2 -> 2 hadronic production cross section

[Safinaz]

Hi all,

Could anyone help for calculating the hadronc production cross section for example for
tree level : p p > t t~ process, I try to calculate, but the first problem I meet is a negative value of the matrix element amplitude (and so cross section ) and a negative $\hat{t}$ Mandelstam variable :

I define $\hat{t}$ : $- \frac{\hat{s}}{2} (1 - \beta \cos \theta) + m^2_{t}$
with: $\beta =\sqrt{1- \frac{4m_{t}^2}{\hat{s}}}$, $\hat{s} = x1 x2 s \sim x^2 s (for x1=x2)$, s = 14000^2 and ## $tree level (partonic) diff. cross section :$ \frac{d\hat{\sigma}}{d\cos\theta} = \frac{\beta}{16\pi \hat{s}}~ | M|^2 ##So did I defined every thing consistently , any suggestions ..
Do you know any good refrence or exercises about that ..Regards,
Safinaz

 

[ChrisVer]

of course you must be doing something wrong... Be careful, when you compute the amplitude squared, you write:
\left|M\right|^{2}= M^{+}M with + I denote the dager/hermitian conjugate.
So it's practically impossible (even if you define something "wrong" in your procedure) to get negative value out of it...Something you are doing wrong in your calculations.

Also please give me to understand better what you did... Did you work with dirac spinors for example?