Connection of $g-2_{\mu }$, electroweak, dark matter, and collider constraints on 331 models

In this paper we compute all contributions to the muon magnetic moment stemming from several 3-3-1 models, namely, minimal 331, 331 with right-handed neutrinos, 331 with heavy neutral leptons, 331 with charged exotic leptons, 331 economical and 331 with two Higgs triplets. Further, we exploit the complementarity among current electroweak, dark matter and collider constraints to outline the relevant parameter space of the models capable of explaining the anomaly. Lastly, assuming that the experimental anomaly has been otherwise resolved, we derive robust $1\sigma$ bounds using the current and projected measurements.

Figure 1

Feynmann diagrams arising in 331 models studied here: (a) neutral scalar; (b) charged scalar; (c) and (d) doubly charged scalar; (e) charged vector; (f) and (g) doubly charged vector; (h) neutral vector; (i) exotic charged lepton ; (j) neutral lepton.

Figure 2

Individual contributions to $g-2_{\mu }$. The solid (dashed) green horizontal lines represent the current (projected) sensitive to $g-2_{\mu }$. The solid (dashed) horizontal red lines are the current and projected $1\sigma$ bound in case the anomaly is resolved otherwise. After summing up all individual corrections we find that the scale of symmetry breaking that reproduces $g-2_{\mu }$ is quite small and excluded by current data. Moreover, we have derived a current (projected) 4 TeV (5.8 TeV) limit on the scale of symmetry breaking. Since this model is valid only up to 5 TeV, we conclude that the upcoming g-2 experiment at Fermilab will be able to undoubtedly exclude this model.

Figure 3

Individual contributions $g-2_{\mu }$ in the 331 r.h.n. Adding up all contributions we conclude that this model cannot explain $g-2_{\mu }$ excess because it requires a scale of symmetry breaking that is already ruled out by current collider, dark matter experiments and electroweak precision data. Additionally, a current (projected) constraint of 1 TeV (1.5 TeV) might be posed.

Figure 4

Individual contributions to the muon magnetic moment in the 331 model with heavy leptons as function of the scale of symmetry breaking. With $M_N=1\mathrm{GeV}$, a scale of symmetry breaking of much smaller than 1 TeV would be needed to accommodate $g-2_{\mu }$, which is already excluded by dark matter, collider and electroweak bounds. Hence the 331LHN can not provide an explanation for the anomaly.

Figure 5

Individual contributions from the 331 economical model. We conclude from the right panel that the overall correction to $g-2_{\mu }$ is negative and small. Thus the model is excluded as an explanation to $g-2_{\mu }$. Moreover, a current (projected) limit of 900 GeV (1.3 TeV) can placed on the scale of symmetry breaking.

Figure 6

Individual contributions to $g-2_{\mu }$ in the RM331 as a function of the scale of symmetry breaking. We conclude with $v_{\chi }\sim 2\mathrm{TeV}$ the model can accommodate the $g-2_{\mu }$ excess while being consistent with existing bounds. If the anomaly is otherwise resolved a current limit of 4 TeV will be placed, and projected of 5.8 TeV will be achieved, ruling out the entire model due to the Landau pole at 5 TeV.

Figure 7

Individual contributions to $g-2_{\mu }$ in the 331 model with exotic leptons. Summing up all corrections we find that overall contribution is negative and small. We could still derive a current (projected) bound of 1 TeV (1.8 TeV) in case the $g-2_{\mu }$ anomaly is otherwise resolved.