Decay width, magnetic moments, and transition moment of nucleon isobars from algebra of currents

Abstract

Using the equal-time commutation relations of axial vector current-current and current-magnetic moment operators, sum rules for the reduced matrix elements of these operators are obtained. These sum rules correspond to a set of an infinite number of coupled equations which are solved by truncating the intermediate states at various stages. A systematic study has been made to examine how quantities like axial vector renormalization constant, decay width ofN*(1238), ratio of\((\mathcal{N}^{ * ( + )} \mathcal{N}^{ * ( + )} \pi ^{(0)} )\) toNNπ couplings, magnetic moments of nucleon isobars, and the transition moments of nucleon toN*(+), vary with truncations. It is also noticed that if one truncates the states in a particular fashion, results normally ascribed to higher symmetry groups are reproduced. Over and above it is found that if all the diagonal statesI=J are retained, the sum rules yield aN* width equal to 125 MeV and the transition moment\(\langle p\left| {\mathcal{M}_3 } \right|\mathcal{N}^{ * ( + )} \rangle = 1.25(2\sqrt 2 /3\mu (p)\), compared with the experimental values 120 MeV and\((1.28 + 0.02)(2\sqrt 2 /3)\mu (p)\) respectively.