When do we need n-point functions for high n?

[metroplex021]

I am new to QFT and found myself wondering the following. Particle physics experiments usually consist of looking at what happens when we smash two protons together. As such, we look to calculate amplitudes for 2-> n scattering, with n the number of particles that emerge from the other side. Is there ever a case in which we need to think about this for high n? And if not, why need we worry about the divergences n-point Green's functions being cured for lower n, since we're unlikely to have to use them to calculate anyway?

Any thoughts most appreciated!

 

[Ben Niehoff]

High-energy QCD collisions produces loads of particles, not just a few:

http://en.wikipedia.org/wiki/Jet_(particle_physics)

 

[mfb]

High-energy QCD collisions produces loads of particles, not just a few:

http://en.wikipedia.org/wiki/Jet_(particle_physics)

That is true (and more than 10 particles are typical, especially for the interesting events), but do you really use those n-point functions for hadronization?
Usually the calculation is split up in the hard interaction (producing heavy bosons, heavy quarks, high-energetic quarks, gluons, photons or whatever happens in the event) and hadronization (can produce jets).

 

[kurros]

That only works for actual hard scattering events right? I am not sure that events with lots of soft quarks and gluons factorise so nicely.

 

[mfb]

I don't know about ALICE (and if lead is involved, you need a different approach anyway), but ATLAS and CMS mainly look for hard scattering events - everything else does not even pass the first stages of the triggers (well, just with a tiny rate to have some unbiased sample). LHCb looks at lower energies, but even there everything below 2-3 GeV (for the final decay products) is background because it does not make it through the magnet.

 

[kurros]

Sure. I guess the main answer to the OP is that it is theoretically important to know these things, even if they are not part of the "everyday toolkit" of experimental particle physics. Though I have no doubt that some QCD expert would indeed think these things super important for the experiments, for modelling the SM backgrounds properly and so on.

 

[RGevo]

The Parton shower does an approximate high n.

The hard suborocess which you calculate the matrix element for using your Feynman rules receives higher order corrections from infrared divergences (real and virtual). So in some sense, the shower does the large n part for you. This is done through leading logarithmic approximation.

This is only accurate for corrections (large n) which are in a particular regime - collinear, soft.

Calculation wise, this is what is reasonably feasible.

So large n is important for calculating the shape of a particle distribution in part of phase space sensitive to these un calculated extra corrections. (Eg pt near 0, where real corrections are turbo fuelled)

 

[DarMM]

And if not, why need we worry about the divergences n-point Green's functions being cured for lower n, since we're unlikely to have to use them to calculate anyway?

One perspective on this is that the n-point functions basically encode information on the inner-products of states in the Hilbert space. This allows you to reconstruct the Hilbert space and the whole theory from the n-point functions.

If some of the n-point functions diverge, then it means that the inner-products between certain states are undefined, that is the transition amplitude from some state to some other state is ill-defined and since the collection of all transition amplitudes essentially tells you the time development of the state, it would mean that the time evolution was ill-defined.

If only the n-point functions for low n were defined, it would mean that the theory only had sensible time evolution for initial configurations with low particle numbers, for all other states it developed divergences. Such a theory couldn't be said to accurately reflect the real world.