BISWAJOY BRAHMACHARI$^{1,4,*}$, SANDHYA CHOUBEY$^{2}$ and RABINDRA N MOHAPATRA$^{3}$

$^{1}$Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700 064, India

$^{2}$Department of Physics and Astronomy, University of Southampton,Highfield, Southampton SO17 1RJ, UK

$^{3}$Department of Physics and Astronomy, University of Maryland, College Park, MD 20742, USA

$^{4}$Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34100 Trieste, Italy

$^*$Email: biswajoy@theory.saha.ernet.in

Abstract. We investigate symmetries in Dirac and Majorana mass matrices of neutrinos in a three-generation scenario. We show that if we invoke $L_e+L_\mu-L_\tau \times S_{\rm 2R}$ symmetry, one combination of right-handed neutrino states remains massless which can be interpreted as a sterile neutrino. Next we consider a $SU(2)_{\rm L} \times U(1)_{Y} \times U(1)_{\rm R}$ gauge model and show how higher-dimensional operators can induce mixing between left- and right-handed states which explains solar, atmospheric and LSND experimental results.

Keywords. Sterile; neutrino; LSND.

PACS Nos 12.60.Fr; 11.30.Hv; 13.15.+g