How do particle scattering cross sections scale with energy in colliders? Particularly photons, electrons, protons, and gold or lead nucleii? (If necessary, break this into four separate questions.)
It is stated that due to the Heisenberg uncertainty principle, it takes more energy to measure a smaller distance and the inverse wavelength energy-wavelength relationship for photons is well known.
Therefore, I would conclude that the (total scattering) cross section for photons at least would vary as the inverse square of the energy.
On the other hand, general relativity says the the longitudinal dimension shrinks with increasing velocity, but the transverse dimensions do not.
Therefore, I would conclude that the cross section of say a gold atom in RHIC or a lead atom in the LHC would basically remain constant as the energy increased.
But how about the electron, supposedly a point particle?
Due to PEP and LEP, we should have good data on this. Looking at PDG figure 41.6,
I see lots of big spikes for resonant particles, but the underlying bacground is clearly a falling powerlaw that I think looks like it could be an inverse square law.
The proton cross sections in the next few figures, e.g. 41.7 and 41.11, show a falling elastic scattering cross section, but they also show an approximately constant total cross section.
What little i've found for RHIC supports the approximately constant cross section.
Therefore I conclude that the cross sections of photons and electrons (neglecting resonances) scale as the inverse square of the energy, but the cross sections of protons and nucleii are roughly constant with energy.
Comments or corrections?
So is it true that the photons and electrons are different from the protons and nucleii?
And why don't the protons scatter as three or six point particles (quarks and gluons) instead of one big blob?