A Note on Symmetric Mass and Interaction Terms for Weyl Spinors and SUSY

Abstract

One can always write the mass matrix for Weyl spinors so that it is symmetric. However this is often not a good idea. It is usually incompatible with irreducibility of the fermion representations. As a result, a symmetrized mass term hides important symmetries and creates misleading difficulties that are not genuinely part of the theory. This is true for the Standard Model for example, and for its supersymmetric versions. There is a related subtlety, involving symmetrization of the interaction terms, that is central to the SUSY breaking mechanism of Cybersusy.