Eikonal Propagators Research Articles

Sivers distribution functions of sea quarks in a proton with the chiral Lagrangian

We propose a mechanism for the Sivers distribution function in proton with chiral Lagrangian. By introducing the gauge link of the vector meson, the transverse momentum dependent distribution of a pion in the nucleon is re-defined which is locally $SU(2)_V$ invariant as the Lagrangian. The eikonal propagator is generated from the gauge link and this scenario is proved to be equivalent to the final state interaction. By combining the calculated splitting function and the valence $\bar{q}$ distribution in $\pi$ from the recent fit, the sea quark Sivers function in proton is obtained. We find reasonable numerical results for the first momentum $x\Delta^Nf_{\bar{q}}^{(1)}(x)$ without any fine tuning of the free parameters.

Equality of hemisphere soft functions for [formula omitted], DIS and pp collisions at [formula omitted

We present a simple observation about soft amplitudes and soft functions appearing in factorizable cross sections in ee, ep, and pp collisions that has not clearly been made in previous literature, namely, that the hemisphere soft functions that appear in event shape distributions in e+e−→dijets, deep inelastic scattering (DIS), and in Drell–Yan (DY) processes are equal in perturbation theory up to O(αs2), even though individual amplitudes may have opposite sign imaginary parts due to changing complex pole prescriptions in eikonal propagators for incoming vs. outgoing lines. We also explore potential generalizations of this observation to soft functions for other observables or with more jets in the final state.

Corrections to the eikonal approximation for nuclear scattering at medium energies

The upcoming Facility for Rare Isotope Beams (FRIB) at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University has reemphasized the importance of accurate modeling of low energy nucleus-nucleus scattering. Such calculations have been simplified by using the eikonal approximation. As a high energy approximation, however, its accuracy suffers for the medium energy beams that are of current experimental interest. A prescription developed by Wallace \cite{Wallace:1971zz,Wallace:1973iu} that obtains the scattering propagator as an expansion around the eikonal propagator (Glauber approach) has the potential to extend the range of validity of the approximation to lower energies. Here we examine the properties of this expansion, and calculate the first-, second-, and third-order corrections for the scattering of a spinless particle off of a ${}^{40}$Ca nucleus, and for nuclear breakup reactions involving ${}^{11}$Be. We find that, including these corrections extends the lower bound of the range of validity of the down to energies of 40 MeV. At that energy the corrections provide as much as a 15\% correction to certain processes.

Collins asymmetry at hadron colliders

We study the Collins effect in the azimuthal asymmetricdistribution of hadrons inside a high energy jet in the single transversepolarized proton proton scattering. From the detailed analysis ofone-gluon and two-gluon exchange diagrams contributions, the Collinsfunction is found the same as that in the semi-inclusive deep inelasticscattering and e+e- annihilations. The eikonal propagators in thesediagrams do not contribute to the phase needed for the Collins-typesingle spin asymmetry, and the universality is derived as a result of theWard identity. We argue that this conclusion depends on the momentum flowof the exchanged gluon and the kinematic constraints in the fragmentationprocess, and is generic and model-independent.

Eikonal propagators and high-energy parton–parton scattering in gauge theories

In this paper we consider “soft” high-energy parton–parton scattering processes in gauge theories, i.e., elastic scattering processes involving partons at very high squared energies s in the center of mass and small squared transferred momentum t ( s →∞, t ⪡ s , typically | t |⩽1 GeV 2 ). By a direct resummation of perturbation theory in the limit we are considering, we derive expressions for the truncated–connected quark (antiquark) propagator in an external gluon field, as well as for the residue at the pole of the full unrenormalized propagator, both for scalar and fermion gauge theories. These are the basic ingredients to derive high-energy parton–parton scattering amplitudes, using the LSZ reduction formulae and a functional integral approach. The above procedure is also extended to include the case in which at least one of the partons is a gluon. The meaning and the validity of the results are discussed.

Charge exchange and excitation in H+He2+ and He++H+ collisions using single- and multichannel perturbed-stationary-state propagators.

Our recently formulated (preceding paper, PP I) semiclassical perturbed-stationary-state single- and multichannel propagators are applied to study the collisions of ${\mathrm{He}}^{2+}$ on H(1s) and ${\mathrm{H}}^{+}$ on ${\mathrm{He}}^{+}$(1s), including as many as 45 molecular adiabatic states unmodified by an electron translation factor. In the energy range below the collisional ionization threshold, a multichannel eikonal propagator with 45 states reproduces the total charge-exchange cross sections---a feat that a single-channel theory cannot accomplish, as convergence with respect to the basis size indicates conclusively. In this region of negligible ionization, the 45-state multichannel cross sections are also in reasonably good agreement with other semiclassical calculations that employ either atomic or molecular basis functions modified by translation factors. Regarding level-selective cross sections, however, our results and previous translation-factor-based predictions are far apart. The multichannel propagator yields higher cross sections for transfer into excited states whose participation is artificially attenuated in the other models by the translation factor. In light of our findings, we discuss recent experimental measurements of uv emission induced in collisions of hydrogen and \ensuremath{\alpha} particles and suggest an interpretation that invokes optical interference to explain the observed Balmer-\ensuremath{\alpha} cross sections and, perhaps, also the slightly low radiative-quenching yield of the product metastable helium ion.

