# Parton model and quark interaction in DIS.

## Main Question or Discussion Point

I'm currently reading about the parton model and deep inelastic scattering.

As I've understood it was observed that when protons collided at high energy very little transverse momentum transfer was observed, while when electrons were collided with protons transverse momentum transfer was observed in accordance with treating the proton as if it were (or consisted of) an elementary charged fermion. I.e. the electron muon scattering formula captured the qualitative behavior of the scattering.

According to the parton model (as explained in Peskin and Schroeder at page 476) this is explained by assuming that the proton is a loosely bound assemblage of partons; which are fermions carrying electric charge incapable of interchanging large momenta at high momentum transfer.
However since these partons interact electromagnetically an electron can knock out a parton of the proton and this parton then exchanges momentum 'softly' with the rest of the proton, so that the pieces of the proton materialize as jets of hadrons.

In my understanding this model has the theoretical support in QCD for which the strong coupling constant goes to zero asymptotically at large momentum transfer.
This should thus explain why the proton constituents do not interact and thus why no transverse momentum transfer is observed.

The problem I have with this picture is that these constituents are assumed to be charged; so why then do they not interact electromagnetically among themselves just as in the case with electron? Since they are charged should we not observe something like the electron muon scattering behavior also between the proton constituents? Why not?

## Answers and Replies

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mfb
Mentor
The electromagnetic contribution is small relative to the QCD interactions in proton-proton scattering. At low parton momenta, the proton is dominated by (electrically uncharged) gluons, and the QCD coupling "constant" is still significant for those collisions.

The electromagnetic contribution is small relative to the QCD interactions in proton-proton scattering. At low parton momenta, the proton is dominated by (electrically uncharged) gluons, and the QCD coupling "constant" is still significant for those collisions.
But arent these experimens are performed at high momenta? In that case the Qcd coupling is small and the Qed is large. Suppose an electron knocks a quark with a large momenum transfer at a given large momentum scale - is it then any reason why that quark can not transfer a comparable momentum to another quark inside the proton trough the electromagnetic interaction?

tom.stoer
Science Advisor
Afaik DIS is always calculated with QCD radiative corrections but first order QED.

mfb
Mentor
"QCD is small" and "QED is large" are meant relative to their value at zero. As long as you are below the GUT scale, the QCD coupling constant is larger than the QED coupling constant. In addition, the proton has "more" color charges than electric charges.

"QCD is small" and "QED is large" are meant relative to their value at zero. As long as you are below the GUT scale, the QCD coupling constant is larger than the QED coupling constant. In addition, the proton has "more" color charges than electric charges.
So when the electron knock the quark - I assume this implies the quarks are much more likely to interact strongly among themselves than trough a QED interaction.

But if the QCD coupling is still strong relative to QED at the momentum scale in interest, why can't the QCD interaction cause a high momentum transfer trough a photon, while the QED interaction can do that?

tom.stoer
Science Advisor
DIS uses two assumptions: 1) one single perturbative QED interaction with a quark in a 2) non-perturbative QCD structure functions. All essential QCD interactions are contained in 2) whereas 1) is nothing else but the microscope to look at the state described by 2)

mfb
Mentor
So when the electron knock the quark - I assume this implies the quarks are much more likely to interact strongly among themselves than trough a QED interaction.
That is always true in a proton.

But if the QCD coupling is still strong relative to QED at the momentum scale in interest, why can't the QCD interaction cause a high momentum transfer trough a photon, while the QED interaction can do that?
It can, and the LHC recorded some nice events with large momentum exchange. But those events are rare.

That is always true in a proton.

It can, and the LHC recorded some nice events with large momentum exchange. But those events are rare.
Alright! Are there any theoretical explanations for why these large momentum exchange processes are rare?

Thanks for your help! :)

mfb
Mentor
The QCD coupling constant goes down :D. In addition, high-energetic partons are rare, especially if you want high-energetic partons in both protons.

The QCD coupling constant goes down :D. In addition, high-energetic partons are rare, especially if you want high-energetic partons in both protons.
But then again, as you said yourself, the coupling is still much larger than the QED coupling and the high momentum transfer QED processes are not rare.. :P

mfb
Mentor
QED processes for proton-proton interactions are rare.
QED processes for proton-electron interactions are rare as well, but you don't have that huge QCD background so it is easier to see them.