Near-Resonant Thermal Leptogenesis

TL;DR

This work establishes a controlled non-resonant, quasi-degenerate regime for leptogenesis by imposing the conservative condition Delta M > 100 Gamma_i, which yields a universal CP asymmetry bound |epsilon_i| <= 1/200 independent of RH neutrino masses and tilde m. It demonstrates that vanilla and flavoured near-resonant leptogenesis can successfully generate the observed baryon asymmetry with RH neutrino masses as low as the electroweak scale (M_1 ≳ 100 GeV) and explores leptogenesis during reheating, showing that the required reheating temperature T_RH can be as low as ~10 GeV under suitable conditions. The analysis includes a consistent treatment of flavour effects in both thermal and reheating contexts, and provides a detailed Boltzmann-equation framework with comoving variables to capture the dynamics. Overall, near-resonant thermal leptogenesis offers a theoretically stable alternative to resonant scenarios, expanding viable parameter space while avoiding regulator ambiguities and extending the possible cosmological histories compatible with successful baryogenesis.

Abstract

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.

Figures (11)

• Figure 1: Feynman diagrams contributing to the CP asymmetry: (a) tree-level, (b) self-energy, and (c) vertex diagrams.
• Figure 2: Benchmark result for completed leptogenesis taking the maximum bound on the CP asymmetry with parameters $M_{N} = 10^{5}\,\text{GeV}$, $\tilde{m}_1 = 10^{-1}$ eV and $\tilde{m}_2= 10^{-5}\rm\ eV$. Left Panel: The evolution of the right-handed neutrino abundances. The right-handed neutrino with the larger corresponding $\tilde{m}$ is able to be produced at greater abundance before becoming non-relativistic and decaying. Right Panel: the evolution of the baryon asymmetry. The resulting baryon asymmetry exceeds the observed value by several orders of magnitude, illustrating the high efficiency of baryon asymmetry generation in near-resonant leptogenesis.
• Figure 3: Benchmark result for low scale near-resonant leptogenesis with parameters are $M_{N} = 10^{3}\,\text{GeV}$, $\tilde{m}_1 = 10^{-4}$ eV and $\tilde{m}_2= 10^{-5}\rm\ eV$ and shows the evolution of the bolztmann equations up to electroweak symmetry breaking. Left Panel: the evolution of the right-handed neutrino abundances, illustrating that their production and decay remain suppressed due to the smaller effective neutrino masses and that the decays are not complete by electroweak symmetry breaking. Right Panel: the baryon asymmetry evolution and demonstrates that despite the incomplete decays, the CP asymmetry is sufficiently enhanced that the observed baryon asymmetry is still reproduced.
• Figure 4: Maximum baryon asymmetry from scans over effective neutrino masses for $M_{N} = 10^{5}\,\text{GeV}$. Left Panel: we fix $\tilde{m}_1$ and scan over $\tilde{m}_2$. We can see that for $\tilde{m}_2<<\tilde{m}_1$ the result is independent of $\tilde{m}_2$ and for $\tilde{m}_2>>\tilde{m}_1$ the result is independent of $\tilde{m}_1$. We can thus conclude that if we have a hierarchy in effective neutrino masses the baryon asymmetry is determined by the larger effective neutrino mass. Right Panel: shows the full scan demonstrating that if either effective neutrino mass is greater than $\simeq 3\times 10^{-6}$ eV then the observed baryon asymmetry can be reproduced.
• Figure 5: The maximum baryon asymmetry for various right-handed neutrino masses with the largest effective neutrino mass scanned over for zero initial conditions. The horizontal dashed line indicates the observed baryon asymmetry. The curves exhibit the characteristic suppression at small $\tilde{m}$ due to inefficient right-handed neutrino production and at large $\tilde{m}$ due to strong washout. For lower $M_N$, additional structure appears when electroweak symmetry breaking and sphaleron freeze-out occur during the intrinsic sign change in the baryon-asymmetry evolution.