Scrutinizing Fermionic Dark Matter in Scotogenic Model with Low Reheating Temperature

The scotogenic model provides a minimal and elegant framework that simultaneously explains neutrino masses and accommodates a viable dark matter (DM) candidate. In this work, we investigate the phenomenology of fermionic DM in the scotogenic model, with a particular emphasis on the effects of a non-standard cosmological history characterized by a low reheating temperature. We demonstrate that entropy injection from inflaton decay can significantly dilute the DM abundance, thereby relaxing the annihilation cross section required to reproduce the observed relic density and opening new regions of viable parameter space. We further analyze the complementarity between current and future direct detection experiments and charged lepton flavour violation (cLFV) searches in probing this scenario. Our results show that next-generation direct detection experiments such as DARWIN and XLZD, together with upcoming cLFV searches (in particular the future sensitivity of $μ\rightarrow 3e$ and $μ\rightarrow e$ conversion experiments), will be capable of testing substantial regions of the parameter space, including those associated with low reheating temperatures.

💡 Research Summary

The paper investigates fermionic dark matter (DM) in the scotogenic model under a non‑standard cosmological history where the reheating temperature (T_R) after inflation is lower than the usual freeze‑out temperature of the DM. In the scotogenic framework, a Z₂‑odd inert scalar doublet η and three singlet fermions N_i are added to the Standard Model. The lightest fermion N₁ is the DM candidate, while neutrino masses arise radiatively at one loop, controlled by the λ₅ coupling which splits the masses of the neutral components η_R and η_I.

The authors fix most scalar potential parameters (λ₂=0, λ₃, λ₄ within electroweak precision limits) and adopt the Casas‑Ibarra parametrisation for the Yukawa matrix Y_ν, but set the orthogonal matrix R to the identity to minimise free parameters. They assume normal ordering of neutrino masses and use current global fit values for the oscillation parameters.

In the low‑T_R scenario, the inflaton decays late, injecting entropy into the plasma. This dilutes the DM number density by a factor Δ, allowing the observed relic density Ω_DM h²≈0.12 to be achieved with a smaller thermally averaged annihilation cross section ⟨σv⟩ than in the standard radiation‑dominated case. Since fermionic DM annihilation is p‑wave suppressed (A=0, B∝y₁⁴/(M_N1²+m_η²)²), the dilution effect is especially beneficial. The authors compute ⟨σv⟩(T) with micrOMEGAs, include all fermion‑fermion co‑annihilation channels, and solve the Boltzmann equation with the entropy injection term.

Direct detection proceeds via a loop‑induced spin‑independent scattering off nuclei. The cross section depends on λ₅ and the Higgs‑portal couplings λ₃, λ₄; when the η_R–η_I mass splitting is small (≲10 GeV), the loop contribution is enhanced, yielding σ_SI≈10⁻⁴⁸ cm². This lies within the projected sensitivities of next‑generation experiments such as DARWIN and XLZD.

Charged lepton flavour violation (cLFV) provides complementary constraints. The same Yukawa couplings that control DM annihilation also generate μ→eγ, μ→3e and μ→e conversion. Using current limits and future sensitivities (MEG II, Mu3e, COMET/Mu2e), the authors show that for λ₅≈10⁻⁶ and modest mass splittings among N_i (ΔM≳5 GeV), the model can satisfy both relic density and cLFV bounds. Near‑degenerate fermions (ΔM≲10 GeV) increase co‑annihilation, relaxing the required ⟨σv⟩, but simultaneously raise cLFV rates, offering a clear experimental target.

Scanning over M_N1≈200 GeV–1 TeV, T_R≈3–10 GeV (above the BBN limit), and appropriate scalar couplings, the study identifies viable regions where entropy dilution, direct detection, and cLFV searches intersect. The work demonstrates that low reheating temperatures open up previously excluded parameter space for fermionic scotogenic DM and that upcoming experiments will be able to probe a substantial portion of this space, highlighting the strong complementarity between cosmology, direct detection, and flavour physics.