Multiple Scattering in the Quark Model

Abstract

We show that a systematic analysis of multiple-scattering contributions in the quark model can explain the detailed structure of the hadronic differential cross sections at high energies. As an extension of previous work on multiple-scattering effects in the quark model, we fit the high-energy differential cross sections for nucleon-nucleon, nucleon-antinucleon, and pion-nucleon scattering, assuming simple forms for the quarkquark scattering amplitudes and the baryon and meson form factors. Of the ten parameters involved, seven are determined by measurements at forward or near-forward angles, leaving the entire wide-angle cross sections to be fitted by the remaining three parameters. Reasonably good fits are obtained to the present data, and calculations at higher t values which may become experimentally accessible in the near future are presented. The parameters found provide some information about the interactions of quarks (should they exist) at high energy and are used to calculate double-scattering corrections to total cross sections and the phase of the nucleon-nucleon amplitude as a function of momentum transfer.

pp Coulomb Phase Shift for Different Proton Charge Distributions

“…The most realistic distribution of these three is the exponential form, which gives good agreement with the experimental data on charge form factors and cross sections of pp scattering at medium and high energy (Elton 1961;Kuroda and Miyazaya 1973;Schiz et al 1981;Fajardo et al 1981). The corresponding form factor for this distribution-the dipole form factor 1/(1+Jd)2 where J-L is a constant and t is the square momentum transfer-is used to describe pp scattering where the composite model of particles is used (Kuroda and Miyazaya 1973;Wakaizumi 1978).…”

“…The corresponding form factor for this distribution-the dipole form factor 1/(1+Jd)2 where J-L is a constant and t is the square momentum transfer-is used to describe pp scattering where the composite model of particles is used (Kuroda and Miyazaya 1973;Wakaizumi 1978). In this model the proton is made of structureless objects (quarks) which are distributed over an extension (Harrington and Pagnamenta 1968).…”

Explanation of Rising Multiplicity with Increasing Perpendicular Momentum Transferred to the Leading Proton, Using the Quark Multiple-Scattering Model

“…In order to produce k pions, we must produce m pions in one collision and k-m pions in the other Thus, summarizing what is shown schematically in Fig. 2, to obtain the differential cross sections for producing k pions we (1) multiply the sum of the squares of the amplitudes for firstorder inelastic pion scattering by the single-order Poisson factor for producing k pions, (2) multiply the sum of the squares of the amplitudes for second-order scattering by the double-order Poisson factor for producing k pions, (3) neglect higher-order diagrams since we know they are small in the momentum-transfer region covered by the experiment, 5 and (4) add all the contributions for producing k pions together.…”

ISR Data on pp Elastic Scattering and Multiple Scattering in the Composite Model

“…Tpp=T~~+T:+T~g>+ ... , (2) where T~~> is the single scattering amplitude between quarks, TJ~> the double scattering one and so on. Each multiple scattering amplitude above, T~~>, involves the corresponding hadronic "form factor" which represents the overlapping of the initial-and the fina1-state wave function of proton constructed from the quark system.…”