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$keV$ sterile neutrino as dark matter in doublet left-right symmetric model with $A_{4}$ modular symmetry

Ankita Kakoti, Mrinal Kumar Das

TL;DR

This work embeds keV-scale sterile neutrino dark matter and double-neutrino mass generation inside a DLRS framework augmented by $A_4$-type modular symmetry (Gamma(3)). By using modular forms $Y=(Y_1,Y_2,Y_3)$, it constructs Dirac, active-sterile, and Majorana masses without flavons, yielding a symmetric light-neutrino mass matrix via the double seesaw mechanism. The study analyzes DM relic density and radiative decay under Lyman-$\alpha$ and X-ray constraints and evaluates neutrinoless double beta decay contributions from light, heavy, and sterile states. Numerical results show viable keV DM masses in the $10$–$28$ keV range with small active-sterile mixing, and illustrate regions where DM phenomenology and $0\nu\beta\beta$ bounds are simultaneously satisfied, underscoring the modular symmetry approach as a minimal, predictive route for beyond-Standard-Model phenomenology.

Abstract

Left-Right Symmetric Model(LRSM) in this work is extended with a sterile fermion per generation, the lightest of the same is considered to be a suitable dark matter candidate for the study and analysis of the associated properties. The model has been realized using $A_{4}$ modular symmetry, the advantage being the non-requirement of the use of extra fields, hence keeping the model minimal. Because of the extension of LRSM with the sterile fermion, the neutrino mass in this work will be generated by the double seesaw mechanism as described thoroughly within the manuscript. And for phenomenological studies, we have considered neutrinoless double beta decay the details of which have been discussed thoroughly within the work.

$keV$ sterile neutrino as dark matter in doublet left-right symmetric model with $A_{4}$ modular symmetry

TL;DR

This work embeds keV-scale sterile neutrino dark matter and double-neutrino mass generation inside a DLRS framework augmented by -type modular symmetry (Gamma(3)). By using modular forms , it constructs Dirac, active-sterile, and Majorana masses without flavons, yielding a symmetric light-neutrino mass matrix via the double seesaw mechanism. The study analyzes DM relic density and radiative decay under Lyman- and X-ray constraints and evaluates neutrinoless double beta decay contributions from light, heavy, and sterile states. Numerical results show viable keV DM masses in the – keV range with small active-sterile mixing, and illustrate regions where DM phenomenology and bounds are simultaneously satisfied, underscoring the modular symmetry approach as a minimal, predictive route for beyond-Standard-Model phenomenology.

Abstract

Left-Right Symmetric Model(LRSM) in this work is extended with a sterile fermion per generation, the lightest of the same is considered to be a suitable dark matter candidate for the study and analysis of the associated properties. The model has been realized using modular symmetry, the advantage being the non-requirement of the use of extra fields, hence keeping the model minimal. Because of the extension of LRSM with the sterile fermion, the neutrino mass in this work will be generated by the double seesaw mechanism as described thoroughly within the manuscript. And for phenomenological studies, we have considered neutrinoless double beta decay the details of which have been discussed thoroughly within the work.

Paper Structure

This paper contains 8 sections, 45 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Doublet Left-Right Symmetric Model and Neutrino Mass.
  3. Doublet LRSM using modular group of level 3 ($\Gamma(3)$) and $k_{Y}=2$ .
  4. Dark matter in Left-Right Symmetric Model
  5. Neutrinoless Double Beta Decay
  6. Numerical Analysis and Results
  7. Discussion
  8. Conclusion

Figures (7)

  • Figure 3: Variation of mass of DM candidate with active-sterile mixing angle for NH(left) and IH(right).
  • Figure 4: Variation of mass of DM candidate with decay rate for NH(left) and IH(right).
  • Figure 5: Variation of mass of DM candidate with relic abundance for NH(left) and IH(right).
  • Figure 6: Variation of mass of DM candidate with total effective mass of $0\nu\beta\beta$ for NH(left) and IH(right).
  • Figure 7: Variation of total effective mass of $0\nu\beta\beta$ with relic abundance for NH(left) and IH(right).
  • ...and 2 more figures