Differential cross section w.r.t rapidity

[neu]

I'm extracting data from a Monte Carlo sim. and i need to extract the differential cross-sections of the resultant protons and neutrons in momentum and rapidity space.

ie
$$\frac{d\sigma}{dy}$$ ; $$\frac{d\sigma}{dp}$$ and $$\frac{d^2\sigma}{dydp}$$

where I know the values of y and p (magnitude).

but how do I do it?

My attempts centre around $$\int{dy\frac{d\sigma}{dy}}=\sigma=\frac{Rate}{Luminosity}$$

I know its simple but I'm confused

 

[Timo]

Just out of interest: Which MC sim and what process? Generally: Could you just create a large number of events, extract the momenta and rapidities from the events, fill the values into a histogram and normalize to the total cross-section?

 

[neu]

It's a Pythia MC sim of proton-antiproton collision.

Is this what you meant?
effectively $$\frac{d\sigma}{dp}=\frac{\sigma_{total}}{p}$$ ?

as

$$\sigma_{total}=\int{dp\frac{d\sigma}{dp}}=\int{dy\frac{d\sigma}{dy}}$$

so in that case $$\frac{d^{2}\sigma}{dydp}=\frac{d\sigma}{dy}\frac{d\sigma}{dp}=\frac{\sigma_{total}^{2}}{yp}$$

This is what i have done but I have little confidence in my reasoning.

 

[Norman]

Uh... you might want to have another look at your 1st semester calculus book.

 

[neu]

I know I've buggered it up. I'm not bad at calculus, but I have a lot of trouble with the seemingly "intuitive" steps like this and I get stuck in a rut.

could you just point me in the right direction?

 

[Norman]

$$\frac{d\sigma}{dp}\approx \frac{\Delta \sigma}{\Delta p}$$

I believe what Timo was trying to explain was that. With the events normalized in such a way that they represent cross sections.

So, if you can get the rapidity and momentum out of the events somehow, make a histogram with that plots each event for a given rapidity (or momentum) and use the above once you have normalized so that the events correlate to the cross section.

 

[neu]

I'm sorry I not quite getting it. I have obtained the momentum and rapidity distributions from the sim ie p versus number of events at p.

So what am I normalising? I don't understand. I only know the total cross section not $$\Delta\sigma$$

could you be more explicit?