of the respective form factors. The parity-violating weak meson-nucleon couplings are strongly suppressed in the medium even for moderate density variations of the mesonic parameters like e.g. the pion decay constant or the vector meson masses. We discuss the implications of these results for the boson-exchange phenomenology of strong and weak nuclear forces. We also study the Δ(1232) resonance in the medium. We find that for constant vector meson masses, the NΔ mass splitting M Δ − M N is not shifted from its free space value whereas for decreasing vector meson masses it is quenched by ∼10%. We compare these results to empirical information gained from the study of the nuclear forward Compton amplitude. We also show that the coupling of scalar particles by means of the QCD trace anomaly does not affect the medium renormalization of the nucleon properties.

Photonuclear dispersion relation and Δ excitations in nuclei

A dispersion relation analysis of the existing photonuclear data from proton and deuterium to uranium is performed. It is found that the real part of the nuclear forward Compton amplitude in the region of the Δ (1232) resonance has its zero at a universal energy ω0≃327±5 MeV throughout the periodic table. This fact can be used to arrive at a representation of the Gell-Mann, Goldberger and Thirring sum rule.

Compton scattering off the deuteron at low and intermediate energies.

Compton scattering off the deuteron is studied for photon energies up to about 100 MeV. This energy limit reflects the fact that only intermediate nucleon-nucleon (NN) states are considered. The NN propagator is constructed in a separable potential model, the parameters of which are fitted to describe the experimental NN scattering phase shifts. The problem of gauge invariance of the Compton amplitude is analyzed and the role of nonlocal currents is discussed. The low-energy theorem is satisfied. Our approach enables a direct calculation of both the real and imaginary part of the Compton scattering amplitude. It turns out that the strongest multipoles are dominated by the Born terms. Numerical results are compared to a previous dispersion theoretical calculation, and we find a strong disagreement between both calculations. We are led to conclude that certain assumptions made in the dispersion theoretical calculation are not justified.

Constraints from the Drell-Hearn-Gerasimov sum rule in chiral models of composite fermions.

We analyze a dispersion relation for a spin-flip Compton amplitude in a chiral model of composite quarks and leptons. We discuss the asymptotic behavior of the amplitude and show under what conditions the Drell-Hearn-Gerasimov sum rule holds. Using a small-mass expansion we derive a consistency condition that relates the photoproduction cross sections for different helicities. We show that this condition suggests the existence of higher-spin excited fermions, as well as relations among a priori independent photoproduction amplitudes.

Compton scattering and pion number in nuclei

We explore the relation between the spin-independent Compton amplitude and the pion excess number per nucleon n π in nuclear matter and for the dueteron. We show that the enhancement factor K of the photonuclear sum rule, which appears as a meson exchange correction to this amplitude, is related to n π by K ≈ 16 3 n πM〈ω π −1〉 where 〈ω π −1〉 is the mean inverse pion energy. This relation is justified by the consideration of the chiral limit where the pion mass vanishes.

Gauge-invariant nuclear Compton amplitude manifesting low-energy theorems.

The electromagnetic field representation of the nuclear electromagnetic interaction is developed, by extending previous work on the nuclear current (one-photon amplitude) to the nuclear Compton amplitude. The resulting form of the Compton amplitude is gauge invariant and, in transverse gauge, manifests the low-energy theorems for the ${0}^{+}$\ensuremath{\rightarrow}${0}^{+}$ case, which is discussed in detail. Deuteron forward photodisintegration is also studied numerically, and it is shown that the generalized Siegert form of the retarded electric dipole interaction efficiently incorporates pion-exchange currents implicitly, while large explicit forms of these currents are needed in the standard representation of the interaction. Gauge invariance and Reiss's strong-field momentum-translation approximation are also discussed.

Photonuclear reactions and dispersion relations

We study the photonuclear reaction in the intermediate region. We evaluate the real part of the forward Compton amplitude through the dispersion relation and analyze its structure.

A second lemma in hadron Compton scattering

Using gauge invariance we show that the time-space part of the excited-state hadron Compton scattering amplitude can be written as E/sub 0j//sup alphabeta/ = k/sub 1//sup prime/GAMMA/sub ij//sup alphabeta/ where GAMMA/sub i/j/sup alphabeta/ is odd under crossing in the Breit frame. The usefulness of this result in obtaining higher-order low-energy theorems for the Compton amplitude is discussed.

Parton distribution functions for twist 4

All O(1/ Q 2) corrections to leptoproduction are described by a small number of generalized multiparton distribution functions which depend only on the longitudinal momentum of the partons. We show that these functions can be represented (in A + = 0 gauge) by sequential emission or absorption by the target of quarks, antiquarks and gluons where (i) all quanta move with 0 ⩽ k +/ p + ⩽ 1; (ii) all intermediate hadronic states are on-mass-shell; (iii) no graphs are semi-disconnected with respect to the target or the intermediate hadronic state. We show how all O(1/ Q 2) corrections to the forward virtual Compton amplitude can be represented in terms of these parton distributions.

Unitarity with quarks despite confinement: Connection between deep inelastic scattering and deep inelastic annihilation processes in the scaling limit

We prove that in a parton model which incorporates confinement there exists a subtle connection between analyticity of the virtual Compton amplitude and unitarity with quarks. Then we show that the experimental data on\(\nu \bar W_2 \) for pions and νW2 for nucleons indicatein our model an exactly zero free mass of at least one of the u or d quarks. This turns out, also, to be essential to understand the accepted behaviour of the pion electromagnetic form factor.