Abstract
We present a three-loop model of neutrino mass whose most-general Lagrangian possesses a softly-broken accidental $Z_2$ symmetry. In the limit that a single parameter vanishes, $\lambda\rightarrow0$, the $Z_2$ symmetry becomes exact and the model contains a stable dark-matter candidate. However, even for finite $\lambda\ll1$, long-lived dark matter is possible, giving a unified solution to the neutrino mass and dark matter problems that does not invoke a new symmetry. Taken purely as a neutrino mass model, the new physics can be at the TeV scale. When dark matter is incorporated, however, only a singlet scalar can remain this light, though the dark matter can be tested in direct-detection experiments.
Highlights
Would otherwise dominate the loop mass, and it gives a stable particle that is taken as the DM
We present a three-loop model of neutrino mass whose most-general Lagrangian possesses a softly-broken accidental Z2 symmetry
We presented a three-loop model of neutrino mass whose most-general Lagrangian contains a softly-broken accidental Z2 symmetry
Summary
We extend the SM to include a charged scalar singlet, S+ ∼ (1, 1, 2), a complex scalar quintuplet, φ ∼ (1, 5, 2), and a real fermion quintuplet, F ∼ (1, 5, 0). We will use MF ≡ M1 for the DM mass In terms of these fields the Yukawa couplings involving the new fermions are written as giα (Fi)abcd φabcd eαR = giα φ+++Fi++ PR eα + φ++Fi+ PR eα +φ+Fi0 PR eα − φ0 (eα)c PRFi+ + φ−(eα)c PR Fi++ ,. Before turning to neutrino mass we would like to discuss a few features of the model To this end, let us briefly consider the theory in the absence of the singlet S. We note that the fermions F ∼ (1, 5, 0) employed in this model were studied in a number of other contexts They allow a generalization of the Type-III seesaw mechanism [44] that achieves neutrino mass via a low-energy effective operator of mass-dimension d = 9 [42, 45, 46]. For related phenomenological studies see refs. [49, 50]
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