content_image/340976.jpg content_image/340978.jpg content_image/340979.jpg content_image/340977.jpg content_image/340980.jpg content_image/340981.jpg content_image/340982.jpg content_image/340983.jpg
<img src='content_image/340976.jpg'>

where φ is the mixing parameter of the LRSM [26–28], u and v are the usual Dirac spinors, and the electron and positron helicity indexes have been suppressed since they will be aver- aged over. We then write 

where 

<img src='content_image/340978.jpg'>

<img src='content_image/340979.jpg'>

<img src='content_image/340977.jpg'>

Here s$_{1}$ and s$_{2}$ are the spin four-vectors associated with the antineutrino and neutrino respectively, while m$_{ν}$ and m$_{e}$ are the neutrino and electron mass. These spin vectors satisfy the Lorentz invariant conditions 

and for a relativistic neutrino, the additional constraint 

holds, where 

<img src='content_image/340980.jpg'>

<img src='content_image/340981.jpg'>

<img src='content_image/340982.jpg'>

with ˆ k being a unit vector along the three-momentum of the neutrino. 

We now introduce two four-vectors associated with the neutrino pair 

<img src='content_image/340983.jpg'>

In conjunction with the properties given in Eqs. (7) and (8), these will allow us to write the amplitude squared for the process under consideration in a compact and physically 

