Why is TeV-scale a geometric mean of neutrino mass and GUT-scale?

TL;DR

This paper proposes a supersymmetric neutrinophilic Higgs model that naturally explains why the TeV-scale is the geometric mean of the neutrino mass scale and the GUT scale, linking these fundamental energy scales.

Contribution

It introduces a simple supersymmetric model with a neutrinophilic Higgs doublet that dynamically reproduces the relation between the TeV-scale, neutrino mass, and GUT-scale without extra scales.

Findings

Successfully reproduces the $M_{NP} \,\simeq\, \sqrt{m_\nu \cdot M_{GUT}}$ relation.

Maintains gauge coupling unification automatically.

Provides a natural mechanism for tiny neutrino masses.

Abstract

Among three typical energy scales, a neutrino mass scale ($m_\nu\sim$ 0.1 eV), a GUT scale ($M_{GUT}\sim 10^{16}$ GeV), and a TeV-scale ($M_{NP}\sim 1$ TeV), there is a fascinating relation of $M_{NP}\simeq \sqrt{m_\nu\cdot M_{GUT}}$. The TeV-scale, $M_{NP}$, is a new physics scale beyond the standard model which is regarded as supersymmetry in this letter. We suggest a simple supersymmetric neutrinophilic Higgs doublet model, which realizes the above relation dynamically as well as the suitable $m_\nu$ through a tiny vacuum expectation value of neutrinophilic Higgs without additional scales other than $M_{NP}$ and $M_{GUT}$. A gauge coupling unification, which is an excellent feature in the supersymmetric standard model, is preserved automatically in this setup.