Cosmic Strings Gravitational Wave Probe of Leptogenesis: Thermal, Non-thermal, Near-resonant and Flavourful

Abstract

Breaking a global or local $U(1)_{\rm B-L}$ symmetry at high scales simultaneously generates Majorana masses for heavy right-handed neutrinos and produces a network of cosmic strings. The evolution and decay of these strings source a stochastic gravitational-wave background that may be probed by current and future gravitational-wave experiments, while the decays of the resulting massive right-handed neutrinos can generate the baryon asymmetry of the Universe via leptogenesis. We derive analytical bounds for successful leptogenesis with a global and a local $U(1)_{B-L}$ symmetry, separately finding an absolute lower bound on the lightest right-handed neutrino mass $M_1 > 1.74 \times 10^{8}\,\mathrm{GeV}$ for thermal initial conditions and $M_1 > \mathcal{O}(10^{6})\,\mathrm{GeV}$ for non-thermal initial conditions. Allowing for near-resonant leptogenesis relaxes these bounds to TeV scale in both cases making it a viable target at collider searches complementing the GW signals. Full flavour effects are included, and crucially, we determine the region where successful leptogenesis can be probed through gravitational-wave observations in upcoming experiments such as LISA and Einstein Telescope. Importantly, we find that flavour effects rescue regions of the parameter space that are ruled out due to current CMB or gravitational wave measurements.

Figures (18)

• Figure 1: Schematic overview linking $U(1)_{B-L}$ symmetry breaking, neutrino mass generation, baryogenesis, cosmic strings and gravitational waves. The spontaneous breaking of the global $U(1)_{B-L}$ symmetry generates Majorana masses for right-handed neutrinos and simultaneously produces a network of cosmic strings. The heavy neutrinos yield light active neutrino masses via the Type-I seesaw and then also generates the Baryon Asymmetry of the Universe (BAU) through CP-violating decays. Meanwhile, the cosmic-string network evolves and sources a stochastic gravitational-wave background (GWB).
• Figure 2: The GW spectral shapes for local strings (left panel) and global strings (right panel) are shown. $\eta$ denotes vev $v_{\rm B-L}$ here.
• Figure 3: Feynman diagrams contributing to the CP asymmetry: (a) tree-level, (b) self-energy, and (c) vertex diagrams.
• Figure 4: Benchmark result. The parameters are $M_{\phi} = 10^{10}$ GeV, $y_1 = 10^{-5}$ and $M_1=1.74\times 10^8\rm\ GeV$. We take a very small effective neutrino mass $\tilde{m}_1=10^{-6}\rm\ eV$ to ensure we are in the weak washout regime, the efficiency factor is unity in this benchmark. Left: Normalised abundances of the symmetry breaking scalar $\phi$ and right-handed neutrino. Right: The baryon asymmetry. This shows with a $U(1)_{\rm B-L}$ symmetry thermal leptogenesis can be achieved at mass range $\mathcal{O}(10^8)\rm\ GeV$, nearly an order of magnitude below the conventional Davidson-Ibarra bound.
• Figure 5: Efficiency factor $\kappa$ as a function of the effective neutrino mass $\tilde{m}_1$ for different values of the right-handed neutrino mass $M_1$. The fixed parameters are $M_{\phi} = 2\times 10^{12}\,\text{GeV}$ and $y = 10^{-4}$. For small $\tilde{m}_1$, the efficiency saturates to unity, while at larger values washout effects suppress $\kappa$ more strongly, with the onset of suppression depending on $M_1$. Deviation from the weak washout regime, and therefore the point at which we need to consider flavour effevcts occurs around $\tilde{m}_1 \approx 10^{-4.5}\,\text{GeV}$. This means our analytical bounds are valid for $\tilde{m}_1\lesssim 10^{-4.5}\rm\ eV$.