Removal of the Tachyons from the Fermionic Sector of the Quadratic ZX Action for the Exotic Model (E8)

Abstract

This paper contains an encouraging result for the development of the Exotic Model (the `XM'). The XM is made from the Supersymmetric Standard Model (the `SSM') by coupling it to the `Exotic Invariant'. This rather unique `Exotic Invariant' is suggested by the detailed form of the SSM, combined with the detailed form of the BRS cohomology of SUSY. The motivation for examining the XM is that the usual SSM has some well-known, and serious, problems in its generally accepted, but unsatisfactory, SUSY breaking mechanism. That mechanism is based on the spontaneous breaking of SUSY. The Exotic Model avoids all of these problems, easily, because its SUSY splitting mechanism does not use, or need, any kind of spontaneous breaking of SUSY. The XM contains a mechanism for SUSY mass splitting because the addition of the Exotic Invariant modifies the algebra of SUSY. This paper is E8 in a series of papers denoted En, n= 1,2, ... all devoted to the XM. There is a lot of work still required to elucidate how the XM functions, and to see if the XM is really a viable alternative to the SSM. The first crucial question, raised in E7, is whether it is possible to constrain the initial XM action, so that the result excludes tachyonic excitations at tree level. If the XM is to be a viable theory, it is essential to first remove the tachyonic excitations, in a sensible way, from the fermionic and the bosonic sectors of the quadratic ZX action. This paper E8 explains how to remove the tachyons from the basic fermionic `ZX sector' at tree level. There are four fermion fields in this ZX sector. The removal requires that all of these fields have the same mass. This result is shown using a Mathematica notebook, which is issued with this paper.