The Need for High Q2

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 Q2 = -q2 since this means that Q2 is always positive, and Q2 specifies the virtuality of the boson. The higher the value of Q2 the higher the virtuality of the photon, and a photon becomes real at Q2 = 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/Q2. 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 Q2 can be used as the hard scale are called Deep Inelastic Scattering (DIS). However, the photoproduction events studied here use low Q2 quasi-real photons since the cross section decreases with increasing Q2, and so Q2 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


The variable which will tell us whether an interaction was a direct or resolved photon interaction is xgobs. 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 xgobs being less than 1.

xgobs is reconstructed using the following equation:

The other variables in this equation are as follows:

ET = transverse energy of the jet

h = peudorapidity of the jet

ye = fraction of positron energy that is carried by the photon

Ee = 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 xgobs can be calculated for each event.


ET 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 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.


Ee is the energy of the incoming positron. It is known from the properties of the DESY accelerators, and is ~30GeV.


ye is the proportion of the positrons energy taken by the photon. This may be directly reconstructed by using the following equation:

where Ee' 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 ye from the other particles that emerge from the interaction; the one which was used by us is the Jaquet-Blondel method.

where Pzi 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. yjb is equivalent to ye and so can be directly substituted into the equation for xgobs. The sum is one of the variables that is provided by the software package orange (explained in its own section).