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cross section for lepton collider

Asked by Yehia Abdelaziz

I have noticed something that I can't understand. When generating a process for ee collider, the cross section decreases when we increasing the sqrt(s). Does anyone have any idea why this happens?

For example e e > mu mu has cross section of O(10^7) pb for cms 1 GeV and of O(1) for cms 500 GeV.

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WHIZARD Edit question
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Juergen Reuter Edit question
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Yehia Abdelaziz
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Juergen Reuter (j.r.reuter) said : 		#1

Dear Yehia,
the scattering cross section for pointlike massless or quasi massless particles always falls off like 1/s. The cross section has the dimension of an area (1/E^2) and the only dimensionful quantity is s. (For certain processes there are enhancements due to divergent t-channel exchange of massless particles, and one gets a behavior of log(s)/s.)
At hadron colliders this is different because protons are composite objects and at higher energies one resolves more and more partonic substructure of quark and especially gluons inside the protons (which can be seen in the steep rise of e.g. gluon PDFs at low Bjorken-x), and hence the cross section rises with the collider energy. This is because the production of SM particles becomes more and more "soft physics" at higher and higher energies. If you take, however, the jet production cross section at a proton collider and demand jet energies larger than e.g. sqrts/20 or so, then also this cross sections falls off like 1/s.
Cheers,
     JRR

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Yehia Abdelaziz (yehia95) said : 		#2

Thank you Juergen. This was very useful.