Gravitational Wave Spectral Shapes as a probe of Long Lived Right-handed Neutrinos, Leptogenesis and Dark Matter: Gobal versus Local B-L Cosmic Strings

TL;DR

This work links the spontaneous breaking of $U(1)_{B-L}$ to a network of cosmic strings and to the heavy RHN states responsible for neutrino masses, leptogenesis, and potentially dark matter. Through analytic and numerical Boltzmann analyses, it shows that an early matter-dominated epoch is viable only for Type I seesaw, and derives how the onset and duration depend on the RHN mass $M$ and effective neutrino mass $\tilde{m}$. The resulting modification of the gravitational-wave background from cosmic strings—including breaks and knees in the spectrum—provides a direct observational handle on $M$ and $\tilde{m}$, with detectors like LISA and ET capable of probing wide ranges of RHN scales. The study also maps the interplay with baryogenesis and dark matter production, showing how $f_{\rm dom}$ and $f_{\rm brk}$ encode leptogenesis and DM outcomes, and highlighting scenarios where joint GW, collider, and astrophysical probes can test the shared origin in the $B-L$ sector.

Abstract

The scale of the seesaw mechanism is typically much larger than the electroweak scale. This hierarchy can be naturally explained by $U(1)_{B-L}$ symmetry, which after spontaneous symmetry breaking, simultaneously generates Majorana masses for neutrinos and produces a network of cosmic strings. Such strings generate a gravitational wave (GW) spectrum which is expected to be almost uniform in frequency unless there is a departure from the usual early radiation domination. We explore this possibility in Type I, II and III seesaw frameworks, finding that only for Type-I, long-lived right-handed neutrinos (RHN) may provide a period of early matter domination for parts of the parameter space, even if they are thermally produced. Such a period leaves distinctive imprints in the GW spectrum in the form of characteristic breaks and a knee feature, arising due to the end and start of the periods of RHN domination. These features, if detected, directly determine the mass $M$, and effective neutrino mass $\tilde m$ of the dominating RHN. We find that GW detectors like LISA and ET could probe RHN masses in the range $M\in[0.1,10^{9}]$ GeV and effective neutrino masses in the $\tilde m\in[10^{-10},10^{-8}]$ eV range. We investigate the phenomenological implications of long-lived right-handed neutrinos for both local and global $U(1)_{B-L}$ strings, focusing on dark matter production and leptogenesis. We map the viable and detectable parameter space for successful baryogenesis and asymmetric dark matter production from right-handed neutrino decays. We derive analytical and semi-analytical relations correlating the characteristic gravitational-wave frequencies to the neutrino parameters $\tilde m$ and $M$, as well as to the relic abundances of dark matter and baryons.

Figures (22)

• Figure 1: The $U(1)_{B-L}$ symmetry breaking generates heavy seesaw states and an initial gravitational-wave background. These heavy states can induce a period of matter domination; in particular, only the Type-I seesaw, where the heavy seesaw state (the right-handed neutrino) dominates the energy density, can achieve such matter domination. This leads to a modified gravitational-wave background (GWB) spectral shape, while the subsequent decays of the right-handed neutrinos can explain the baryon asymmetry via leptogenesis or, alternatively and simultaneously, produce dark matter.
• Figure 2: Thermal production of right-handed neutrinos in global $U(1)_{B-L}$ model. The s-channel production of right-handed neutrinos proceeds through the exchange of the real scalar antiparticle $\phi^*$.
• Figure 3: Thermal Production of right-handed neutrinos via a $Z'$ mediator.
• Figure 4: Dominant $s$–channel processes mediated by the electroweak $Z$ boson: (a) production of scalar triplets $\Delta\Delta^\dagger$ in the type II seesaw, (b) production of fermion triplets $\Sigma\bar{\Sigma}$ in the type III seesaw.
• Figure 5: Left Panel: Energy density evolution for $\tilde{m}=10^{-10}\ \text{eV},\ M=10^9\ \text{GeV}$ showing how the right-handed neutrino comes to dominate the energy budget of the universe. Right Panel: effective equation of state $w(z)$ for a few effective neutrino mass values. $\rho_N$ becomes the dominant component of the energy budget at the vertical dashed line.