New Sum Rule for Meson-Baryon Total Cross Sections at High Energy

Abstract

Assuming that the dominant underlying mechanism of high-energy meson-nucleon elastic scattering is the exchange of $S{U}_{3}$ octet meson states, a new sum rule relating meson-nucleon total cross sections is derived: ${\ensuremath{\sigma}}_{t}({K}^{\ensuremath{-}}p)\ensuremath{-}{\ensuremath{\sigma}}_{t}({K}^{+}p)={\ensuremath{\sigma}}_{t}({K}^{\ensuremath{-}}n)\ensuremath{-}{\ensuremath{\sigma}}_{t}({K}^{+}n)+{\ensuremath{\sigma}}_{t}({\ensuremath{\pi}}^{\ensuremath{-}}p)\ensuremath{-}{\ensuremath{\sigma}}_{t}({\ensuremath{\pi}}^{+}p).$Comparison of the sum rule with experiment indicates substantial agreement from 10 to 18 BeV/c. The $\frac{f}{d}$ ratio for the charge coupling of the vector-meson octet to the baryon octet is also determined from ratios of total cross-section differences.