SU(5) unification of two triplet seesaw and leptogenesis with dark matter and vacuum stability

We investigate unification prospects of two heavy scalar triplet extension of the standard model where, in the absence of any right-handed neutrino (RHN), type-II seesaw accounts for current oscillation data with hierarchical neutrino masses consistent with cosmological bounds and the lighter triplet decay explains baryon asymmetry of the Universe via leptogenesis. We note that the absence of RHNs in the fundamental fermion representations of SU(5) delineates its outstanding position compared to SO(10) (or $E_6$). In addition, SU(5) needs smaller scalar representations ${15}_{H1}\oplus {15}_{H2}$ compared to much larger representations ${126}_{H1}\oplus {126}_{H2}\subset$ SO(10) (or ${351}_{H1}^{\prime }\oplus {351}_{H2}^{\prime }\subset E_6$). We show how precision gauge coupling unification is achieved through SU(5) with the predictions of different sets of two heavy triplet masses which, besides being compatible with type-II seesaw, are also consistent with unflavoured or τ− flavoured leptogenesis predictions for baryon asymmetry of the Universe. In addition to an intermediate mass colour octet fermion, completion of precision gauge coupling unification is found to require essentially the presence of the well known weak triplet fermion $\Sigma (3,0,1)$ in its mass range $M_{\Sigma }\simeq O(500-3000)$ GeV out of which the dominant dark matter (DM) resonance mass $M_{\Sigma }\ge 2.4$ TeV is known to account for the observed cosmological relic density. The deficiency in relic density for the other class of lighter $M_{\Sigma }$ solutions allowed under indirect search constraints is circumvented by the introduction of a scalar singlet DM which could be as light as 62 GeV. A GUT ansatz is noted to ensure vacuum stability of the SM scalar potential for all types of unification solutions realised in this work. We discuss proton lifetime estimations for $p\to e^{+}{\pi }^0$ compatible with the present Hyper-Kamiokande bound as a function of an unknown mixing parameter in the model.