Bootstrap Mechanism and Symmetries of Strong Interactions

Abstract

It is discussed what kinds of symmetries are consistent with the bootstrap mechanism in the baryon-pseucloscalar meson scattering problem. There, the one baryon exchange ap­ proximation is used. The masses of baryons ancl their coupling constants are calculated numerically. The global-, the cosmic- and the G 2-symmetrie;, are allowable, hut the 5'U(3) symmetry is excluded. ~ l. lntroduction Recently some authors 1 l have shown that the bootstrap mechanism predicts such a relation between the coupling constants of the strong interactions that is equal to the one of the octet scheme. The purpose of this article is twofold. We confirm Okabayashi's conjecture about the symmetry character imposed by the bootstrap mechanism on one hand, and on the other hand calculate the masses . of concerned bound states and coupling constants of strong interactions. As to the first problem, rr. Okabayashi 2 l pointed out that the bootstrap -mechanism introduces equalities between the coupling constants in the s-channel and the ones in the t (or u) -channel, and that the equalities give a kind of symmetry character of the strong interactions, which is not always represented by a group, in general. For instance, in Cutkosky's example, this symmetry character inevitably imposes the octet scheme, because he assumed a group character with the eight-dimensional representation and the tri-linear form of the interaction of the eight-component vector field beforehand. These assumptions are sufficient to restrict the symmetry to SU (3) among the groups which include the group of the charge independence. In other words, the equalities imposed by the bootstrap mechanism are accidentally fitted for the assumptions. In ~ 3, the conjecture mentioned above will be confirmed in the baryon-pseudoscalar meson scattering process, and it will be shown that the global symmetry, the cosmic symmetry, the G2 symmetry and the SU (3) symmetry accompanied with the R symmetry are consistent with the bootstrap mechanism, up to this step. The second problem is not so clear. Namely, there may not be any solu­ tion or there may be redundant solutions. Really, in the case of SU (3) sym­ metry there is an undesirable solution. As an example of the calculation of the bound states in a bootstrap mechanism, we have the calculation of the mass