Gravitational footprints of massive neutrinos and lepton number breaking

We investigate the production of primordial Gravitational Waves (GWs) arising from First Order Phase Transitions (FOPTs) associated to neutrino mass generation in the context of type-I and inverse seesaw schemes. We examine both “high-scale” as well as “low-scale” variants, with either explicit or spontaneously broken lepton number symmetry U(1) in the neutrino sector. In the latter case, a pseudo-Goldstone majoron-like boson may provide a candidate for cosmological dark matter. We find that schemes with softly-broken U(1) and with single Higgs-doublet scalar sector lead to either no FOPTs or too weak FOPTs, precluding the detectability of GWs in present or near future measurements. Nevertheless, we found that, in the majoron-like seesaw scheme with spontaneously broken U(1) at finite temperatures, one can have strong FOPTs and non-trivial primordial GW spectra which can fall well within the frequency and amplitude sensitivity of upcoming experiments, including LISA, BBO and u-DECIGO. However, GWs observability clashes with invisible Higgs decay constraints from the LHC. A simple and consistent fix is to assume the majoron-like mass to lie above the Higgs-decay kinematical threshold. We also found that the majoron-like variant of the low-scale seesaw mechanism implies a different GW spectrum than the one expected in the high-scale seesaw. This feature will be testable in future experiments. Our analysis shows that GWs can provide a new and complementary portal to test the neutrino mass generation mechanism.The work of R.P. was also sup-ported in part by The Ministry of Education, Youth and Sportsof the Czech Republic, project LT17018. The work of A.P.M. has been performed in the framework of COST Action CA16201 “Un-raveling new physics at the LHC through the precision frontier” (PARTICLEFACE). A.P.M.is supported by the Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT -Fun-dação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020 and by national funds (OE), through FCT, I.P., in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Law 57/2017, of July 19.A.P.M.is also supported by the Enabling Green E-science for the Square Kilometer Array Research Infras-tructure(ENGAGESKA), POCI-01-0145-FEDER-022217, and by the projects PTDC/FIS-PAR/31000/2017 and CERN/FIS-PAR/0027/2019. R.V. and J.W.F.V. are supported by the Spanish grants SEV-2014-0398 and FPA2017-85216-P (AEI/FEDER, UE), PROMETEO/2018/165 (Generalitat Valenciana) and the Spanish Red Consolider MultiDark FPA2017-90566-REDC