Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Minimal Majorana neutrino mass models

Antonio Herrero-Brocal, Avelino Vicente

TL;DR

The paper develops an extended Casas-Ibarra parametrization to describe Yukawa couplings in any Majorana neutrino mass model and uses it to count free parameters, revealing the existence of minimal models with as few as $2$ real degrees of freedom. It shows that phenomenologically relevant combinations like $Y$ and $y_i^\dagger y_i$ can depend on far fewer parameters in certain reduced scenarios, yielding concrete, testable predictions in heavy neutrino decays and charged-lepton flavor violation. The authors illustrate the approach with two minimal models: a Minimal Type-I Seesaw and a Minimal Linear Seesaw with spontaneous lepton-number breaking, each producing distinctive predictions that could falsify the models with future data. The framework connects to the master parametrization and provides clear pathways for experimental falsification, while acknowledging limitations such as potential extra contributions from additional states.

Abstract

We present an extension of the Casas-Ibarra parametrization that applies to all possible Majorana neutrino mass models. This framework allows us to systematically identify minimal models, defined as those with the smallest number of free parameters. We further analyze the phenomenologically relevant combination of the Yukawa matrix, $y^\dagger y$, and show that in certain scenarios it exhibits an unexpected reduction in the number of free parameters, depending on just one real degree of freedom. Finally, the application of our results is illustrated in specific models, which can be tested or falsified due to their definite experimental predictions in heavy neutrino and charged lepton flavor violating decays.

Minimal Majorana neutrino mass models

TL;DR

The paper develops an extended Casas-Ibarra parametrization to describe Yukawa couplings in any Majorana neutrino mass model and uses it to count free parameters, revealing the existence of minimal models with as few as real degrees of freedom. It shows that phenomenologically relevant combinations like and can depend on far fewer parameters in certain reduced scenarios, yielding concrete, testable predictions in heavy neutrino decays and charged-lepton flavor violation. The authors illustrate the approach with two minimal models: a Minimal Type-I Seesaw and a Minimal Linear Seesaw with spontaneous lepton-number breaking, each producing distinctive predictions that could falsify the models with future data. The framework connects to the master parametrization and provides clear pathways for experimental falsification, while acknowledging limitations such as potential extra contributions from additional states.

Abstract

We present an extension of the Casas-Ibarra parametrization that applies to all possible Majorana neutrino mass models. This framework allows us to systematically identify minimal models, defined as those with the smallest number of free parameters. We further analyze the phenomenologically relevant combination of the Yukawa matrix, , and show that in certain scenarios it exhibits an unexpected reduction in the number of free parameters, depending on just one real degree of freedom. Finally, the application of our results is illustrated in specific models, which can be tested or falsified due to their definite experimental predictions in heavy neutrino and charged lepton flavor violating decays.

Paper Structure

This paper contains 16 sections, 6 theorems, 113 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The extended Casas-Ibarra parametrization
  3. Yukawa combinations of phenomenological relevance
  4. $Y$ matrix
  5. $y_i^\dagger y_i$ matrix
  6. Reduced scenario 1
  7. Reduced scenario 2
  8. Phenomenological applications
  9. Minimal Type-I Seesaw
  10. Minimal Linear Seesaw with spontaneously broken lepton number
  11. Summary
  12. Equivalence with the master parametrization
  13. Finding the extended Casas-Ibarra from the master parametrization
  14. Finding the master parametrization from the extended Casas-Ibarra
  15. Counting free parameters in the master parametrization
  16. ...and 1 more sections

Key Result

Lemma 1

This, together with Lemma lemma3, are already well-known results in algebra. We include them here for completeness.Let $P \in \mathbb{C}^{n \times n}$ be a PSD matrix of rank $p$. Then there exists a full-rank matrix $B \in \mathbb{C}^{p \times n}$ such that $P = B^\dagger B$.

Figures (2)

  • Figure 1: Ratios of $N_1 \to \ell_\alpha W$ branching fractions as functions of the free parameter $z_i$, for fixed values of $z_r$ ($z_r=0$ and $z_r=1$ for the solid and dashed lines, respectively), in the minimal Type-I Seesaw model. The colors indicate different ratios: $\text{BR}(N_1 \to eW)/\text{BR}(N_1 \to \mu W)$ (blue), $\text{BR}(N_1 \to eW)/\text{BR}(N_1 \to \tau W)$ (orange), and $\text{BR}(N_1 \to \tau W)/\text{BR}(N_1 \to \mu W)$ (black). Neutrino oscillation data are taken at their best-fit values for NH (left) and IH (right) deSalas:2020pgw.
  • Figure 2: Ratios of $\ell_\alpha \to \ell_\beta \, \gamma$ branching ratios as a function of the free parameter $a$ in the minimal Type-I Seesaw model. $\text{BR}\left(\mu \to e \gamma\right)/\text{BR}\left(\tau \to e \gamma\right)$ in black, $\text{BR}\left(\tau \to \mu \gamma\right)/\text{BR}\left(\tau \to e \gamma\right)$ in blue and $\text{BR}\left(\tau \to \mu \gamma\right)/\text{BR}\left(\mu \to e \gamma\right)$ in orange. Best-fit values and NH (left) and IH (right) are assumed for the neutrino oscillation data deSalas:2020pgw.

Theorems & Definitions (12)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • ...and 2 more