Chew-Frautschi plot and string structure of baryons

Abstract

In this let ter we show tha t the baryon Chew-Frautschi plots exhibit some regular i ty suggested by the string structure of baryons. I t has been argued (1,2) tha t for the string structure of baryons there are theoret ical ly three possible string configurations which connect the three quarks as shown in fig. 1. The regular i ty we are concerned with is just the one due to the th i rd configuration (fig. lc)). At present, the string with quarks a t tached at the end points has not yet been successfully formulated. The spin and the un i ta ry spin of the quark are, however, impor tan t in discussing the structure of baryons. So tha t we take into account these spins, but we ignore the mass of the quark. In what follows, the whole orbital angular momentum J5 is assumed due to the string motion. A~TRU has recently invest igated (~) the classical motion of the relativistic string with the junction (fig. le)). He found a s ta t ionary solution where all three branches of the revolving string have the same length (the symmetric configuration). There might exist other excitat ion modes: only one or two branches can have large length and the remainders are infinitesimal (no excitation). In the la t te r modes, the baryonic string behaves like a mesonic string because the infinitesimal branches may give no marked contributions to the energy and to the angular momentum. These modes will produce the leading baryon Regge trajectories with almost the same slope as tha t of meson trajectories, i.e. ~'___ 1 (GeV) -2. On the other hand, the slope of the t ra jec tory corresponding to the symmetr ic configuration is predicted to be equal to ~ t imes the slope of the leading t ra jec tory mentioned above (2). In the meson theory, the well-known classical solution (the rotat ing single r igid string) gives the maximum angular momentum for a given energy and corresponds to the upper boundary of the continuum of more general classical solutions. This fact gives the unique connection between the t ra jec tory of this classical solution and the quantummechanical (leading) Reggc trajectory. For our classical solutions the symmetric configuration gives lower angular momenta than those of the mesonlike configuration. However, these two classical motions cannot be superposed on each other, since these have the junction at quite different positions and may belong to different branches