Matrix and cross section of the Xf -> Xf process

[Homer_J]

Homework Statement:

Find the matrix and cross section of neutralino fermion to neutralino fermion scattering process

Relevant Equations:

\xi f -> \xi f

The attempt at a solution follows as an attachment. If you are only interested in the solution without the derivation, look at page 1 and page 9.

 

[berkeman]

Welcome to the PF.

Unfortunately, your hand-written, scanned work is not very readable. What class is this for, and which year in university?

 

[berkeman]

BTW, there is a link to the PF LaTeX tutorial at the lower left corner of the Reply/Edit window at the bottom of your thread. It's a pretty easy tutorial to get you going typing math equations using LaTeX.

 

[Homer_J]

Thanks. But there is no way I can fit the 9 pages on this forum. However, I can write down the matrix and cross section found. The course is quantum field theory.

Welcome to the PF.

Unfortunately, your hand-written, scanned work is not very readable. What class is this for, and which year in university?

 

[Homer_J]

$$ M = -((g_Z^2)/(q^2 - m^2) g_/uv) [\bar{u}(p3)\gamma^u \frac{1}{2} (C_V^X - C_A^X \gamma^5) u(p1)] [\bar{u}(p4)\gamma^v \frac{1}{2}(C_V^f - C_A^f \gamma^5)u(p2)]$$

 

[Homer_J]

$$ \sigma = \frac{1}{192\pi} \frac{-g_Z^4}{(s-m_Z^2)^2 + m_Z^2 \Gamma^2)} ((C_V^X)^2 + (C_A^X)^2 + (C_V^f)^2 + (C_A^f)^2) $$