Planck scale origin of nonzero ${\theta }_{13}$ and super-WIMP dark matter

We study a discrete flavor symmetric scenario for neutrino mass and dark matter under the circumstances where such global discrete symmetries can be explicitly broken at the Planck scale, possibly by gravitational effects. Such explicit breaking of discrete symmetries mimic as Planck suppressed operators in the model, which can have nontrivial consequences for neutrino and dark matter sectors. In particular, we study a flavor symmetric model which, at a renormalizable level, gives rise to tri-bimaximal type neutrino mixing with vanishing reactor mixing angle ${\theta }_{13}=0$, a stable inert scalar doublet behaving like a weakly interacting massive particle (WIMP) and a stable singlet inert fermion that does not interact with any other particles. The introduction of Planck suppressed operators that explicitly break the discrete symmetries can give rise to the generation of nonzero ${\theta }_{13}$ in agreement with neutrino data and also open up decay channels of inert scalar doublet into singlet neutral inert fermions leading to the realization of the super-WIMP dark matter scenario. We show that the correct neutrino phenomenology can be obtained in this model while discussing three distinct realizations of the super-WIMP dark matter scenario.

Figure 1

$y_1$ vs $y_2$ and $y_1$ vs $y_3$ satisfying correct neutrino data for normal hierarchy.

Figure 2

Left panel represents $\alpha$ vs ${\varphi }_{ba}$ satisfying correct neutrino data. Right panel represents predicted regions for the Majorana phases ${\alpha }_{21}$ and ${\alpha }_{31}$ for normal hierarchy.

Figure 3

Predictions for lightest neutrino mass ($m_1$ for normal hierarchy) vs sum of absolute neutrino masses (left panel). Predictions for lightest neutrino mass ($m_1$ for normal hierarchy) vs effective mass parameter for neutrinoless double beta decay (right panel).

Figure 4

$y_1$ vs $y_2$ and $y_1$ vs $y_3$ satisfying correct neutrino data for inverted hierarchy.

Figure 5

Left panel represents $\alpha$ vs ${\varphi }_{ba}$ satisfying the correct neutrino data. Right panel represents the predicted regions for the Majorana phases ${\alpha }_{21}$ and ${\alpha }_{31}$ for inverted hierarchy.

Figure 6

Predictions for lightest neutrino mass ($m_3$ for inverted hierarchy) vs sum of absolute neutrino masses (left panel). Predictions for lightest neutrino mass ($m_3$ for inverted hierarchy) vs effective mass parameter for neutrinoless double beta decay (right panel).

Figure 7

The evolution of $\eta ,\psi \equiv \mathrm{DM}$ number density and radiation energy density with time for case I.

Figure 8

Comparison of ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2$ with respect to different model parameters for case I.

Figure 9

Scan of model parameters for case I so that correct DM relic abundance is obtained.

Figure 10

Comparison of ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2$ with respect to different model parameters for case II.

Figure 11

Scan of model parameters for case II so that correct DM relic abundance is obtained.

Figure 12

Comparison of ${\mathrm{\Omega }}_{\mathrm{DM}}{h}^2$ with respect to different model parameters for case III.

Figure 13

Lifetime of mother particle $\eta$ as a function of effective Yukawa coupling $Y_{\mathrm{eff}}$ for its two body decay into dark matter.