# Cross section

## Main Question or Discussion Point

Hello,

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

I think this must be trivial...

thanks..

Related High Energy, Nuclear, Particle Physics News on Phys.org
By dimensional analysis if you know the dimensions of each of the quantities involved.

ah..lol..I think it's just...events = sigma * luminosity...right?

Ok, how did you conclude that?

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...

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 $\mathcal{L}$ is the luminosity of the incident beam, and:
$$K = N_{\mathrm{scatters}} \, \sigma$$
where $N_{\mathrm{scatters}}$ is the total number of scatterers in the target, and $\sigma$ is the total scattering cross-section for a single scattering event.

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"...

mfb
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.