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Could any one 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