Abstract
We find that spontaneously broken parity (P) or left-right symmetry stabilizes dark matter in a beautiful way. If dark matter has a non-real intrinsic parity \pm i (e.g. Majorana fermions), parity can ensure that it cannot decay to all normal particles with real intrinsic parities. However if Majorana couplings are absent either in the Lepton or the dark sector, P symmetry can be redefined to remove relative non-real intrinsic phases. It is therefore predicted that neutrinos and dark matter fermions must have Majorana masses if dark matter is stable due to parity. We also consider vectorlike doublet fermions with intrinsic parity \pm i. Strong CP problem is solved by additionally imposing CP. Leptonic CP phases vanish at the tree level in the minimal strong CP solving model, which is a testable prediction. Experimentally if leptonic CP phases are not found (they are found to be consistent with 0 or \pi) it can be evidence for the type of models in this work where CP is spontaneously or softly broken and there is also a second hidden or softly broken symmetry such as P, Z_2 or Z_4. However leptonic CP violation can be present in closely related or some non-minimal versions of these models.
Highlights
Astronomical observations of galactic rotation curves [1] and velocity distribution of galaxies in clusters [2], smallness of anisotropies in the Cosmic Microwave Background radiation [3], and in a striking manner the Bullet Cluster [4], have all provided significant evidence that there is 5 times more matter in the universe that interacts gravitationally than is visible
We predict that if dark matter is stable due to parity, there must be a relative purely imaginary intrinsic parity phase, and Majorana masses must exist both for neutrinos and for neutral X -particles
Dark matter can be matter with a relative purely imaginary intrinsic parity phase that cannot be removed through field or parity symmetry redefinitions
Summary
Astronomical observations of galactic rotation curves [1] and velocity distribution of galaxies in clusters [2], smallness of anisotropies in the Cosmic Microwave Background radiation [3], and in a striking manner the Bullet Cluster [4], have all provided significant evidence that there is 5 times more matter in the universe that interacts gravitationally than is visible. 2 we provide a quantum mechanical argument to show that if there are relative non-real intrinsic parity phases, P can stabilize dark matter though it is spontaneously broken. 5 we show that if the Lagranigain is invariant under both discrete space-time symmetries P and CP, we can simultaneously solve the strong CP problem, have stable dark matter, and predict the absence of leptonic CP violation without requiring any other symmetry. Due to the presence of Majorana terms (couplings that give rise to Majorana masses), along with all the usual terms consistent with parity and gauge symmetry, there is not enough symmetry to remove the purely imaginary relative intrinsic parity phase by P redefinitions In this case, as shown in a basis independent manner,.
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