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 can not have more than five-zeros in $m_\nu$.