High-energy pion-nucleus elastic scattering.

We investigate theoretical approaches to pion--nucleus elastic scattering at high energies (300 $\le T_\pi \le$ 1 GeV). A ``model--exact'' calculation of the lowest--order microscopic optical model, carried out in momentum space and including the full Fermi averaging integration, a realistic off--shell pion--nucleon scattering amplitude and fully covariant kinematics, is used to calibrate a much simpler theory. The simpler theory utilizes a local optical potential with an eikonal propagator and includes the Coulomb interaction and the first Wallace correction, both of which are found to be important. Comparisons of differential cross sections out to beyond the second minimum are made for light and heavy nuclei. Particularly for nuclei as heavy as $^{40}$Ca, the eikonal theory is found to be an excellent approximation to the full theory. (8 Figures available from authors)

Total reaction cross sections and the matter density of finite nuclei

A simple model for total reaction cross sections based on the impulse approximation and the use of an eikonal propagator is derived. Semiquantitative approximations are used to demonstrate that total reaction cross sections are determined by the radius at which the profile function is equal to one mean free path for the incident particle. A simple quantitative relation between the density and the profile function is also provided. The model is tested against existing data for proton-nucleus total reaction cross sections for $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{40,44,48}\mathrm{Ca}$, and $^{208}\mathrm{Pb}$ targets at energies from 100 MeV to 1 GeV. The total reaction cross sections are generally found to be in agreement (with several exceptions) with neutron densities determined either theoretically or from other experiments.NUCLEAR REACTIONS Total reaction cross sections, matter densities and radii.

Eikonal and Fresnel corrections to the Glauber theory of nuclear multiple scattering

Starting from a Watson-type multiple scattering series we study first-order corrections to the Glauber high-energy collision model. These are obtained by replacing the free-space Green function between successive scatterings by the second-order eikonal propagator. We distinguish between Fresnel corrections and eikonal-type corrections. Due to large cancellation effects the eikonal contribution is very small compared to the Fresnel contribution. First-order corrections to Glauber theory are calculated explicitly for high-energy elastic scattering of protons from light nuclei ( 4He, 12C, 16O).

Fresnel diffraction in high-energy multiple scattering

Abstract We study the effects of Fresnel diffraction on the multiple scattering of high-energy hadrons in complex nuclei. Starting from a Watson-type multiple scattering series, we approximate the free-space propagators by Fresnel propagators. By employing the unitary transformation that connects the Fresnel and eikonal propagators, we derive a closed expression for the multiple scattering amplitude which is formally similar to the corresponding Glauber expression. The Fresnel diffraction effects manifest themselves in a characteristics Dyson-type ordering of the profile operators with respect to the z -coordinates of the target nucleons. The general formulae are then applied to elastic scattering by a target nucleus represented by an independent particle model. As an example, the amplitude for nucleon-deuteron scattering is explicitly evaluated and compared with a result previously derived by Gottfried.

Schwinger's Proper-Time Method and the Eikonal Approximation

Eikonal techniques are used to present an alternative treatment of the electron's Green's function in the presence of a plane-wave field. After studying the propagation of an electron in a prescribed electromagnetic field we eikonalize the corresponding Green's function. If the external field is chosen to be a laser field, the approximate eikonal propagator is turned into an exact one: Additional assumptions characterizing the eikonal approximation are automatically satisfied. The methods employed are Schwinger's pre-source-theory functional techniques.

Relativistic eikonal propagators and high-energy scattering in QED

Functional methods are presented for constructing the relativistic eikonal propagator in an external electromagnetic field whereby large virtual momenta of the exchanged vector meson are taken into account. The high-energy scattering amplitude is presented in the Levy-Sucher representation. Results include the usual cancellation of ln s terms and unitarity correction if non-ladder-type diagrams (towers) are included. Contact is made with earlier work on eikonal amplitudes in the forward direction.

Eikonal formulation in neutral scalar field theory

A detailed study is presented of the eikonal approximation in a field theory with interaction Lagrangian L′ = − 1 2 gψ 2φ . Eikonal propagators are obtained in a prescribed external field and used to evaluate a certain subclass of Feynman diagrams. Contrary to QED it is not possible to generate a bound state spectrum by an infinite mass limit. We approach our problem using Schwinger's functional methods.