Seesaw scale discrete dark matter and two-zero texture Majorana neutrino mass matrices

In this paper we present a scenario where the stability of dark matter and the phenomenology of neutrinos are related by the spontaneous breaking of a non-Abelian flavor symmetry ($A_4$). In this scenario the breaking is done at the seesaw scale, in such a way that what remains of the flavor symmetry is a $Z_2$ symmetry, which stabilizes the dark matter. We have proposed two models based on this idea, for which we have calculated their neutrino mass matrices achieving two-zero texture in both cases. Accordingly, we have updated this two-zero texture phenomenology finding an interesting correlation between the reactor mixing angle and the sum of the light neutrino masses. We also have a correlation between the lightest neutrino mass and the neutrinoless double beta decay effective mass, obtaining a lower bound for the effective mass within the region of the nearly future experimental sensitivities.

Figure 1

Correlation between ${\sin }^2{\theta }_{23}$ and the sum of the light neutrino masses, $\sum m_{\nu }$, in model A ($B_3$) on the left and model B ($B_4$) on the right, for NH (IH) in magenta (cyan). The horizontal red (blue) shaded region is the $1\sigma$ in ${\sin }^2{\theta }_{23}$ for NH (IH). The red (blue) horizontal dashed line is the best fit value in NH (IH), and the doted red line is the value of local minimum in NH appearing in the data analysis used. The data was taken from [13]. The vertical gray shaded region is disfavored by the current Planck data [34].

Figure 2

Effective $0\nu \beta \beta$ parameter $|m_{ee}|$ versus the lightest neutrino mass $m_{{\nu }_{\text{light}}}$ in model A (B) on the left (right). In both models $m_{{\nu }_{\text{light}}}$ is $m_1(m_3)$ for NH (IH). The model allowed regions for NH are in magenta (dark magenta) for the $1\sigma$ ($3\sigma$) atmospheric mixing angle region and for IH in cyan (dark cyan) for the $1\sigma$ ($3\sigma$) on the atmospheric mixing angle region from [13]. The yellow (green) band correspond to the “flavor-generic” inverse (normal) hierarchy neutrino spectra for $3\sigma$. The horizontal red shaded region is the current experimental limit on $0\nu \beta \beta$, and the red (blue) horizontal (vertical) lines are the forthcoming experimental sensitivity on $|m_{ee}|$ ($m_{{\nu }_{\text{light}}}$), see [35, 36, 37, 38, 39, 40]. The vertical blue shaded regions are disfavored by the current Planck data [34].

Figure 3

Correlation between ${\sin }^2{\theta }_{23}$ and the sum of the light neutrino masses, $\sum m_{\nu }$, in model A ($B_3$) on the left and model B ($B_4$) on the right, for NH (IH) in magenta (cyan). The red (blue) horizontal dashed line is the best fit value in NH (IH). The data was taken from [14]. The vertical gray shaded region is disfavored by the current Planck data [34].

Figure 4

Effective $0\nu \beta \beta$ parameter $|m_{ee}|$ versus the lightest neutrino mass $m_{{\nu }_{\text{light}}}$ in model A (B) on the (right). In both models $m_{{\nu }_{\text{light}}}$ is $m_1(m_3)$ for NH (IH). The model allowed regions for NH is in magenta (dark magenta) for the $1\sigma$ ($3\sigma$) for the atmospheric mixing angle and for IH in cyan (dark cyan) for the $1\sigma$ ($3\sigma$) for the atmospheric mixing angle region from [14]. The horizontal blue (red) shaded region is the $1\sigma$ in ${\sin }^2{\theta }_{23}$ for IH (NH). The yellow (green) band correspond to the $3\sigma$ “flavor-generic” inverse (normal) hierarchy neutrino spectra. The horizontal red shaded region is the current experimental limit on $0\nu \beta \beta$, and the red (blue) horizontal (vertical) lines are the forthcoming experimental sensitivity on $|m_{ee}|$ ($m_{{\nu }_{\text{light}}}$), see [35, 36, 37, 38, 39, 40]. The vertical blue shaded regions are disfavored by the current Planck data [34].

Figure 5

Correlation between ${\sin }^2{\theta }_{23}$ and the sum of the light neutrino masses, $\sum m_{\nu }$, in model A ($B_3$) on the and model B ($B_4$) on the right, for NH (IH) in magenta (cyan). The horizontal red (blue) shaded regions are the $1\sigma$ in ${\sin }^2{\theta }_{23}$ for NH (IH). The case for IH has two favored $1\sigma$ regions according to the data used. The red (blue) horizontal dashed line is the best fit value in NH (IH). The data was taken from [15]. The vertical gray shaded region is disfavored by the current Planck data [34].

Figure 6

Effective $0\nu \beta \beta$ parameter $|m_{ee}|$ versus the lightest neutrino mass $m_{{\nu }_{\text{light}}}$ in model A (B) on the (right). Regions for NH is in magenta (dark magenta) for the $1\sigma$ ($3\sigma$) atmospheric mixing angle region and the IH in cyan (dark cyan) for the $1\sigma$ ($3\sigma$) for the atmospheric mixing angle region from [15]. The yellow (green) band correspond to the $3\sigma$ “flavor-generic” inverse (normal) hierarchy neutrino spectra. The horizontal red shaded region is the current experimental limit on $0\nu \beta \beta$, and the red (blue) horizontal (vertical) lines are the forthcoming experimental sensitivity on $|m_{ee}|$ ($m_{{\nu }_{\text{light}}}$), see [35, 36, 37, 38, 39, 40]. The vertical blue shaded regions are disfavored by the current Planck data [34].