Probing $0νββ$ and $μ o eγ$ via Fully Determined Dirac Mass Terms in LRSM with Double Seesaw

Neutrinoless double beta decay ($0νββ$) and charged lepton flavor violation (cLFV) experiments provide promising avenues to probe new physics contributions from extended neutrino sectors in beyond Standard Model (BSM) scenarios. We consider a Left-Right Symmetric Model (LRSM) extended with three generations of sterile neutrinos to realize a double type-I seesaw mechanism for light neutrino mass generation. The double seesaw induces maximal lepton number violation in the right-handed sector and facilitates enhanced Majorana masses for right-handed neutrinos, thereby leading to their dominant contributions in both cLFV and $0νββ$ processes. We perform a comprehensive exploration of the parameter space for new-physics contributions to the cLFV decay $μ\to e γ$ and to $0νββ$, considering two different textures for the Dirac mass matrices: (i) a symmetry-motivated limit with $M_D \propto \mathbb{1}$, and (ii) a texture fully determined by the model framework. A detailed analysis of the common parameter regions accessible to current experiments like KamLAND-Zen and LEGEND-200, and upcoming experiments, such as MEG-II and LEGEND-1000, is presented, underscoring the phenomenological relevance of this framework. Our results aim to provide optimistic benchmarks for future searches targeting right-handed current-mediated neutrino interactions.

💡 Research Summary

This paper investigates the phenomenology of neutrinoless double‑beta decay (0νββ) and the charged‑lepton‑flavour‑violating decay μ→eγ within a TeV‑scale Left‑Right Symmetric Model (LRSM) that incorporates three generations of sterile singlet fermions S L. The presence of the singlets enables a double type‑I seesaw (often called a cascade or double seesaw) in which the heavy singlets first generate a large Majorana mass for the right‑handed neutrinos (RHNs) and subsequently the RHNs generate the light neutrino masses via the usual type‑I seesaw. The hierarchy M_S ≫ M_{RS} ≫ M_D is assumed, guaranteeing that the light neutrino masses are naturally suppressed without fine‑tuning.

Two distinct textures for the Dirac neutrino mass matrix M_D are examined:

1. Case I (symmetry‑motivated) – M_D is taken proportional to the identity matrix, a choice often justified by flavour symmetries. This texture maximises the mixing between active and heavy states while keeping the number of free parameters minimal.

2. Case II (model‑determined) – The LR symmetry is taken to be charge‑conjugation (C) and the “screening” condition is imposed, which forces a specific relation between M_D and the RHN‑sterile coupling matrix M_{RS}. In this setup M_D and M_{RS} are fully fixed by the low‑energy oscillation data and the LR symmetry, leaving essentially no free phases.

Because the double seesaw generates sizable Majorana masses for the RHNs (of order a few TeV), right‑handed currents dominate both the LNV and cLFV amplitudes. The authors compute the full set of contributions to 0νββ: the standard light‑neutrino exchange, the λ‑diagram (W_L–W_R mixing), the η‑diagram (pure W_R exchange), and the heavy‑RHN exchange diagram. Nuclear matrix elements are taken from recent QRPA/IBM‑2 calculations. For μ→eγ they evaluate the one‑loop diagrams involving W_R and the heavy RHNs, using exact loop functions rather than large‑mass approximations.

A comprehensive parameter scan is performed over:

• The right‑handed gauge boson mass M_{W_R} (4–8 TeV),
• The sterile Majorana scale M_S (10–100 TeV),
• The RHN mass hierarchy (normal, inverted, quasi‑degenerate),
• The overall scale of M_D (controlled by the chosen texture).

Key findings include:

• In both cases, for M_D of order 10 GeV the branching ratio BR(μ→eγ) lies in the 10^{-13}–10^{-12} range, comfortably within the projected sensitivity of MEG‑II (≈6×10^{-14}) and well above the current limit.
• The effective Majorana mass ⟨m_{ββ}⟩ relevant for 0νββ can reach 10–50 meV, placing it squarely inside the discovery reach of the ongoing KamLAND‑Zen and LEGEND‑200 experiments, and certainly within the future LEGEND‑1000 goal (<10 meV).
• The RHN mass hierarchy strongly influences the correlation between the two observables. For a normal hierarchy (m_{N1}<m_{N2}<m_{N3}) the μ→eγ rate is typically larger, whereas a quasi‑degenerate RHN spectrum enhances the 0νββ amplitude.
• When M_{W_R}≈4 TeV and the RHNs are as light as 1–3 TeV, the same parameter region yields observable signals in both low‑energy experiments and at the LHC via same‑sign dilepton plus jets signatures (pp→W_R→N_Rℓ).

The paper emphasizes that the model‑determined Dirac texture (Case II) provides a highly predictive framework: once the oscillation parameters are fixed, the rates for 0νββ and μ→eγ are essentially determined, allowing a direct test of the underlying LR symmetry and the double‑seesaw mechanism. The authors also discuss the impact of theoretical uncertainties in nuclear matrix elements and suggest that future improvements could sharpen the experimental tests.

In conclusion, the double‑seesaw LRSM naturally yields TeV‑scale RHNs with large Majorana masses, leading to dominant right‑handed current contributions to both lepton‑number‑violating and charged‑lepton‑flavour‑violating processes. The simultaneous exploration of 0νββ, μ→eγ, and collider signatures offers a powerful, complementary strategy to probe the model. The work provides concrete benchmark points and highlights the promising discovery potential of upcoming experiments such as LEGEND‑1000 and MEG‑II, while also outlining avenues for further theoretical refinement.