Current-Generated Algebra and Mass Levels of the Hadrons

The mass splittings of the U(3) [or SU(3)] multiplets of the hadrons are investigated under the following assumptions: (i) The Hamiltonian decomposes into an invariant part plus an eighth component of an octet of U(3), and the latter is a space integral of the scalar current transforming like 1 / 2(q†βλ8q), where q stands for the quark. (ii) An algebra of the positive parity operators generating a nonchiral U(3)×U(3) is a "good symmetry," where the generators consist of the scalar currents and the fourth components of the vector currents. It is shown that if a universal constant with the dimensions of a mass together with the average mass of the multiplet are given, then the splitting is calculated exactly for any multiplet under the above assumptions. A kind of competition of the kinematical group U(3) and the dynamical group U(3)×U(3) can predict the average masses of U(3) multiplets if they belong to the same multiplet of U(3)×U(3). The multiplets that concern us are the ½+ octet, 3 / 2+ decuplet, 3 / 2- octet, 0- nonet, 2+ nonet, and 1- nonet. The results show good agreement with experiment