Vacuum Structure of the BNT Model of Neutrino Mass Generation

TL;DR

The paper analyzes the vacuum structure of the BNT model, which extends the SM with a scalar quadruplet of $Y=3/2$ and a vector-like triplet to generate neutrino masses via a dimension-seven operator. It derives comprehensive theoretical constraints on the scalar potential, including boundedness-from-below and perturbative unitarity, and performs a detailed stationarity analysis to assess whether the electroweak vacuum is the global minimum or whether charge-breaking minima can be deeper. A key result is that the electroweak-like vacuum with vanishing quadruplet VEV ($N_2$) is globally stable against charge-breaking directions under two simple mass inequalities; for the general electroweak vacuum ($N_1$) with both doublet and quadruplet VEVs, no simple analytic criterion exists, but a practical criterion emerges from requiring $N_1$ to be deeper than $N_2$ and $N_2$ to be deeper than all charge-breaking minima. Because neutrino masses require $\lambda_5\neq0$, only the $N_1$ vacuum is phenomenologically viable, making these analytic stability conditions a crucial tool for exploring the model’s viable parameter space.

Abstract

We analyze the vacuum structure of the Babu--Nandi--Tavartkiladze (BNT) model of neutrino mass generation, in which the Standard Model is extended by an $SU(2)_L$ scalar quadruplet with hypercharge $Y=3/2$ and a vector-like $SU(2)_L$ triplet fermion with $Y=1$, generating neutrino masses via an effective dimension-seven operator. We delineate the theoretical constraints on the model, requiring the scalar potential to be bounded from below in all field directions, ensuring perturbative unitarity of scattering amplitudes, and demanding that the electroweak vacuum corresponds to the global minimum of the potential. We find that the electroweak vacuum is not generically guaranteed to be the global minimum: several charge-breaking stationary points may coexist with -- and potentially lie below -- it in potential depth. For the electroweak-like vacuum with vanishing quadruplet expectation value, the condition of global stability reduces to two simple mass inequalities involving the doubly- and triply-charged scalars. In contrast, for the general electroweak vacuum with nonzero doublet and quadruplet expectation values -- compatible with neutrino-mass generation -- no comparably simple analytic condition emerges, and the stability must be assessed for each specific choice of scalar couplings. Nonetheless, by combining the analytic condition governing the relative depth of the two electroweak stationary points with the mass inequalities ensuring the stability of the electroweak-like configuration against charge breaking, we obtain a practical criterion for determining when the general electroweak vacuum is globally stable.