[Paper Review] LFV radiative Decays and Leptogenesis in the SUSY seesaw model

S.T. Petcov, Tetsuo Shindou|ArXiv.org|May 18, 2006

Cosmology and Gravitation Theories3 citations

TL;DR

This paper investigates the interplay between lepton flavor violation (LFV) in $μ\to e+\gamma$ decays and thermal leptogenesis in the minimal supersymmetric seesaw model with hierarchical right-handed neutrino masses. It shows that suppressing the dominant $M_3$ contribution to LFV via a specific texture-zero structure in the neutrino Yukawa matrix $Υ_{\mathbf{N}}$ allows successful leptogenesis while keeping $\text{BR}(\mu\to e+\gamma)$ within experimental bounds, leading to a predictive correlation between the baryon asymmetry, LFV rate, and effective Majorana mass in $0\nu\beta\beta$ decay.

ABSTRACT

The lepton flavour violating charged lepton decays mu to e + gamma and thermal leptogenesis are analysed in the minimal supersymmetric standard model with see-saw mechanism of neutrino mass generation and soft supersymmetry breaking terms with universal boundary conditions. Hierarchical spectrum of heavy Majorana neutrino masses, M_1 << M_2 << M_3, is considered. In this scenario, the requirement of successful thermal leptogenesis implies a lower bound on M_1. For the natural GUT values of the heaviest right-handed Majorana neutrino mass, M_3 > 5 times 10^{13} GeV, and supersymmetry particle masses in the few times 100 GeV range, the predicted mu to e + gamma decay rate exceeds by few order of magnitude the experimental upper limit. This problem is avoided if the matrix of neutrino Yukawa couplings has a specific structure. The latter leads to a correlation between the baryon asymmetry of the Universe predicted by leptogenesis, BR(mu to e + gamma) and the effective Majorana mass in neutrinoless double beta decay.

Motivation & Objective

• To reconcile the experimental upper limit on $\text{BR}(\mu\to e+\gamma)$ with the prediction from supersymmetric seesaw models featuring hierarchical heavy Majorana neutrino masses.
• To ensure successful thermal leptogenesis in the same framework, requiring a lower bound on the lightest right-handed neutrino mass $M_1$.
• To identify a specific texture-zero structure in the neutrino Yukawa coupling matrix $\mathbf{Y_N}$ that simultaneously suppresses LFV and satisfies leptogenesis constraints.
• To establish a predictive correlation between the baryon asymmetry of the Universe, $\text{BR}(\mu\to e+\gamma)$, and the effective Majorana mass in neutrinoless double beta decay.

Proposed method

• Analyzes the renormalization group running of slepton mass matrices from the GUT scale $M_X$ down to the seesaw scale $M_R$, where heavy Majorana neutrinos are integrated out.
• Uses the seesaw formula $(m_\nu)^{ij} = v_u^2 \, \mathbf{Y_N^T} \mathbf{M_N}^{-1} \mathbf{Y_N}$ to relate the light neutrino mass matrix to the Yukawa couplings and heavy neutrino masses.
• Derives the leading-order contribution to $\text{BR}(\mu\to e+\gamma)$ as proportional to $|\mathbf{Y_N^\dagger L Y_N}|_{21}^2$, with $\mathbf{L}$ encoding logarithmic running from $M_1$ to $M_X$.
• Imposes a texture-zero condition on $\mathbf{Y_N}$, specifically $(\mathbf{Y_N})_{21} = 0$, to suppress the dominant $M_3$-dominated contribution to LFV.
• Relies on the parametrization $\mathbf{Y_N} = \frac{1}{v_u} \sqrt{\mathbf{D_N}} \mathbf{R} \sqrt{\mathbf{D_\nu}} \mathbf{U}^\dagger$, where $\mathbf{R}$ is a complex orthogonal matrix encoding CP phases relevant to leptogenesis.
• Fixes the complex angle $\omega$ in $\mathbf{R}$ to satisfy both the texture-zero condition and the requirement of successful leptogenesis, linking $\omega$ to the Majorana phase $\alpha$.

Experimental results

Research questions

• RQ1 Can the $\text{BR}(\mu\to e+\gamma)$ rate in the SUSY seesaw model be suppressed below the current experimental limit while maintaining successful thermal leptogenesis?
• RQ2 What specific structure of the neutrino Yukawa coupling matrix $\mathbf{Y_N}$ allows suppression of the dominant $M_3$ contribution to $\text{BR}(\mu\to e+\gamma)$ without violating leptogenesis constraints?
• RQ3 How are the baryon asymmetry of the Universe, the $\mu\to e+\gamma$ branching ratio, and the effective Majorana mass in $0\nu\beta\beta$ decay correlated in this constrained model?
• RQ4 What is the role of the Majorana CP phase $\alpha$ in linking the leptogenesis CP asymmetry to the texture of $\mathbf{Y_N}$ and the resulting LFV rates?
• RQ5 Can a specific form of $\mathbf{Y_N}$, such as $Y_{21} = 0$, be derived from the requirement of both LFV suppression and successful leptogenesis in the context of hierarchical $M_1 \ll M_2 \ll M_3$?

Key findings

• For hierarchical $M_1 \ll M_2 \ll M_3$ and $M_3 \gtrsim 5 \times 10^{13}$ GeV, the standard SUSY seesaw model predicts $\text{BR}(\mu\to e+\gamma)$ at least three orders of magnitude above the experimental upper limit of $1.2 \times 10^{-11}$ when SUSY particles are in the few 100 GeV range.
• The dominant contribution to $\text{BR}(\mu\to e+\gamma)$ arises from the $M_3$-dependent term in $\mathbf{Y_N^\dagger L Y_N}$, which is suppressed by setting $(\mathbf{Y_N})_{21} = 0$ via a specific complex angle $\omega = \tan^{-1}(\tan\theta_{12} e^{-i\alpha/2})$.
• The requirement of successful thermal leptogenesis imposes a lower bound $M_1 \gtrsim 6.7 \times 10^{12}$ GeV, which, when combined with the $M_2 \gtrsim 3 \times 10^{13}$ GeV scale, would otherwise lead to an $M_2$-dominated contribution to $\text{BR}(\mu\to e+\gamma)$ exceeding the bound by ~3 orders of magnitude.
• The texture-zero condition $(\mathbf{Y_N})_{21} = 0$ forces the leptogenesis CP phase $\omega$ to be fully determined by the low-energy neutrino mixing parameters $\theta_{12}$ and the Majorana phase $\alpha$, linking the CP asymmetry to the LFV rate.
• A predictive correlation emerges between the baryon asymmetry $Y_B$, $\text{BR}(\mu\to e+\gamma)$, and the effective Majorana mass $\langle m \rangle$ in $0\nu\beta\beta$ decay, all of which depend on the same Majorana phase $\alpha$.
• The model predicts that $\text{BR}(\mu\to e+\gamma)$ can be within the sensitivity reach of the upcoming MEG experiment if the Yukawa matrix has the specified texture-zero structure.