Electromagnetic masses of baryons and unitary symmetry

Abstract

Electromagnetic masses of the octet and the decuplet baryons are investigated in the (symmetry-breaking) unitary symmetry model of Gell-Mann and Ne'eman. The symmetry breaking arising from the medium strong interaction is introduced into the electromagnetic mass operator in the direct product form of the SU 3 group. The masses of the decuplet baryons are found to satisfy the relation 3M( N ∗+)−3M( N ∗0)=M( N ∗++)−M N ∗−) . A main purpose of this paper is to give a clear physical interpretation of the various theoretical relations between the electromagnetic masses of the octet baryons and to derive some useful information. First the isotensor contribution is found to be small (about 20%) compared to the isovector one. It is well known that in low-energy nuclear physics the former is negligibly small compared to the latter. Assuming then a similar effect for the decuplet baryons, we get two more approximate relations, M( N ∗+)−M( N ∗0) ≈ M( N ∗++)−M( N ∗+) and M( Y 1 ∗+)−M( Y 1 ∗0) ≈ M( Y 1 ∗0)−M( Y 1 ∗−) . Moreover the isoscalar and the isovector contributions are found to be small if they arise from the operators belonging to the highest irreducible representation of the problem in question. From the detailed analysis of the transient masses (one is purely electromagnetic and the other is mixed strong and electromagnetic) we determine the effect of non-electromagnetic origin due to the second-order symmetry breaking. The nature of the electromagnetic masses for the baryons and the nucleides need not necessarily be the same but that of the various contributions obtained from the octet baryons should remain the same for the decuplet baryons if they arise from the same physical origin of the symmetries.