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Differential cross section w.r.t rapidity

  1. Oct 26, 2007 #1

    neu

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    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
    [tex]\frac{d\sigma}{dy}[/tex] ; [tex]\frac{d\sigma}{dp}[/tex] and [tex]\frac{d^2\sigma}{dydp}[/tex]

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

    but how do I do it?

    My attempts centre around [tex]\int{dy\frac{d\sigma}{dy}}=\sigma=\frac{Rate}{Luminosity}[/tex]

    I know its simple but I'm confused
     
  2. jcsd
  3. Oct 26, 2007 #2
    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?
     
  4. Oct 27, 2007 #3

    neu

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

    Is this what you meant?
    effectively [tex]\frac{d\sigma}{dp}=\frac{\sigma_{total}}{p}[/tex] ???

    as

    [tex]\sigma_{total}=\int{dp\frac{d\sigma}{dp}}=\int{dy\frac{d\sigma}{dy}}[/tex]

    so in that case [tex]\frac{d^{2}\sigma}{dydp}=\frac{d\sigma}{dy}\frac{d\sigma}{dp}=\frac{\sigma_{total}^{2}}{yp}[/tex]

    This is what i have done but I have little confidence in my reasoning.
     
  5. Oct 27, 2007 #4
    Uh... you might want to have another look at your 1st semester calculus book.
     
  6. Oct 27, 2007 #5

    neu

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    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?
     
  7. Oct 27, 2007 #6
    [tex]\frac{d\sigma}{dp}\approx \frac{\Delta \sigma}{\Delta p}[/tex]

    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.
     
  8. Oct 27, 2007 #7

    neu

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    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 [tex]\Delta\sigma[/tex]

    could you be more explicit?
     
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