Quark-Orbital Regge Trajectories

Abstract

It is shown that the pattern of Regge trajectories of hadrons becomes very much simpler and more regular than the usual Chew-Frautschi plot when one uses the orbital angular mo­ mentum of the quarks in a hadron instead of the spin of the meson and the spin minus 1/2 of the baryon, as the Reggeized angular momentum. Available data on particles and resonances are classified by means of the quark-orbital Regge trajectories, and as a result of it, the following pattern appears: there are linear rising quark-orbital trajectories with the universal slope for each irreducible representation of SU(6); actual hadron spectra are reproduced by adding the spin- and unitary spin-exchange interactions and the mass shift of the .l-quark. The Gell-Mann-Okubo mass formula holds rather good including resonances with high mass. Effects of the spin-orbit interaction are clearly recognized and its magnitude is nearly of the same order as those of the spin- and unitary spin-exchange interactions for mesons, whereas they are not so obvious for baryons. It follows from this splitting pattern of the quark-orbital Regge trajectories that the exchange degeneracies hold better for mesons than for baryons and that many doublets exist apparently and several parity partners should not appear, in conformity with experimental data. Classification of resonances using the orbital angular momentum between incoming two hadrons does not show much regularity. It is suggested from these results that strong interactions are essentially characterized by the degree of freedom of the spatial motion at the urbaryon level. § I. Introduction The fact that the hadron spectra obey the classification due to SU(6) @0 (3) very well*l and that the properties of the exotic and nonexotic channels are quite different, seems to show the importance of pursuing seriously the consequences of the quark model. On the other hand, we also recognize the importance of analytic properties of amplitudes, especially the Regge trajectories. Then the following question arises naturally: Which is the most important quantity that essentially determines the dynamics of strong interactions: the three angular momenta, total angular momentum of a hadron (denoted by J in the following), total orbital angular momentum of a hadron in the quark model (denoted by L) or the total orbital angular momentum of hadrons in the most dominant decay mode of the hadron (denoted by l)? It is the purpose of this paper to shed some light on this question by a comprehensive investigation of experimental data on hadron spectra. We will discuss the classification of mesons and baryons in the quark model in § 2 and *> This does not necessarily mean that the SU(6) symmetry applies to the wholeS-matrix as