Surprises from complete vector portal theories: New insights into the dark sector and its interplay with Higgs physics

We study UV complete theories where the standard model (SM) gauge group is extended with a new Abelian $U(1{)}^{\prime }$, and the field content is augmented by an arbitrary number of scalar and fermion SM singlets, potentially including dark matter (DM) candidates. Considerations such as classical and quantum gauge invariance of the full theory and S-matrix unitarity, not applicable within a simplified model approach, are shown to have significant phenomenological consequences. The lack of gauge anomalies leads to compact relations among the $U(1{)}^{\prime }$ fermion charges and puts a lower bound on the number of dark fermions. Contrary to naive expectations, the DM annihilation to $Zh$ is found to be p-wave suppressed, as hinted by the perturbative unitarity of the S-matrix, with dramatic implications for DM thermal relic density and indirect searches. Within this framework, the interplay between dark matter, new vector boson, and Higgs physics is rather natural and generic.

Figure 1

Cross section for $\chi \chi \to Zh$ as a function of $\sqrt{s}$. The $Z^{\prime }$ exchange diagram alone (dashed red) signals a breakdown of unitarity at large $\sqrt{s}$. Summing over both $Z$ and $Z^{\prime }$ exchange diagrams restores unitarity (blue).

Figure 2

DM relic density for the benchmark model as a function of the $Z^{\prime }$ mass. The full calculation (black) is compared with the result for annihilations to $Zh$, accounting for $Z^{\prime }$ exchange only (dashed red) and both $Z$ and $Z^{\prime }$ (dotted blue).

Figure 3

Phenomenological constraints for $m_{\chi }=300\mathrm{GeV}$. LHC dilepton bounds [56, 57] are imposed by evaluating the parton distribution functions from Ref. [58]. Renormalization group effects for direct detection [59, 60, 61] are accounted for by evolving the couplings with the code runDM [62].