Predicting the singlet vector channel in a partially Higgsed gauge theory

Understand

We study a toy version of a grand-unified theory on the lattice: An $SU(3)$ gauge theory, which experiences a Brout-Englert-Higgs effect due to a single Higgs field in the fundamental representation.

• This yields a perturbative breaking pattern $SU(3) \rightarrow SU(2)$.
• We investigate the singlet vector channel, finding an apparently non-degenerate and massive ground state.
• This is in contradistinction to the perturbative prediction of three massless and five massive vector states, even though the correlation functions of the gauge bosons exhibit a weak-coupling behavior, being almost tree-level-like.