Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Cross section

  1. Sep 18, 2012 #1

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

    I think this must be trivial...

  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:
    \frac{d N_{\mathrm{reactons}}}{d t} = K \, \mathcal{L}
    where [itex]\mathcal{L}[/itex] is the luminosity of the incident beam, and:
    K = N_{\mathrm{scatters}} \, \sigma
    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


    User Avatar
    2017 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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook