Self-Consistent Multiple-Quark-Scattering Analysis and Its Application to Elastic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mi/><mml:mi>p</mml:mi></mml:math>Scattering

Abstract

We discuss a viewpoint for interpreting elastic scattering of hadrons in terms of a picture in which the hadrons behave as if they are comprised effectively of $A$ distinct subparticles $Q$ which contribute essentially individually to multiple-internal-scattering processes within the hadrons. The formalism of this multiple-internal-scattering picture is developed and applied to the analysis of elastic $\mathrm{pp}$ scattering. The discontinuities in the slope of the $\mathrm{pp}$ differential cross section at large momentum transfers are interpreted as transitions between domains of momentum transfer that are dominated by successively higher-order multiple-scattering contributions. The structure of the $\mathrm{pp}$ cross section is fitted in good detail with a self-consistent analysis that circumvents the necessity for conjectures about the wave functions of internal motion of the subparticles $Q$ within $p$ by exploiting simpler and more direct conditions and conjectures on the effective generalized form factors and scattering amplitudes. The higher-order multiple-scattering contributions are self-consistently calculated in terms of the effective $\mathrm{QQ}$ scattering amplitude determined from the region of the first slope. The analysis distinguishes among subparticle models to yield an essentially exclusive fit to the experimental data with the value of the quark number of the proton $A=3$, thereby affording corroborative evidence in favor of the ${\mathrm{SU}}_{3}$ quark model from a non-group-theoretical, dynamical basis. Our results are compatible with quarks of very small, or even pointlike, spatial extension as compared to the effective electromagnetic radius of the proton.