Mass formula

Abstract: We derive the lagrangian and transformation laws of the coupled Yang-Mills-matter-supergravity system for unextended n = 1 local supersymmetry. We study the super-Higgs effect and the normal Higgs effect of the Yang-Mills gauge group G. In the case of N chiral multiplets “minimally” coupled to supergravity, transforming according to some N-dimensional, generally reducible representation of G, we find a model-independent mass formula: Supertrace M 2 = ∑ J=0 3 2 (−) 2J (2J+1)m J 2 = (N−1)(2m 3 2 2 −κ 2 D α D α ) − 2 g α D α Tr T α , where m 3 2 is the gravitino mass, κ and g α the gravitational and gauge couplings, respectively, Dα is the auxiliary component of the gauge multiplet of G and Tα the generators of G in the representation of the matter chiral multiplets.

Abstract: The Clebsch-Gordan (CG) coefficients of SU(3) are derived for the products of the most important irreducible representations. Useful symmetry relations for the CG coefficients are derived. The Wigner-Eckart theorem for this group is given and applied to derive a general mass formula for the octets. The Gell-Mann-Okubo mass relation and a mass relation foi the octets that is very well satisfied by the vector mesons, if one takes as the K/sup */ the 730-Mev (K- pi ) resonance, are given. The Yukawa couplings between baryons and mesons are considered. The mathematical framework of the octet model for strong interactions is examined. (C.E.S.)

Abstract: Assuming invariance of a theory under three-dimensional unitary group, various consequences are investigated. Both the Sakata and Gell-Mann schemes can be treated in this fashion in a simple way. A mass formula for particles belonging to the same irreducible representation is derived and compared with experiments. (auth)

Abstract: After the work of Seiberg and Witten, it has been seen that the dynamics of N = 2 Yang-Mills theory is governed by a Riemann surface ϵ In particular, the integral of a special differential ωSW over (a subset of) the periods of ϵ gives the mass formula for BPS-saturated states. We show that, for each simple group G, the Riemann surface is a spectral curve of the periodic Toda lattice for the dual group, GV whose affine Dynkin diagram is the dual of that of G. This curve is not unique, rather it depends on the choice of a representation ϱ of GV; however, different choices of ϱ lead to equivalent constructions. The Seiberg-Witten differential ωSW is naturally expressed in Toda variables, and the N = 2Yang-Mills pre-potential is the free energy of a topological field theory defined by the data eg, π and ωSW.

Abstract: Beta-decay half-lives have been calculated by the use of the gross theory which was formulated by Takahashi, Yamada, and Koyama. Both allowed and first-forbidden transitions have been taken into account, and consideration also has been given to the possibility that all the transitions to the levels near the ground states may be highly forbidden. The Q -values used in the calculation have been taken from the mass formula of Myers and Swiatecki. The calculated half-lives are shown in the PLOTS together with the experimental data and the Q -values. The PLOTS cover all the isotopes between the proton-drip and neutron-drip lines with Z = 3 to Z = 100.