Isospin andU-Spin Dependence of Hadron-Nucleon Total Cross Sections

The difference ${\sigma }_{\mathrm{tot}}\left({\pi }^{-}p\right)-{\sigma }_{\mathrm{tot}}\left(K^{-}p\right)$ is constant within experimental errors from 6 to 20 BeV/c, while other differences, e.g., ${\sigma }_{\mathrm{tot}}\left({\pi }^{+}p\right)-{\sigma }_{\mathrm{tot}}\left(K^{+}p\right)$ and ${\sigma }_{\mathrm{tot}}\left({\pi }^{-}p\right)-{\sigma }_{\mathrm{tot}}\left({\pi }^{+}p\right)$, decrease considerably in this energy range. All present data agree with the quark-model description which places all energy variation and isospin dependence in quark-antiquark amplitudes, while quark-quark amplitudes are constant and isospin-independent. Quark-model predictions relating the isospin dependence of meson-baryon and baryon-baryon cross sections require better data for a significant test. The use of ${\mathrm{H}}^3$ and ${\mathrm{He}}^3$ targets for direct measurement of isospin dependence is suggested. Errors are enhanced by taking small differences between direct proton- and indirect neutron-target measurements. The importance of direct measurements of these differences goes beyond the quark model, as similar predictions follow from a Regge picture with finite-energy sum rules. Glauber corrections and consistency tests are discussed. Better measurements are of interest also for $U$-spin differences, which are an order of magnitude larger than isospin differences and seem to approach finite values at high energies, indicating $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry breaking at asymptotic energies.