# Multi-Higgs-Doublet Models and Singular Alignment

## TL;DR

This paper proposes a four-Higgs-doublet model explaining fermion mass hierarchies through vacuum expectation value hierarchies, employing singular alignment to prevent flavor-changing neutral currents, and incorporating a type-I seesaw for neutrino masses.

## Contribution

It introduces a novel 4-Higgs-doublet framework with singular alignment to naturally explain fermion mass hierarchies and suppress flavor-changing neutral currents.

## Key findings

- Model successfully explains fermion mass hierarchies.
- Singular alignment prevents flavor-changing neutral currents.
- Neutrino masses generated via type-I seesaw with PeV-scale singlet neutrinos.

## Abstract

We consider a 4-Higgs-doublet model in which each Higgs doublet gives mass to one of the fermion sets $\{ m_t\}$, $\{ m_b,m_\tau,m_c \}$, $\{ m_\mu,m_s \}$, and $\{ m_d,m_u,m_e \}$. The sets have the feature that within each of them the masses are similar. Our model explains the mass hierarchies of the sets by hierarchies of the vacuum expectation values of the Higgs doublets associated to them. All Yukawa couplings are therefore of order one. Neutrino masses are generated by a type-I seesaw mechanism with PeV-scale singlet neutrinos. To avoid the appearance of tree-level flavor changing neutral currents, we assume that all Yukawa matrices are singularly aligned in flavor space. We mean by this that the Yukawa matrices are given as linear combinations of the rank $1$ matrices that appear in the singular value decomposition of the mass matrix. In general, singular alignment allows to avoid flavor changing neutral currents in models with multiple Higgs doublets.