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

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.

Comments: Version 2: Minor corrections following acceptance for JHEP publication, inclusion of additional references, and correction of a typo in the title