Differential cross sections for high energy elastic hadron-hadron scattering in nonperturbative QCD

Total and differential cross sections for high energy and small momentum transfer elastic hadron-hadron scattering are studied in QCD using a functional integral approach. The hadronic amplitudes are governed by vacuum expectation values of lightlike Wegner-Wilson loops, for which a matrix cumulant expansion is derived. The cumulants are evaluated within the framework of the Minkowskian version of the model of the stochastic vacuum. Using the second cumulant, we calculate elastic differential cross sections for hadron-hadron scattering. The agreement with experimental data is good. Received: 3 September 1998 / Published online: 19 November 1998     

Forward hadron-hadron scattering at high energy

The high energy elastic scattering of pp, , pπ⁺, pπ⁻, pk⁺ andpk ⁻ processes is studied at forward directions. The expressions for total scattering cross-sections and the ratios of real-to-imaginary parts of the forward amplitude are derived inP+f model. For the Regge part of the scattering amplitude, the standard form is taken. For the pomeron part, the Harari-Freund conjecture is assumed. The background is assumed to get dominant contributions from the multiparticle exchanges in that channel. These contributions are obtained by parametrising the branch cuts by conformal mapping and polynomial expansion methods. The agreement with the experiment is good. The fits suggest strong exchange degeneracy forpp andkp which in turn is consistent with the Harari-Freund duality.     

Factorization at higher twist in hadron-hadron scattering

We study one-loop soft gluon effects in a scalar quark QCD model of the Drell-Yan process. We find that factorization of the type suggested by Politzer holds at order m²/s, but fails at order m⁴/s². We suggest that this pattern holds to higher orders, and that the non-factoring terms are not suppressed by form factors. We compute the non-factoring contributions, and give a classical interpretation of our results.     

Spin effects in high energy hadron-hadron scattering

The spin-flip amplitudes of the meson-nucleon and nucleon-nucleon scattering are calculated in the framework of the dynamic model taking into account the interactions at large distances. The consideration of the strong form factors at the corresponding vertex and prea-symptotic contributions allowed us to describe correctly the differential cross sections and spin effects of hadron-hadron scattering at high energies. On this basis predictions at high and superhigh energies are made.     

Large corrections to high-pT hadron-hadron scattering in QCD

We have computed the first non-trivial QCD corrections to the quark-quark scattering process which contributes to the production of hadrons at large p_T in hadron-hadron collisions. Using quark distribution functions defined in deep inelastic scattering and fragmentation functions defined in one particle inclusive e⁺e^? annihilation, we find that the corrections are large. This implies that QCD perturbation theory may not be reliable for large-p_T haron physics.     

About the vacuum structure in QCD and hadron-hadron scattering

We comment on an unconventional factorization scheme which has been recently proposed by Nachtmann and Reiter. These authors propose to take into account the influence of the vacuum structure of QCD by including a correlation in spin and colour for the partons that initiate a hard scattering process. We show on a specific example that such a factorization is either trivial in colour or spoiled by leading twist infrared divergences.     

Diffraction model analysis of pion-12C elastic scattering at 800 MeV/c: Optical potential by inversion

Elastic scattering of 800 MeV/c pions by¹²C has been studied in the diffraction model with a view to determine pion optical potential by the method of inversion. Finding an earlier diffraction model analysis to be deficient in some respects, we propose a Glauber model based parametrization for the elasticS-matrix and show that it provides an exceedingly good fit to the pion-carbon data. The proposed elasticS-matrix gives a closed expression for the pion-¹²C optical potential by the method of inversion in the high energy approximation.     

The vacuum structure in QCD and hadron-hadron scattering

Standard ideas on the structure of the vacuum in QCD suggest it to be full of fluctuating color fields. We investigate the possible influence of the chromomagnetic vacuum fields on high energy hadron-hadron reactions. We suggest that high energy quarks traversing these fields will produce soft gluon and photon radiation analogous to synchrotron radiation from electrons and positrons in a storage ring. We argue that this radiation will lead to polarization phenomena for quarks in spin- and colorspace which in turn can explain theK-factor in the Drell-Yan reaction. We point out that jet production offers another way to study these polarization phenomena. We present then a calculation of the number of “synchrotron” photons which should be emitted inp?p collisions at high energies. Thus, we predict a sizable signal of prompt photons of nnergy less than a few hundred MeV with a characteristic frequency distribution. Observation of such photons would give strong support to our naive picture. Finally we point out a number of other phenomena like charmed particle decays where our “synchrotron” effect may be of importance.     

Four-body adiabatic model applied to elastic scattering

Elastic scattering of a projectile, composed of three clusters, from a spherical target is analysed using a four-body adiabatic model. The model is a generalisation of the three-body adiabatic model of Johnson and Soper. Calculations of the elastic scattering of ¹¹Li from ¹²C are compared to both experimental data and the results of recent four-body eikonal model calculations.     

Boundary condition model for diffractive elastic scattering

Diffractive elastic scattering is studied by a boundary condition model that does not utilize a potential model.S-matrix elements are calculated and compared to those found from an optical potential model calculation. The unitarity of the model is related to the boundary condition imposed. A radially ingoing boundary condition is imposed on the wave function at one angle only, at a scattering angle of 180 °. This condition is required to hold in the vicinity of the nuclear radius, but not for all radii. Elastic scattering peaks at forward and backward angles are reproduced and discussed. The model is applied to composite particle scattering above the Coulomb barrier.     

Ab-initio optical model theory of elastic electron-atom scattering

We analyze the elastic scattering of fast electrons by atoms, using a second order optical potential obtained from first principles. Our results are in excellent agreement with recent absolute experimental data for electron-helium and electron-neon collisions.     

The optical model for the elastic deuteron scattering

An optical model for the elastic scattering of deuterons by nuclei is derived from first principles. The influence of the Pauli principle is investigated in nuclear matter and found to be small. Surface effects due to the finite size of the deuteron are studied in terms of a perturbation expansion. The first order term agrees well with the 100 MeVfit of the real potential depth to the experimental data, the second order term is shown to be two orders of magnitude smaller.