# Super-weak force and neutrino masses

## TL;DR

This paper proposes an extension of the Standard Model with an additional U(1) gauge symmetry to explain neutrino masses and the muon g-2 anomaly, analyzing the model's constraints and potential consequences.

## Contribution

It introduces a new anomaly-free U(1) extension of the Standard Model that accounts for neutrino masses and addresses the muon g-2 discrepancy.

## Key findings

- Constraints on the new gauge coupling and boson mass from muon g-2 data
- Possible implications for neutrino mass generation mechanisms
- Discussion of the model's phenomenological consequences

## Abstract

We consider an anomaly free extension of the standard model gauge group $G_{\rm SM}$ by an abelian group to $G_{\rm SM}\otimes U(1)_Z$. The condition of anomaly cancellation is known to fix the $Z$-charges of the particles, but two. We fix one remaining charge by allowing for all possible Yukawa interactions of the known left handed neutrinos and new right-handed ones that obtain their masses through interaction with a new scalar field with spontaneously broken vacuum. We discuss some of the possible consequences of the model. Assuming that the new interaction is responsible for the observed differences between the standard model prediction for the anomalous magnetic moment of the muon and its measured value, we constrain the size of the new gauge coupling, the mass of the new gauge boson and the vacuum expectation value of the new scalar field.