# New Weinberg operator for neutrino mass and its seesaw origin

## TL;DR

This paper introduces a novel Weinberg operator involving two different Higgs doublets, originating from a specific gauge symmetry setup, leading to a new type of seesaw mechanism with potential large unitarity violations in neutrino mixing.

## Contribution

It proposes a new form of the Weinberg operator with two Higgs doublets and a corresponding type Ib seesaw model, expanding the theoretical landscape of neutrino mass generation.

## Key findings

- The new Weinberg operator can be generated via right-handed neutrinos charged under a U(1)' gauge symmetry.
- The model allows large violations of unitarity in the leptonic mixing matrix.
- Adding an uncharged right-handed neutrino can recover the usual type Ia seesaw contributions.

## Abstract

We consider a new Weinberg operator for neutrino mass of the form $H_u\tilde{H_d}L_iL_j$ involving two different Higgs doublets $H_u, H_d$ with opposite hypercharge, where $\tilde{H_d}$ is the charge conjugated doublet. It may arise from a model where the two Higgs doublets carry the same charge under a $U(1)'$ gauge group which forbids the usual Weinberg operator but allows the mixed one. The new Weinberg operator may be generated via two right-handed neutrinos oppositely charged under the $U(1)'$, which may be identified as components of a fourth vector-like family in a complete model. Such a version of the type I seesaw model, which we refer to as type Ib to distinguish it from the usual type Ia seesaw mechanism which yields the usual Weinberg operator, allows the possibility of having potentially large violations of unitarity of the leptonic mixing matrix whose bounds we explore. We also consider the relaxation of the unitarity bounds due to the further addition of a single right-handed neutrino, neutral under $U(1)'$, yielding a usual type Ia seesaw contribution.