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Cross section

  1. Sep 18, 2012 #1
    Hello,

    How can I convert the number of events + the luminosity in a cross section?

    I think this must be trivial...

    thanks..
     
  2. jcsd
  3. Sep 18, 2012 #2
    By dimensional analysis if you know the dimensions of each of the quantities involved.
     
  4. Sep 18, 2012 #3
    ah..lol..I think it's just...events = sigma * luminosity...right?
     
  5. Sep 18, 2012 #4
    Ok, how did you conclude that?
     
  6. Sep 18, 2012 #5
    hm?...I wanted to get a cross section limit for monojet signals...and I always found only the luminosity and the events...and event has no dimension..luminosity is inverse barn and XS is barn..so..if I really only need those paramaters..then it's trivial...I thought maybe I also need sth else...
     
  7. Sep 18, 2012 #6
    Usually luminosity is a flux density, with dimension L-2 T-1, instead of dimension L-2. Thus, what we get as a result proportional to luminosity is not # of events, but, instead, an event rate (# events per unit time) with a dimension T-2.

    The proportionality constant must have a dimension L2. However, the proportionality constant should be proportional to the number of scatterers, which is dimensionless. The proportionality constant corresponding to ONE scatterer is a characteristic of the dynamics of the scattering event, and is customarily referred to as a cross-section.

    What I tried to say could be summarized as:
    [tex]
    \frac{d N_{\mathrm{reactons}}}{d t} = K \, \mathcal{L}
    [/tex]
    where [itex]\mathcal{L}[/itex] is the luminosity of the incident beam, and:
    [tex]
    K = N_{\mathrm{scatters}} \, \sigma
    [/tex]
    where [itex] N_{\mathrm{scatters}}[/itex] is the total number of scatterers in the target, and [itex]\sigma[/itex] is the total scattering cross-section for a single scattering event.
     
  8. Sep 19, 2012 #7
    Thanks a lot...
    but I think in the paper I have read they have used the integrated luminosity...because they have used exactly the dimension "inverse barn"...
     
  9. Sep 19, 2012 #8

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    "Integrated luminosity" is sometimes just called "luminosity" - wrong, but shorter, and fine for talks/meetings and so on, where it is clear what is meant. In papers and other publications, it should be called "integrated luminosity" everywhere.
     
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