Pair Production and Angular Distribution of Helicity Flipped Neutrinos in a Left-Right Symmetric Model

We assume that a massive Dirac neutrino is characteized by two phenomenological parameters, a magnetic moment, and a charge radius, and we calculate the cross-section of the scattering $e^+e^-\to \nu \bar \nu$ in a left-right symmetric model. We also analyze the angular distribution of the neutrino (antineutrino) with respect to the original direction of the electron (positron) to different state of helicity of the neutrino. We find that the favored directions for the neutrino (antineutrino) with respect to the electron (positron) is forward $(\theta =0)$ and backward $(\theta= \pi)$, and is not very probable in the perpendicular direction $(\theta = \frac{\pi}{2})$. The calculation is for $\phi = -0.005$ and $M_{Z_2}=500$ $GeV$, parameters of the Left-Right symmetric model.