Nucleon-nucleon, γp and γγ scattering using factorization: the Aspen model and analytic amplitude analysis

Abstract

Using the Aspen, model, a QCD-inspired eikonal model, we fit high energy nucleon-nucleon total cross sections, nuclear slopes and ϱ-values, including cosmic ray p-air data. This model which is crossing symmetric, insures unitarity and analyticity, as well as satisfying the Froissrt bound. Assuming that the ratio of σelastic/σtotal is independent of process, the Aspen model predicts factorization. Utilizing the model parameters found for nucleon-nucleon scattering, we predict the total cross sections and nuclear slope parameters for γp reactions, as well as total cross sections for γγ scattering, by invoking the naive quark model and vector dominance. In particular, by making a χ2 fit to the nuclear slope parameters for the ‘elastic’ reactions γ + p → ϱ+p, γ+p → φ+p, γ+p → ω+p, we find the proportionality constant κ = 0.661±0.008, in excellent agreement with the value of κ = 23 predicted by the naive vector quark model (2 quarks in the vector meson-like photon and 3 quarks in the nucleon). We next test the (lack of) sensitivity of the factorization theorems to the assumed distributions of the impact parameter b, for nucleon-nucleon, γp and γγ scattering, that are used in the eikonal. Finally, making an independent analysis utilizing real analytical amplitudes and assuming factorization, we make a simultaneous fit to the total cross sections for pp, pp, γp and γγ cross sections, as well as the ϱ-values for pp and pp. In this global fit we separately fit to the results of L3 and OPAL obtained using either the PHOJET or PYTHIA Monte Carlo program—the published values use the average of the two. It should be noted that these two Monte Carlos give different normalizations as well as different energy behaviors. The overall fit is good using PHOJET and poor using PYTHIA, lending strong support for the factorization hypothesis, as well as the naive quark model and vector dominance.