Nonrelativistic quark model for baryons

Abstract

A nonrelativistic quark model is proposed for baryons, according to which any two quarks are assumed to interact with each other through p-wave forces. Such forces are shown to be capable of producing strong binding in a three-quark system in a spatially antisymmetric state of angular-momentum unity, and making the model compatible with an extension of the [56] representation of SU₆. If the strength of the quark-quark force is adjusted to fit some central baryon mass (m₀), the model predicts a 2-quark bound state at a mass ∼1/2(M+m₀), where M is the central mass of a quark. The validity of the nonrelativistic description is shown to depend on the smallness of a certain "inverse range parameter" β compared with the quark mass M, and this condition is shown to be fully compatible with the present experimental knowledge on baryon sizes, as measured by the charge radius of the proton. Further, using an SU₃-invariant interaction, an "equal interval rule" for the baryon masses is shown to follow dynamically from the assumption of a mass difference between the singlet and doublet quarks, under the same condition, β≪M, as above. It is argued that a p-wave quark interaction, which leads more easily to the formation of antisymmetric spatial states than of symmetric ones, gives a sort of "saturated system" at the 3-quark level. This reduces considerably the (undesirable) prospects of very strong binding of a larger number of quarks, compared to the situation with s-wave forces (which facilitate the formation of symmetric states in multiquark systems with stronger and stronger binding as the number of quarks is increased). By ruling out the generally stronger s-wave forces as the main bond between two quarks, the model leaves scope for their action in quark-antiquark systems, which should require stronger binding in order to generate the (less massive) mesons.