Dynamical model for baryon resonances

Mitra, A. N. (1966) Dynamical model for baryon resonances Physical Review, 151 (4). pp. 1168-1171. ISSN 0031-899X

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Official URL: http://link.aps.org/doi/10.1103/PhysRev.151.1168

Related URL: http://dx.doi.org/10.1103/PhysRev.151.1168


We propose a nonrelativistic three-quark (Q) model of baryons and their resonances with the assumptions of (i) parastatistics which, in constrast to Fermi statistics, allows totally symmetric wave functions, and (ii) operation of Q-Q forces of the factorable type in s and p waves which facilitate an exact solution of the three-body problem. It is found that the s-wave force gives rise to a strong attraction in a spatially symmetric (S) state of L=0, but repulsion in a mixed-symmetric (M) state. This provides a natural dynamical realization of the 56 representation of SU(6) for the familiar octet and decuplet of baryons. The same s-wave force also predicts a set of negative-parity resonances but these are of much too high energy to be of any physical consequence. The p-wave force leads to a set of negative-parity L=1 resonances via strong attraction in M-type spatial states of L=1, thus making up the representation (70,3) of SU(6)×O(3). A p-wave spin-orbit Q-Q force splits these states in a manner which fits in rather well with Dalitz's recent analysis of experimental data for the negative-parity baryonic resonances. Finally, the p-wave force generates a strong attraction in a spatially antisymemtric state (A) of even parity and L=1, giving rise to the representation (20,3) of SU(6)×O(3), of which the lowest states are an octet and a singlet of JP=1/2+, the central mass of each lying lower than the corresponding lowest mass multiplet of negative parity. This provides a natural explanation of the so-called "Roper" resonance (at 1450 MeV), and in addition, strongly predicts an even-parity singlet of a mass lower than the Y0(1405). The distinction between Fermi statistics and paraststistics is discussed in the context of the above results, and it is argued that while Fermi statistics could in principle generate negative-parity L=1 resonances (via M functions), it could not possibly account for the 56 of baryons, since with Q-Q forces alone,the A function of L=0 that should go with it has a strongly repulsive kernel.

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Deposited On:09 Apr 2011 06:41
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