content_image/364586.jpg content_image/364584.jpg content_image/364588.jpg content_image/364590.jpg content_image/364592.jpg content_image/364595.jpg
revealing form. As a first step towards this, we note that the spin vector may be expressed as 

Using this and Eq. (10), we write 

with 

<img src='content_image/364586.jpg'>

<img src='content_image/364584.jpg'>

<img src='content_image/364588.jpg'>

Note that for m$_{ν}$ << E$_{ν}$ we have 

<img src='content_image/364590.jpg'>

We now evaluate the traces given in Eqs. (5) and (6) and the contraction N $^{µν}$E$_{µν}$ is given by 

<img src='content_image/364592.jpg'>

where g e V = − 1 2 + 2 sin $^{2}$θ$_{W}$ and g e A = − 1 $_{2}$. From this expression and Eqs. (12) and (14) above, we see that the amplitude of transition vanishes for massless neutrino, as expected. Furthermore, Eq. (15) is taken as the usual weak pair production amplitude with the replacement K$_{i}$ → k$_{i}$ . 

From Eqs. (4) and (15) the explicit form for the squared transition amplitude is 

<img src='content_image/364595.jpg'>

