[Paper Review] Neutrino radiative decay and lepton flavor violation in supersymme tric models

Marie-Bernadette Causse|ArXiv.org|Feb 11, 2002

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper investigates radiative neutrino decay ($ar{ u}_\tau \to \nu_\mu + \gamma$) and lepton flavor violation (LFV) in supersymmetric models with right-handed neutrinos, using the minimal supersymmetric standard model (MSSMRN) and $SU(5)$ grand unified theory (SU(5)RN). It employs the multi-mass insertion method to compute transition magnetic moments, finding they can reach values comparable to or exceeding the standard model prediction (1.32×10⁻¹⁹ $m_\nu$/eV) under large mixing and relic density-compatible SUSY parameters, particularly for heavy right-handed neutrinos.

ABSTRACT

The radiative decay of neutrino,such as (\bar{ν_τ}: \longrightarrow: ν_μ+γ), in the minimal supersymmetric standard model with right-handed neutrinos (MSSMRN) and in the (SU(5)) grand unified theory with right-handed neutrinos((SU(5)RN))model is examined.In these models,the transition magnetic moment of neutrino is directly proportional to the neutrino mass.For different values on SUSY parameters (compatible with the relic density) and for large mixing angle solution to the atmospheric neutrino problem,the transition magnetic moment can be a few times greater than,or comparable to,the value of the standard model (with a right-handed neutrino singlet added).

Motivation & Objective

• To investigate the radiative decay of neutrinos, specifically $\bar{\nu}_\tau \to \nu_\mu + \gamma$, in supersymmetric models with right-handed neutrinos.
• To assess lepton flavor violation (LFV) in the MSSMRN and $SU(5)$ grand unified theory with right-handed neutrinos (SU(5)RN).
• To compute the transition magnetic moment of Majorana neutrinos in these models using the multi-mass insertion method.
• To determine the impact of SUSY parameters and right-handed neutrino masses on the magnetic moment, under constraints from relic density.
• To explore the connection between neutrino oscillation and LFV processes via common Yukawa couplings in the seesaw mechanism.

Proposed method

• Uses the multi-mass insertion method to compute amplitudes for chargino contributions to $\bar{\nu}_\tau \to \nu_\mu + \gamma$ decay in MSSMRN and SU(5)RN models.
• Incorporates slepton mass mixing and chargino sector mixing, particularly for large mixing between second and third generations as suggested by atmospheric neutrino data.
• Applies the seesaw mechanism with a heavy right-handed neutrino, assuming Yukawa couplings similar to up-type quarks.
• Evaluates Feynman integrals using analytic expressions for loop integrals, including functions like $H_a$, $H_d$, $H_e$, $I$, $f$, $g$, $h$, and $F$.
• Uses numerical integration over Feynman parameters to compute the amplitudes, with $X_{\widetilde{W}_n} = M_2^2 / \overline{M}_n^2$ and $X_{\widetilde{\mu}_n} = \mu^2 / \overline{M}_n^2$.
• Relies on an interface between DarkSUSY and Suspect2 for numerical analysis, ensuring SUSY parameters are compatible with relic density constraints.

Experimental results

Research questions

• RQ1 Can the transition magnetic moment of Majorana neutrinos in SUSY models with right-handed neutrinos reach values comparable to or exceeding the standard model prediction?
• RQ2 How do large mixing angles in the slepton sector—suggested by atmospheric neutrino data—affect the radiative decay rate of $\bar{\nu}_\tau \to \nu_\mu + \gamma$?
• RQ3 What is the role of the right-handed neutrino mass and Yukawa couplings in generating lepton flavor violation and enhancing the magnetic moment?
• RQ4 To what extent do SUSY parameters (e.g., $M_2$, $\mu$) and relic density constraints influence the predicted magnetic moment?
• RQ5 Can the same Yukawa couplings responsible for neutrino mass generation also mediate significant LFV in charged lepton decays?

Key findings

• The transition magnetic moment of neutrinos in MSSMRN and SU(5)RN models can be comparable to or even a few times larger than the standard model value of $1.32 \times 10^{-19} \, \text{eV}^{-1} \times m_\nu$.
• For large mixing between second and third generation slepton states—consistent with the large mixing angle solution to the atmospheric neutrino problem—the magnetic moment is enhanced.
• The magnetic moment remains sensitive to the mass of the right-handed neutrino, with larger values observed for heavier $M_R$.
• Numerical results show that under relic density-compatible SUSY parameters, the magnetic moment can reach $\sim 10^{-19} \, \text{eV}^{-1}$, approaching or exceeding the SM prediction.
• The multi-mass insertion method successfully captures the dominant contributions from chargino and slepton mixing, with analytic integrals evaluated via parameter-dependent functions like $H_a$, $I$, and $F$.
• The study confirms that Yukawa couplings in the seesaw mechanism can simultaneously explain neutrino masses and mediate observable LFV processes, including radiative decay.