Cross section

Taking a closer look at LHC

Cross section (σ) is a measurement of the probability that an event occurs.

It´s measured in “barn” – 1 b = 10-24 cm2

The number of events per second ( Nev) for a specific result is got from:

Nevents/sec = Luminosity · Cross Section

Nevent/sec = L·σevent

It´s therefore easy to understand that luminosity is very important in order to consider the possibilities that an expected event can occur.

Since in the LHC the value of L is 100 times greater than that of LEP or Tevatron makes CERN a leader in this field.

The total proton-proton cross section at 7 TeV is approximately 110 mbarns. This total can be broken down in contributions from:
       inelastic = 60 mbarn 
      • single diffractive = 12 mbarn
      • elastic = 40 mbarn

The cross section from elastic scattering of the protons and diffractive events will not be seen by the detectors as it is only the inelastic scatterings that give rise to particles at sufficient high angles with respect to the beam axis.

Inelastic event rate at nominal luminosity is:

Nevent/sec = L·σ event

1034 x [(60x10-3)x10-24]= 600 million/second

With about 30 millions crosses/s:

600/30    20 inelastic events per crossing.

Let´s see an other example:

The cross section to get a 350 GeV Higgs Boson is 50 fb(femto-barn) via qq  ⇒ Zh 

So,    σ = (50·10-15)·10-24cm2        σ = 5·10-38 cm2

Nevent/sec =(1034(5·10-38)

 Nevents/sec = 5·10-4


Therefore there are 5·10-4 events per second in which this Higgs boson will be appearing(whether that kind of Higgs boson exists, obviously).

To understand this better we can calculate the inverse of that quantity,

t = 1/(5·10-4) = 2000 s            t = 33 minutes

So, every 33 minutes one Higgs particule should be appearing. Therefore, in ten hours-day work, 20 Higgs particules should be detected.

But thousands of billions of collisions will be produced in the detector in that time. The work of the computers is collosal.

The next figure shows de cross section Higgs production at LHC.

(Taken from Flip Tanedo,  An Idiosyncratic Introduction to the Higgs)


Let’s study a third exemple.

LHCb is the experiment dedicated to quark b physics at the LHC. Its primary goal is to look for indirect evidence of new physics in CP violation and rare decays of hadrons which contains b and c quarks.

Compared to other existing accelerators that are in operation the LHC is by far the most copious source of B mesons, due to the high bƃ cross section (σ  ~ 500 μb at 14 TeV) and high luminosity (2·1032 cm-2 s-1, on average).

So, let’s calculate the number of events  ( pairs):  

 Nevent/sec = σ x L    Nevent/sec = (500·10-6·10-24)x(2·1032)    

 Nevent/sec = 105  pairs/second

The canonical one year data taking correponds to ~280 hours (~107 s)


(105  pairs/s)x(10s/yr) =1012  pairs/year


Xabier Cid Vidal, PhD in experimental Particle Physics for Santiago University (USC). Research Fellow in experimental Particle Physics at CERN from January 2013 to Decembre 2015. Currently, he is in USC Particle Physics Department (Spanish Postdoctoral Junior Grants Programme).

Ramon Cid Manzano, secondary school Physics Teacher at IES de SAR (Santiago - Spain), and part-time Lecturer (Profesor Asociado) in Faculty of Education at the University of Santiago (Spain). He has a Degree in Physics and in Chemistry, and is PhD for Santiago University (USC).



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