The Quark Parton Model
The protons that interact are not fundamental particles like the positron or photon. Instead they are made up of smaller point-like particles, the general term for which is a parton. Until the 1970's the nature of these partons was not known, but since then it has been generally accepted that they are quarks, which indeed have the property of being point-like and are thought to be fundamental particles. This is the quark parton model of the proton. If the proton is made up of smaller particles then it is reasonable to assume that in hard processes (where the quarks can be resolved) the positron-proton interaction is actually an elastic positron-parton interaction. This causes the parton to be knocked out and thus the proton breaks up, causing the hadron jets to form. In much the same way as a resolved photon, this leads to the proportion of the proton momentum being involved in the interaction to be less than 1. This is what is observed. In this simple model the quarks that make up the proton are all travelling co-linearly, and so the transverse momentum of the proton is zero.
There is a problem with this model, however. If the quarks are the only constituents of the proton, then the sum of their momenta should be equal to the momentum of the proton. Experimentally the fraction of the protons momentum carried by the quarks is found to be approximately 0.5, implying that they are not the sole constituents of the proton. There must be something else taking the other half of the momentum.
In Quantum Chromodynamics (QCD) quarks interact by the radiation of bosons called gluons. These can then split into quark/anti-quark pairs ('sea quarks') or more gluons. This results in the proton, rather than consisting simply of three point-like particles separately bouncing around, being seen as a sea of quarks and gluons. In this model it is not simply one of three quarks with pretty nicely defined momentum that interacts, but it could be a quark, a gluon, a quark which has just emitted a gluon, a sea quark and so on. The gluon radiation also leads to a transverse momentum component to the proton.
At low Q2 the sea structure is not observed since the resolution is broad and only the quark substructure is seen, with the detail being 'smeared out'. At high Q2 the resolution is good enough to see the finer detail, and the history of the quark affects the reaction, e.g. whether a quark has just emitted a gluon etc. This means that the cross-section of the interaction varies with Q2, and so for our study this must be kept constant. This is a major reason for restricting the scattering angle to low angles, since this is related to the momentum transfer.
The fact that the cross section varies with scattering angle , and hence Q2, stems from the differing lifetime of particles at different Q2. At small scattering angles the cross section of resolved photon interaction rises much faster than that of direct photon interactions, because the longer the lifetime of a particle the greater the probability that it will form a complex hadronic state. The particles lifetime is inversely proportional to Q2, so lower angle scattering is associated with lower values of Q2.
Direct Photon Interactions
In these interactions the photon interacts directly with a parton from the proton in a point-like manner. This is unique to photons when compared to hadrons, for example, which are composite objects. The type of parton may be a quark from the proton, or a sea quark produced from gluon.
In the first case the quark achieves a high virtuality and becomes real again by emitting a gluon. This process is known as QCD Compton scattering. The remnants of the proton are not stable and become so by forming a hadron jet, which is detected. The affected quark/gluon pair is not allowed to exist on its own by the rules of quantum chromodynamics, and these too form a hadron jet which will be detected (this is a leading order process, there could be complex hadronic states formed at any stage which would produce different outcomes).
If the interacting quark is a sea quark then once again (in the leading order process) two hadron jets are produced. This is known as photon gluon fusion.
In both of the above interactions the whole photon enters the hard sub-process, and so these will have higher transverse momentum than the hadronic processes described later. These direct events require high virtuality in order that we can see the partons in the proton.
Since the whole photon interacts it is expected that these processes will return a value of xgobs equal to unity.
Resolved Photon Interactions
The general resolved interaction can be split into two parts: Vector Meson Dominance (VMD) and Anomalous Photon Interactions.
Vector Meson Dominance
Experiments have shown that the photon can interact like a vector meson with the proton. There is a probability that the photon will fluctuate into a meson (a bound state of a quark/anti-quark pair) with the same quantum numbers as itself for a short time. In this interaction it is not the high Q2 that gives the interaction its hard scale (and hence the ability to resolve the partons) but the high transverse momentum of the final state particles. This high transverse momentum also suggests that it is the constituent partons that interact rather than the meson and proton as a whole.
Anomalous Photon Interactions
The production of unbound quark/anti-quark pairs with higher virtuality than the mesons in VMD leads to the anomalous photon. The high virtuality of this state provides the hard scale, and high momentum transfer processes are dominated by anomalous and direct photon interactions. However, the effect of VMD interactions cannot be neglected.
The separation of these two processes is not well defined, and since neither can be neglected at any value of transverse momentum they are bundled together to form the resolved photon. This means that the photon has acted as a source of partons for the scatter and for this process it would be expected that the proportion of the photons momentum participating in the interaction, xgobs, will be less than 1. This is because it is the partons in the hadronic state formed by the photon which will take part in the interaction rather than the whole photon, making it much the same as the proton. Also, there will be a photon remnant formed from the partons which did not interact which will be seen as a hadron jet. Thus there are more opportunities for hadron jets to form in a resolved photon event than in a direct photon interaction.