Connecting pseudo-Nambu-Goldstone dark matter with pseudo-Dirac neutrinos in a left-right symmetry model

Stringent constraints from the dark matter (DM) direct detection experiments can be naturally evaded for a pseudo-Nambu-Goldstone boson (pNGB) DM. We propose a realization of pNGB DM in the context of a left-right symmetric model, wherein the neutrinos are pseudo-Dirac in nature. The Dirac mass term for neutrinos arises from two-loop quantum corrections, whereas the Majorana mass terms are generated from Planck-induced corrections. This class of model also provides a parity solution to the strong CP problem without the need for an axion. We show an interesting correlation between the lifetime of the DM and the mass-squared differences between active and sterile neutrinos while maintaining a solution to the strong CP problem.