Towards a complete theory of thermal leptogenesis in the SM and MSSM

TL;DR

The paper develops a comprehensive, finite-temperature treatment of thermal leptogenesis in the SM and MSSM, incorporating RG running, gauge scatterings, and correct on-shell subtraction to avoid double counting. It provides robust predictions and bounds, notably mν < 0.15 eV (3σ) and mN1 > 2×10^7 GeV in the SM, with MSSM results similar, and derives a lower bound on the reheating temperature THR of about 2–3×10^9 GeV, highlighting tension with gravitino overproduction. The authors also study scenarios to alleviate this tension, including soft leptogenesis and inflaton-sneutrino–driven or condensate-based mechanisms, and discuss the implications for neutrino physics and early-universe cosmology. The work offers practical analytic approximations and a modular framework that improves precision beyond prior treatments and informs model-building in neutrino physics and baryogenesis.

Abstract

We perform a thorough study of thermal leptogenesis adding finite temperature effects, RGE corrections, scatterings involving gauge bosons and by properly avoiding overcounting on-shell processes. Assuming hierarchical right-handed neutrinos with arbitrary abundancy, successful leptogenesis can be achieved if left-handed neutrinos are lighter than 0.15 eV and right-handed neutrinos heavier than 2 10^7 GeV (SM case, 3sigma C.L.). MSSM results are similar. Furthermore, we study how reheating after inflation affects thermal leptogenesis. Assuming that the inflaton reheats SM particles but not directly right-handed neutrinos, we derive the lower bound on the reheating temperature to be T_RH > 2 10^9 GeV. This bound conflicts with the cosmological gravitino bound present in supersymmetric theories. We study some scenarios that avoid this conflict: `soft leptogenesis', leptogenesis in presence of a large right-handed (s)neutrino abundancy or of a sneutrino condensate.

Figures (17)

• Figure 1: The dispersion relation $|\omega(k)|$ (fig. \ref{['fig:mT']}a) and the residue (fig. \ref{['fig:mT']}b) of particle (dotted line) and 'hole' (dashed line) excitations of a fermion with thermal mass $m$ at temperature $T$ for $m\ll T$. The solid line shows the approximation $\omega^2 = m^2 + k^2$.
• Figure 2: Thermal masses in the SM (left) and in the MSSM (right), in units of the temperature $T$.
• Figure 3: Universal running of $m_\nu$ in the SM and in the MSSM. The bands give an indication of the uncertainties, as explained in the text.
• Figure 4: Feynman diagrams contributing to SM thermal leptogenesis.
• Figure 5: The SM reaction densities for $\tilde{m}_1 \equiv (Y_\nu Y_\nu^\dagger)_{11} v^2/m_{N_1} = 0.06\,{\rm eV}$ and $m_{N_1}=10^{10}\,{\rm GeV}$. Blue line: decays ($\gamma_D$). Red long-dashed lines: $\Delta L = 1$ scatterings ($\gamma_{Ss,t}=\gamma_{Hs,t}+\gamma_{As,t}$). Green dashed lines: $\Delta L = 2$ scatterings ($\gamma_N$).