Strong CP Problem, Neutrino Masses and the 750 GeV Diphoton Resonance

We present an $SU(3)^{}_{c}\times SU(2)^{}_{L}\times SU(2)^{}_{R}\times U(1)_{L}^{}\times U(1)_{R}^{}\rightarrow SU(3)^{}_{c}\times SU(2)^{}_{L}\times SU(2)^{}_{R}\times U(1)^{}_{B-L}$ left-right symmetric model with a discrete parity symmetry to realize a universal seesaw scenario. The model can simultaneously solve the strong CP problem without resorting to the unobserved axion and explain the 750 GeV diphoton resonance reported recently by the ATLAS and CMS collaborations at the LHC. Owing to large suppressions in the two-loop induced Dirac mass terms, the Majorana mass matrices of left- and right-handed neutrinos naturally share the same structure. That allows us to quantitatively study the neutrinoless double beta decay induced by the right-handed currents.