The Standard Model Gauge Group, SMEFT, and Generalized Symmetries
Abstract
We discuss heavy particles that can be used to pin down the faithful Standard Model (SM) gauge group and their patterns in the SM effective field theory (SMEFT). These heavy particles are not invariant under a specific $\mathbb{Z}_6$ subgroup of $SU(3)_c\times SU(2)_L \times U(1)_Y$, which however acts trivially on all the SM particles, hence the faithful SM gauge group remains undetermined. Different realizations of the faithful SM gauge group correspond to different spectra of heavy particles, and they also correspond to distinct sets of line operators with oneform global symmetry acting on them. We show that the heavy particles not invariant under the $\mathbb{Z}_6$ group cannot appear in treelevel ultraviolet completions of SMEFT, this enforces us to consider oneloop UV completions of SMEFT to identify the $\mathbb{Z}_6$ noninvariant heavy particles. We demonstrate with examples that correlations between Wilson coefficients provide an efficient way to examine models with $\mathbb{Z}_6$ noninvariant heavy particles. Finally, we prove that all the scalars that can trigger electroweak symmetry breaking must be invariant under the $\mathbb{Z}_6$ group, hence they cannot be used to probe the faithful SM gauge group.
 Publication:

arXiv eprints
 Pub Date:
 April 2024
 DOI:
 10.48550/arXiv.2404.04229
 arXiv:
 arXiv:2404.04229
 Bibcode:
 2024arXiv240404229L
 Keywords:

 High Energy Physics  Phenomenology;
 High Energy Physics  Experiment;
 High Energy Physics  Theory
 EPrint:
 20 pages, 4 figures