
The Need for High Q^{2} q is the amount of momentum transferred to the mediating photon from the positron. This is not usually expressed in this way, instead being described by Q^{2 }= q^{2} since this means that Q^{2} is always positive, and Q^{2} specifies the virtuality of the boson. The higher the value of Q^{2 }the higher the virtuality of the photon, and a photon becomes real at Q^{2 }= 0. It is this which determines the scale of structure which we see in an interaction. In general terms the size of object which can be 'seen' is ~1/Q^{2}. I use the word seen in inverted commas because we only see the effects of the increased resolving power indirectly; we don't observe the particles in the normal sense of the word. This means that the higher the momentum transferred to the photon, the smaller the object that can be detected. A larger momentum transfer requires higher and higher energy collisions, and this is one of the main reasons that particle physicists are always striving for higher energy accelerators. What is actually observed when we go to higher energy/smaller scales is a change in scattering behaviour of the composite particles involved when the scale passes that of a smaller constituent particle. Indeed, one compelling piece of evidence for the belief that the fundamental particles are not made up of even smaller particles is that no such change in scattering behaviour has yet been observed at scales smaller than, say, quarks or electrons. So, in order to observe the fundamental exchange of the photon between the positron and one of the partons in the proton we need a suitably good resolution. The process which leads to the ability to resolve the partons is known as the hard scale for the interaction. Events where Q^{2} can be used as the hard scale are called Deep Inelastic Scattering (DIS). However, the photoproduction events studied here use low Q^{2} quasireal photons since the cross section decreases with increasing Q^{2}, and so Q^{2} cannot be reliably used as the hard scale. A common choice for the hard scale is the transverse momentum of the jets produced, and that is what is used here. Other important variables x_{g}^{obs} The variable which will tell us whether an interaction was a direct or resolved photon interaction is x_{g}^{obs}. This is the proportion of the photons momentum (Q) which has gone into the interaction with the parton in the proton. If the interaction is a direct photon interaction then the whole photon is absorbed by the parton and thus the proportion of the photons momentum which has been involved is 1, i.e. all of it. However, if the interaction involved a resolved photon, only part of the photons momentum will be involved since not all of the partons into which the photon has split will be involved. This leads to x_{g}^{obs} being less than 1. x_{g}^{obs} is reconstructed using the following equation: The other variables in this equation are as follows: E_{T} = transverse energy of the jet h = peudorapidity of the jet y_{e} = fraction of positron energy that is carried by the photon E_{e} = incoming positron energy The significance of jets 1 and 2 is that these are the two highest energy jets that emerge from the interaction. Providing that all these variables can be measured the value of x_{g}^{obs} can be calculated for each event. E^{T} E^{T} is the transverse energy of the jet. This is measured by the calorimeters in the ZEUS detector. The two highest energy jets are chosen because the proportion of energy taken by any other jets is low (£ 20%). Also, as long as this is consistently adhered to, we are always going to be comparing like events, and so the theory still holds true. h h is the pseudorapidity of the jet. This is explained more comprehensively in its own section, but essentially it takes into account the relativistic nature of the motion of the particles. h = ln(tan(q/2)) where q is the angle between the beams and the jet. E_{e} E_{e} is the energy of the incoming positron. It is known from the properties of the DESY accelerators, and is ~30GeV. y_{e} y_{e} is the proportion of the positrons energy taken by the photon. This may be directly reconstructed by using the following equation: where E_{e}^{'} is the scattered positron energy. However, since we are looking at low scattering angle situations the scattered positron is lost down the beam pipe and so its energy cannot be measured. Fortunately there are techniques for reconstructing y_{e} from the other particles that emerge from the interaction; the one which was used by us is the JaquetBlondel method. where P_{zi} is the z component of particle momentum. The sum runs over all particles in all calorimeter cells, except when the scattered positron enters the detector. If this happens, the positron is emitted from the sum. y_{jb} is equivalent to y_{e} and so can be directly substituted into the equation for x_{g}^{obs}. The sum is one of the variables that is provided by the software package orange (explained in its own section). 