SMART U(1)$$_X$$: standard model with axion, right handed neutrinos, two Higgs doublets and U(1)$$_X$$ gauge symmetry
Abstract To address five fundamental shortcomings of the Standard Model (SM) of particle physics and cosmology, we propose a phenomenologically viable framework based on a $$U(1)_X \times U(1)_{PQ}$$ U ( 1 ) X × U ( 1 ) PQ extension of the SM, that we call “SMART U(1) $$_X$$ X ”. The $$U(1)_X$$ U ( 1 ) X gauge symmetry is a well-known generalization of the $$U(1)_{B-L}$$ U ( 1 ) B - L symmetry and $$U(1)_{PQ}$$ U ( 1 ) PQ is the global Peccei–Quinn (PQ) symmetry. Three right handed neutrinos are added to cancel $$U(1)_X$$ U ( 1 ) X related anomalies, and they play a crucial role in understanding the observed neutrino oscillations and explaining the observed baryon asymmetry in the universe via leptogenesis. Implementation of PQ symmetry helps resolve the strong CP problem and also provides axion as a compelling dark matter (DM) candidate. The $$U(1)_X$$ U ( 1 ) X gauge symmetry enables us to implement the inflection-point inflation scenario with $$H_{inf} \lesssim 2 \times 10^{7}$$ H inf ≲ 2 × 10 7 GeV, where $$H_{inf}$$ H inf is the value of Hubble parameter during inflation. This is crucial to overcome a potential axion domain wall problem as well as the axion isocurvature problem. The SMART U(1) $$_X$$ X framework can be successfully implemented in the presence of SU (5) grand unification, as we briefly show.