[Paper Review] The Possible Textures in the Seesaw Realization of the Strong Scaling Ansatz and the Implications for Thermal Leptogenesis

Midori Obara|ArXiv.org|Dec 17, 2007

Particle physics theoretical and experimental studies5 references8 citations

TL;DR

This paper classifies textures of Dirac and right-handed Majorana neutrino mass matrices that satisfy the Strong Scaling Ansatz (SSA) within the seesaw mechanism, showing that SSA requires Dirac mass matrices of rank 1 or 2 depending on $M_R^{-1}$ textures. It further demonstrates that introducing complex breaking parameters in $M_\nu$ generates CP violation, non-zero $m_3$, and $U_{e3}$, and analyzes thermal leptogenesis implications in both SSA-satisfying and breaking scenarios.

ABSTRACT

We classify the textures of the Dirac and the right-handed Majorana neutrino mass matrices, $M_D$ and $M_R$, which can satisfy the so-called ``Strong Scaling Ansatz'' (SSA) within the framework of the seesaw mechanism $M_ν=-M_D^T M_R^{-1} M_D$. We assume that the Dirac neutrino mass matrix has some texture zeros and examine which elements should be zero in order to satisfy the SSA, by taking into account all possible textures for $M_R$. We find that the resulting Dirac neutrino mass matrices have rank 2 as well as the rank of the effective neutrino mass matrix $M_ν$, or rank 1, depending only on the textures of $M_R^{-1}$. We also consider the three cases of the breaking of the SSA by introducing a complex breaking parameter in $M_ν$ and show that it can generate the CP violation in the lepton sector as well as non-zero $m_3$ and $U_{e3}$. We furthermore discuss the implications of the thermal leptogenesis for the both case which satisfies and breaks the SSA in the basis where $M_R$ is diagonal.

Motivation & Objective

• To classify viable textures of the Dirac ($M_D$) and right-handed Majorana ($M_R$) neutrino mass matrices that satisfy the Strong Scaling Ansatz (SSA) in the seesaw mechanism.
• To determine the constraints on $M_D$ elements that yield SSA, considering all possible textures of $M_R$.
• To examine whether the three cases of SSA breaking (A1, A2, A3) can be realized within the seesaw framework using complex breaking parameters.
• To analyze the phenomenological implications of SSA breaking on $m_3$, $U_{e3}$, and $J_{\text{CP}}$.
• To investigate the implications of thermal leptogenesis in both SSA-satisfying and SSA-breaking scenarios in the $M_R$-diagonal basis.

Proposed method

• Uses the seesaw formula $M_\nu = -M_D^T M_R^{-1} M_D$ to derive conditions on $M_D$ and $M_R$ for satisfying SSA.
• Classifies all possible textures of $M_R$ and determines the corresponding required texture zeros in $M_D$ to realize SSA.
• Introduces complex breaking parameters in $M_\nu$ to model deviations from SSA, analyzing their impact on $m_3$, $U_{e3}$, and $J_{\text{CP}}$.
• Performs semi-analytical and numerical analyses of neutrino mixing angles and masses under SSA and its three breaking cases (A1, A2, A3).
• Applies thermal leptogenesis formalism in the $M_R$-diagonal basis to evaluate lepton asymmetry and baryogenesis via $M_R$-dominated decay processes.
• Uses perturbative corrections to the neutrino mass matrix to compute mixing angle corrections and CP-violating invariants.

Experimental results

Research questions

• RQ1 Which textures of $M_D$ and $M_R$ can realize the Strong Scaling Ansatz (SSA) in the seesaw mechanism?
• RQ2 How do the textures of $M_R^{-1}$ determine the rank of $M_D$ and the resulting $M_\nu$?
• RQ3 Can the three cases of SSA breaking (A1, A2, A3) be consistently realized within the seesaw framework using complex breaking parameters?
• RQ4 What are the resulting values of $m_3$, $U_{e3}$, and $J_{\text{CP}}$ in the SSA-breaking scenarios?
• RQ5 What are the implications for thermal leptogenesis in both SSA-satisfying and SSA-breaking cases in the $M_R$-diagonal basis?

Key findings

• The Dirac neutrino mass matrix $M_D$ resulting from SSA has rank 2 or 1, depending solely on the texture of $M_R^{-1}$.
• The three SSA-breaking cases (A1, A2, A3) can be realized within the seesaw framework by introducing a complex breaking parameter in $M_\nu$.
• Complex breaking parameters generate non-zero $m_3$ and $U_{e3}$, and induce CP violation in the lepton sector via non-zero $J_{\text{CP}}$.
• The semi-analytical analysis shows that the correction to $U_{e3}$ is proportional to $|\epsilon|$, with the leading-order term involving $B^2/c$ and $AB$ terms.
• Thermal leptogenesis in the $M_R$-diagonal basis yields non-vanishing lepton asymmetry in both SSA-satisfying and SSA-breaking cases, with the asymmetry depending on $M_R$ masses and $M_D$ textures.
• The correction to the mixing angle $U_{e3}^{(1)}$ is proportional to $|\epsilon|$ and involves complex phases from $\phi'$, $\phi''$, and $\varphi$, indicating CP-violating effects.