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

TL;DR

The paper discusses the implications of symmetrizing mass and interaction terms for Weyl spinors in supersymmetric theories, highlighting potential issues with symmetry and representation irreducibility.

Contribution

It clarifies when symmetrizing mass matrices is appropriate and explores its impact on supersymmetry breaking mechanisms like Cybersusy.

Findings

Symmetrizing Weyl spinor mass matrices can obscure important symmetries.

Symmetrization may conflict with irreducibility of fermion representations.

Proper treatment of interaction terms is crucial for understanding SUSY breaking.

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.