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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>C</a:mi><a:mi>P</a:mi></a:math> 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>C</c:mi><c:mi>P</c:mi></c:math> problem.