Near-Resonant Thermal Leptogenesis

We study leptogenesis in the quasi-degenerate but non-resonant regime. Expanding the CP asymmetry parameter near degeneracy and imposing the conservative non-resonance condition that the mass splitting must be much greater than the right-handed neutrino decay rates $ΔM > 100Γ_i$, yields the universal upper bound $ε\leq 1/200$, independent of both the effective neutrino masses and the right-handed neutrino mass. We investigate vanilla and flavoured near-resonant leptogenesis and find that successful leptogenesis by right-handed neutrino decays can occur for $M \gtrsim 100~\mathrm{GeV}$ independent of washout regime, extending the viable parameter space of thermal leptogenesis down to the electroweak scale without invoking resonance. We also analyse near-resonant thermal leptogenesis during reheating and show that successful baryon asymmetry generation is compatible with reheating temperatures as low as $T_{RH}\simeq 10\rm GeV$ without relying on non-thermal production. Finally, we present a consistent framework for incorporating flavour effects in near-resonant leptogenesis during reheating. Overall, near-resonant thermal leptogenesis offers a controlled alternative regime to resonant leptogenesis, lowering the leptogenesis scale to the electroweak scale, without reliance on a disputed regulator used in resonant leptogenesis.

💡 Research Summary

The paper investigates leptogenesis in a regime where two heavy right‑handed (RH) neutrinos are quasi‑degenerate but far enough from the fully resonant limit. By expanding the CP‑asymmetry parameter εi around the degenerate point and imposing a conservative non‑resonance condition ΔM > 100 Γi (the mass splitting must exceed the decay widths by at least two orders of magnitude), the authors derive a universal upper bound ε ≤ 1/200, independent of the RH neutrino masses Mi or the effective neutrino masses \tilde m_i. This bound removes the need for the regulator that is required in resonant leptogenesis, where the CP asymmetry formally diverges and its finite value depends on the chosen regularisation scheme.

Using this bound, the authors solve the standard Boltzmann equations for thermal leptogenesis, first in the “vanilla” single‑flavour approximation and then including full flavour effects. The decay term Di(z) and wash‑out term Wi(z) are expressed through the usual decay parameter Ki = \tilde m_i/m_* (with m_* ≈ 10⁻³ eV). Whether Ki≫1 (strong wash‑out) or Ki≪1 (weak wash‑out), the CP‑asymmetry cannot exceed 0.5 %, so the generated lepton asymmetry can be large enough to reproduce the observed baryon‑to‑photon ratio YB ≈ 8.9 × 10⁻¹¹. Numerical examples show that for Mi as low as 10⁵ GeV (and even down to 10³ GeV when the electroweak phase transition halts the decay) the final asymmetry overshoots the observed value by several orders of magnitude, demonstrating the high efficiency of near‑resonant leptogenesis.

Flavour effects become relevant below ≈10¹² GeV, when charged‑lepton Yukawa interactions decohere the lepton flavours. The authors introduce flavour‑dependent CP asymmetries εi^α and decay parameters Ki^α, and solve a set of three coupled Boltzmann equations (one for each flavour). They find that the universal bound ε ≤ 1/200 still holds for each flavour, and that flavour decoherence can even reduce wash‑out in some channels, slightly enhancing the final asymmetry. Hence, flavour dynamics do not weaken the viability of the scenario.

The paper then turns to leptogenesis during reheating, where the inflaton’s decay populates the RH neutrinos non‑thermally. By adapting the Boltzmann system to the reheating background (including the time‑dependent temperature T∝a⁻³⁄⁸ and the Hubble rate dominated by the inflaton), the same ε bound is applied. The analysis yields a remarkably low lower bound on the reheating temperature: successful baryogenesis can be achieved for TRH ≈ 10 GeV, far below the conventional requirement of TRH ≳ 10⁹ GeV for thermal leptogenesis. The inclusion of flavour effects during reheating leads to qualitatively similar conclusions.

A comparative table highlights that previous works derived the CP‑asymmetry bound only in extended U(1)_{B‑L} models or without a systematic treatment of flavours and reheating. This study provides the first comprehensive treatment within the minimal Type‑I seesaw framework, incorporating the universal non‑resonant CP bound, full flavour dynamics, and reheating effects.

In summary, by staying safely outside the resonant regime and exploiting the universal ε ≤ 1/200 limit, the authors demonstrate that leptogenesis can operate at RH neutrino masses as low as the electroweak scale (∼100 GeV) and with reheating temperatures as low as 10 GeV. This opens a theoretically clean and experimentally more accessible window for baryogenesis, avoiding the regulator‑dependence that plagues resonant leptogenesis while still achieving the required baryon asymmetry.