Radiative Corrections to Electron-Proton Scattering

The radiative corrections to elastic electron-proton scattering are analyzed in a hadronic model including the finite size of the nucleon. For initial electron energies above 8 GeV and large scattering angles, the proton vertex correction in this model increases by at least two percent the overall factor by which the one-photon exchange (Rosenbluth) cross section must be multiplied. The contribution of soft photon emission is calculated exactly. Comparison is made with the generally used expressions previously obtained by Mo and Tsai. Results are presented for some kinematics at high momentum transfer.Comment: 31 pages, 4 figure

Relativistic Effects in the Electromagnetic Current at GeV Energies

We employ a recent approach to the non-relativistic reduction of the electromagnetic current operator in calculations of electronuclear reactions. In contrast to the traditional scheme, where approximations are made for the transferred momentum, transferred energy and initial momentum of the struck nucleon in obtaining an on-shell inspired form for the current, we treat the problem exactly for the transferred energy and transferred momentum. We calculate response functions for the reaction $^2H(e,e'p)n$ at CEBAF (TJNAF) energies and find large relativistic corrections. We also show that in Plane Wave Impulse Approximation, it is always possible to use the full operator, and we present a comparison of such a limiting case with the results incorporating relativistic effects to the first order in the initial momentum of the struck nucleon.Comment: 31 pages, 8 figures, Revte

The Role of Final State Interactions in Quasielastic 56^{56}Fe(e,e′)(e,e') Reactions at large ∣q⃗∣|\vec q|

A relativistic finite nucleus calculation using a Dirac optical potential is used to investigate the importance of final state interactions [FSI] at large momentum transfers in inclusive quasielastic electronuclear reactions. The optical potential is derived from first-order multiple scattering theory and then is used to calculate the FSI in a nonspectral Green's function doorway approach. At intermediate momentum transfers excellent predictions of the quasielastic $^{56}$Fe$(e,e')$ experimental data for the longitudinal response function are obtained. In comparisons with recent measurements at $|{\vec q|}=1.14$~GeV/c the theoretical calculations of $R_L$ give good agreement for the quasielastic peak shape and amplitude, but place the position of the peak at an energy transfer of about $40$~MeV higher than the data.Comment: 13 pages typeset using revtex 3.0 with 6 postscript figures in accompanying uuencoded file; submitted to Phys. Rev.

Field transformations and simple models illustrating the impossibility of measuring off-shell effects

In the context of simple models illustrating field transformations in Lagrangian field theories we discuss the impossibility of measuring off-shell effects in nucleon-nucleon bremsstrahlung, Compton scattering, and related processes. To that end we introduce a simple phenomenological Lagrangian describing nucleon-nucleon bremsstrahlung and perform an appropriate change of variables leading to different off-shell behavior in the nucleon-nucleon amplitude as well as the photon-nucleon vertex. As a result we obtain a class of equivalent Lagrangians, generating identical S-matrix elements, of which the original Lagrangian is but one representative. We make use of this property in order to show that what appears as an off-shell effect in an S-matrix element for one Lagrangian may originate in a contact term from an equivalent Lagrangian. By explicit calculation we demonstrate for the case of nucleon-nucleon bremsstrahlung as well as nucleon Compton scattering the equivalence of observables from which we conclude that off-shell effects cannot in any unambiguous way be extracted from an S-matrix element. Finally, we also discuss some implications of introducing off-shell effects on a phenomenological basis, resulting from the requirement that the description of one process be consistent with that of other processes described by the same Lagrangian.Comment: 19 pages, Latex, using RevTe

Form factors and photoproduction amplitudes

We examine the use of phenomenological form factors in tree level amplitudes for meson photoproduction. Two common recipes are shown to be fundamentally incorrect. An alternate form consistent with gauge invariance and crossing symmetry is proposed.Comment: To be published in PR

Gauge-invariant tree-level photoproduction amplitudes with form factors

We show how the gauge-invariance formulation given by Haberzettl is implemented in practice for photoproduction amplitudes at the tree level with form factors describing composite nucleons. We demonstrate that, in contrast to Ohta's gauge-invariance prescription, this formalism allows electric current contributions to be multiplied by a form factor, i.e., it does not require that they be treated like bare currents. While different in detail, this nevertheless lends support to previous ad hoc approaches which multiply the Born amplitudes by an overall form factor. Numerical results for kaon photoproduction off the nucleon are given. They show that the gauge procedure by Haberzettl leads to much improved $\chi^2$ values as compared to Ohta's prescription.Comment: 5 pages, RevTeX, two eps figure

Consistent off-shell πNN\pi N N vertex and nucleon self-energy

We present a consistent calculation of half-off-shell form factors in the pion-nucleon vertex and the nucleon self-energy. Numerical results are presented. Near the on-shell point the pion-nucleon vertex is dominated by the pseudovector coupling, while at large nucleon invariant masses we find a sizable pseudoscalar admixture.Comment: 23 pages, 7 figures, REVTeX, submitted to Phys. Rev. C, replaced with corrected versio

Gauge-invariant theory of pion photoproduction with dressed hadrons

Based on an effective field theory of hadrons in which quantum chromodynamics is assumed to provide the necessary bare cutoff functions, a gauge-invariant theory of pion photoproduction with fully dressed nucleons is developed. The formalism provides consistent dynamical descriptions of pi-N --> pi-N scattering and Gamma-N --> pi-N production mechanisms in terms of nonlinear integral equations for fully dressed hadrons. Defining electromagnetic currents via the gauging of hadronic n-point Green's functions, dynamically detailed currents for dressed nucleons are introduced. The dressed hadron currents and the pion photoproduction current are explicitly shown to satisfy gauge invariance in a self-consistent manner. Approximations are discussed that make the nonlinear formalism manageable in practice and yet preserve gauge invariance. This is achieved by recasting the gauge conditions for all contributing interaction currents as continuity equations with ``surface'' terms for the individual particle legs coming into or going out of the hadronic interaction region. General procedures are given that approximate any type of (global) interaction current in a gauge-invariance preserving manner as a sum of single-particle ``surface'' currents. It is argued that these prescriptions carry over to other reactions, irrespective of the number or type of contributing hadrons or hadronic systems.Comment: 33 pages, RevTeX; includes 8 postscript figures (requires psfig.sty). This version corrects some minor errors, etc.; contains updated references. Accepted for publication in Phys. Rev. C56 (Oct. 97

A Gauge Invariant Unitary Theory for Pion Photoproduction

A covariant, unitary and gauge invariant theory for pion photoproduction on a single nucleon is presented. To achieve gauge invariance at the operator level one needs to include both the $\pi N$ and $\gamma\pi N$ thresholds. The final amplitude can be written in terms of a distorted wave in the final $\pi N$ channel provided one includes additional diagrams to the standard Born term in which the photon is coupled to the final state pion and nucleon. These additional diagrams are required in order to satisfy gauge invariance.Comment: 4 pages, LaTeX, 1 figure as a separate uuencoded compressed tar fil

Compactification near and on the light front

We address problems associated with compactification near and on the light front. In perturbative scalar field theory we illustrate and clarify the relationships among three approaches: (1) quantization on a space-like surface close to a light front; (2) infinite momentum frame calculations; and (3) quantization on the light front. Our examples emphasize the difference between zero modes in space-like quantization and those in light front quantization. In particular, in perturbative calculations of scalar field theory using discretized light cone quantization there are well-known ``zero-mode induced'' interaction terms. However, we show that they decouple in the continuum limit and covariant answers are reproduced. Thus compactification of a light-like surface is feasible and defines a consistent field theory.Comment: 24 pages, 4 figure