# Mass vs cross-section studies

Let's assume we have a event generator like "Pythia", and from that I have collected four momentum of a certain lepton production.

the leptons are from excited gamma state. And the excited gamma state can be produced from head to head proton scattering.

My question is that how experimental physicist do the scattering measurement, since I have seen a lot of plots like mass vs cross-sections plots, like below. And why this kind of plot is very important? Is it because to look at certain mass distributions in a given energy range?

If that's true we can also plot Mass vs Events no plot. How this two are different and correlated.

I would appreciate if you have any example macro for this kind of plot.

• A couple of nomenclature comments. First it is usual to say you plot [quantity on the vertical axis] [versus | against | as-a-function-of] [quantity on the horizontal axis], so the plot you have included is cross-section against the mass of the pair, rather than "mass vs cross-sections". Secondly plots of the number of events against some measured quantity may be called "histograms", so that when you say "Mass vs Events no plot" you could say "a histogram of the pair masses". – dmckee Oct 14 '18 at 19:50

In the case that you exhibit, the process can proceed through two possible (and experimentally indistinguishable) channels: photons and $$Z^0$$ weak bosons. Both processes are stronger when the mass of the pair is near the on-shell mass of the carrier boson, so the peak you see in the graph tells you the mass of the $$Z^0$$ (the mass of the photon is zero) while the sloping background is attributable (in aggregate; you can't tell them apart on an event-by-event basis) to the photon channel. That makes the plot enormously important for this measurement.
Protons are composite objects, so when you get a photon of $$Z^0$$ even it generally comes from the interaction of two partons (either a quark and an anti-quark or two gluons), but each of those particles can have a momentum relative the CoM of it's host particle. So unlike the case of a lepton collider, you get a broad range of Mandelstam $$s$$ out for each configuration of the beam, but they aren't evenly distributed. So the histogram of pair-masses folds together the underlying event cross-section and the relative momentum distribution of the partons.
Both can be used to say "See the peak here? That's the $$Z$$ mass.", but the histogram is easier to produce from the raw data while the cross-section plot exhibits a more fundamental quantity (having laboriously deconvolved the parton-distribution-functions from the data).