Texture zeros of low-energy Majorana neutrino mass matrix in $3+1$ scheme

In this work we revisit the zero textures in low energy Majorana neutrino mass matrix when the active neutrino sector is extended by a light sterile neutrino in the eV scale, i.e., the $3+1$ scheme. In $3+1$ scenario, the low energy neutrino mass matrix ($m_{\nu }$) has ten independent elements. Thus in principle one can have minimum one-zero texture to maximum ten-zero texture. We summarize the previous results of one, two, three, and four-zero textures which already exist in the literature and present our new results on five-zero textures. In our analysis we find that among six possible five-zero textures, only one is allowed by the present data. We discuss possible theoretical model which can explain the origin of the allowed five-zero texture and discuss other possible implications of such a scenario. Our results also concludes that in $3+1$ scheme, one cannot have more than five-zeros in $m_{\nu }$.

Figure 1

Correlation plots of class $B$ in NH. $m_0$ is the lowest neutrino mass which is $m_1$ in NH.

Figure 2

Breaking of $\mu -\tau$ symmetry in the active-sterile sector and generation of nonzero ${\theta }_{13}$.

Figure 3

Correlation plots between muon ($g-2$) and the model parameters.