How to; polarized reaction ee--->WW

[moss]

I want to compute the polarized cross-section of $$ {e^{-}e^{+}\rightarrow W^{-}W^{+}} $$
but this reaction is chiral and only 2 input helicities are allowed while 9 out put combinations of W-boson helicities/polarization are possible. W(+-0) & W(+-0) are the possible polarization of W-bosons.

The Qs. I am given is that compute the above reaction in high-energy limit so I guess I have to compute the matrix-M but does it also mean to compute the cross-section??

Further;

1: I am having difficulty to understand that how a left-handed positron has a right-handed spinor
and a right handed electron has a left-handed spinor, they are mostly denoted as v(p) & u(p').

2: From the matrix element M how can I draw a graph between $$ {\frac{d}{dcos\theta}} $$ and $$ {cos\theta} $$. OR how can I show the energy dependence of this reaction in graph?

this is the almost the same problem as peskin & schroeder 21.1 and the graphs are 21.10 and 5.1 of the same book.

any hint is much appreciated.

 

[moss]

Okay, I got my Qs-1, actually I wrote wrong, only the spinor of anti-particle has opposite handedness and for the particle its the same handedness.
Some of the matrix-M are zero because of the orthogonality of the polarization vectors of the W-bosons.

Qs-2 still stand as how to draw the graph.
Any help??

 

[moss]

Okay, I have completed the complete polarized reaction and cross section of $$e^{-}e^{+}\rightarrow W^{-}W^{+}$$.
Anybody interested in this can download the pdf. or email me and I will mail you the pdf.