[Paper Review] Neutrino and Charged Lepton Flavour Today

Rodrigo Alonso, M.B. Gavela+3 more|arXiv (Cornell University)|Nov 7, 2013

Particle physics theoretical and experimental studies69 references4 citations

TL;DR

This paper investigates neutrino and charged lepton flavour violation in the context of the type-I Seesaw mechanism, focusing on $μ\to e$ conversion in nuclei as a probe of new physics. It shows that an $O(2)_{N}$ flavour symmetry in the right-handed neutrino sector leads to maximal mixing angles and a maximal Majorana phase, strongly correlating neutrino mass hierarchy with mixing patterns, while also providing precise predictions for the relative rates of $μ\to e$ conversion, $μ\to e\gamma$, and $μ\to eee$ across different target nuclei.

ABSTRACT

Flavour physics is a priceless window on physics beyond the Standard Model. In particular, flavour violation in the lepton sector looks very promising, as high precision measurements are prospected in future experiments investigating on $μ ightarrow e$ conversion in atomic nuclei: the predictions for this observable are analysed in the context of the type I Seesaw mechanism. Furthermore, new ideas to explain the Flavour Puzzle recently appeared, mainly based on a possible dynamical origin of the Yukawa couplings and on flavour symmetries. The focus of this proceeding will be set on the Minimal Flavour Violation ansatz and on the role of the neutrino Majorana character: when an $O(2)_{N}$ flavour symmetry acts on the right-handed neutrino sector, the minimum of the scalar potential allows for large mixing angles -in contrast to the simplest quark case- and predicts a maximal Majorana phase. This leads to a strong correlation between neutrino mass hierarchy and mixing pattern.

Motivation & Objective

• To analyze the prospects for observing charged lepton flavour violation via $μ\to e$ conversion in atomic nuclei as a probe of new physics beyond the Standard Model.
• To investigate how dynamical origins of Yukawa couplings and flavour symmetries—particularly $O(2)_{N}$—can explain the observed neutrino mixing patterns and mass hierarchy.
• To clarify the role of the Majorana nature of neutrinos in generating maximal mixing angles and a maximal Majorana phase within the Seesaw framework.
• To provide precise, model-independent predictions for the ratios of $μ\to e$ conversion, $μ\to e\gamma$, and $μ\to eee$ rates across different target nuclei (Al, Ti, Au), enabling discrimination among theoretical models.
• To assess the sensitivity of future experiments to right-handed neutrino masses, showing that $μ\to e$ conversion can probe scales up to $>1000$ TeV and down to $\sim 2$ GeV in titanium.

Proposed method

• The analysis employs the type-I Seesaw mechanism, where heavy right-handed neutrinos are integrated out to generate light neutrino masses via the Weinberg operator.
• The paper computes form factors for $μ\to e$ conversion in nuclei, including both logarithmic and constant terms in the heavy neutrino mass, resolving discrepancies with prior calculations.
• It uses the Minimal Flavour Violation (MFV) ansatz to constrain the structure of flavour-violating operators in the effective theory.
• The authors analyze the scalar potential under $O(2)_{N}$ symmetry, showing that only this symmetry leads to a minimum with maximal mixing and a $\pi/2$ Majorana phase.
• For the three-family case, the model considers $G_{f}^{\ell} = U(3)_{\ell_{L}} \times U(3)_{E_{R}} \times O(2)_{N}$ with two degenerate right-handed neutrinos, allowing one maximal mixing angle and phase in the degenerate sector.
• The interplay between bi-fundamental and fundamental representations of the flavour symmetry is used to generate a second sizable mixing angle, with the third angle arising from small perturbations.

Experimental results

Research questions

• RQ1 Can $O(2)_{N}$ flavour symmetry in the right-handed neutrino sector naturally lead to maximal mixing angles and a maximal Majorana phase in the neutrino mass matrix?
• RQ2 How do the rates for $μ\to e$ conversion, $μ\to e\gamma$, and $μ\to eee$ correlate across different target nuclei, and can these ratios distinguish between models?
• RQ3 What is the impact of non-logarithmic terms in the form factors on the $μ\to e$ conversion rate, and why are they numerically significant?
• RQ4 How does the inclusion of dynamical Yukawa couplings and flavour symmetries resolve the flavour puzzle in the lepton sector?
• RQ5 Can a two-degenerate-right-handed-neutrino scenario with $O(2)_{N}$ symmetry generate a realistic neutrino mixing pattern with one maximal angle and a perturbatively generated third angle?

Key findings

• The $O(2)_{N}$ symmetry in the right-handed neutrino sector leads to a minimum of the scalar potential with maximal mixing angles and a maximal Majorana phase of $\pi/2$, in contrast to the quark case.
• In the two-family case, the model predicts a degenerate light neutrino spectrum and maximal mixing, with the Majorana phase fixed at $\pi/2$.
• For the three-family case with two degenerate right-handed neutrinos, the model predicts one maximal mixing angle and phase in the degenerate sector, while the third mixing angle arises from small perturbations.
• The ratios of $μ\to e$ conversion rates (in Al, Ti, Au) to $\u03bc\to e\gamma$ and $\u03bc\to eee$ exhibit distinct mass dependences, enabling model discrimination: for example, a ratio of $\sim1$ between $\u03bc\to e(Ti)$ and $\u03bc\to e\gamma$ implies $m_{N} \sim 10^{3}$ or $10^{4}$ GeV.
• The model predicts a ratio of $\sim10$ ($\sim1$) between $\u03bc\to e(Ti)$ and $\u03bc\to eee$ for $m_{N} \sim 10^{3}$ GeV ($10^{4}$ GeV), providing a testable signature.
• Future $μ\to e$ conversion experiments can probe right-handed neutrino masses up to $>1000$ TeV and down to $\sim 2$ GeV in titanium, making them highly sensitive to a broad range of Seesaw models.