Coupling-constant sum rules from fixed-momentum-transfer dispersion relations

Abstract

Fixed-momentum-transfer dispersion relations for the process π+N→ρ+N are considered. Noticing that two of the invariant amplitudes decrease faster than 1/E for large energy E, we have obtained two sum rules involving the coupling constants g_NNπ, g_N^∗Nπ', g_N^∗Nρ(1), g_N^∗Nρ(2), F_N^∗Nρ(1), and F_N^∗Nρ(2). Using experimental information, we determine that F_N^∗Nρ(1)=-2.84 and F_N^∗Nρ(2)=1.03. These results are in agreement with the SU(6) values and are also consistent with the experimental analysis of Albright and Liu.