What is the meaning of negative mass (in a SUSY spectrum)?

Question

I was playing around with SuSpect to generate some SUSY mass spectrums and I'm often encountering situations where I get a negative neutralino mass.

1. What is the physical meaning of this negative mass I am getting?

2. Does this mean the parameters I am putting in is giving an unphysical spectrum?

Answer 1

Negative fermion masses just mean that there is a relative phase between some terms in the Lagrangian. This doesn't usually mean that anything is wrong.

Answer 2

Negative mass (equivalently tachyonic states) mean that the spectrum was computed in an unstable (and unphysical) pseudo-vacuum, which would undergo a rapid phase transition.

This means that the fields must be shifted (e.g., broken symmetry in Higgs) and/or linearly transformed by a Bogoliubov transformation (e.g., superconductivity) before they are Fourier expanded in terms of creation and annihilation operators used to find the spectrum.