Numerical Analysis of Hadron Total Cross Sections in the Quark Model

The linear parametrization of the hadron-hadron total-scattering cross sections at high energy given by the additive quark model are compared with experiment by a least-squares analysis using several different kinematic assumptions. Expressions for the corrections due to shadowing and double scattering are obtained, and the corrections are shown to be large enough to be important. A nonlinear parametrization obtained from the expression for the shadowing correction is compared with experiment by a least-squares analysis. The agreement is good under two different kinematic assumptions. Agreement is also good using the linear parametrization with the kinematic assumptions of James and Watson. In all cases studied, the amplitude for scattering of the $\lambda$ quark from a nonstrange quark is significantly lower than the amplitude for scattering of two nonstrange quarks. The amplitude for the scattering of the nonstrange quark and antiquark in an iso-singlet state is both significantly larger and much more energy-dependent than any of the other amplitudes.