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Introduction

The world around us is perceived by the human by our five senses, and our reality is built up from how our brain is interpreting the signals from our sensor organs. Presumably our vision, formed by the light detected in our eyes, is the most fundamental way to describe the world we live in. Light is however not only confined to the light we can see, light (or more general electromagnetic radiation) is also the origin of a numerous phenomena in every day life. Among these are for instance, the earth magnetic field, heat radiation and all types of radio communication, and it is clear that life would quickly perish without any source of light.

The interest for light has always been in focus of the curiosity of mankind. Already in the most ancient religions man was worshipping the sun god, but it was not until the 20th century that we started to grasp what light really is. For a long time light was thought to be a wave propagating in the so called ether, which was thought to be a medium that filled all space (including vacuum). The ether theory poses the problem that it results in a fixed reference system, in which the ether is at rest. The Michelson-Morley experiment in 1887 more or less put an end to the ether theory as it showed that there is no preferred system of motion for the light.

Light was showing properties of being quantized in particles (from Planck's explanation of the blackbody radiation in 1905), which however seemed to be in total disagreement with light diffraction experiments (Fig. 1.1). The solution to this was presented by Einstein in his work about the photo electric effect, when he showed that light can be described both as a wave or as a particle. In 1924 Louis de Broglie suggested that particles can be described as waves, to make the wave-particle duality complete. In an experiment similar to the one in Fig. 1.1, electron diffraction was observed independently by Davisson and Germer in 1927 and by G. P. Thomson in 1928.

Quantum mechanics tells us that we cannot determine an object's position exactly, we can only measure a probability to see an object at a certain place. For large (bigger than atoms) and slow (non relativistic) moving objects there is no wave function to speak about and things are actually where we see them. The photon (which is point-like and relativistic) is however much more elusive and cannot be fixed in position and momentum at the same time. It therefore behaves like a wave, with an amplitude determined by the probability to be in that location. It has been shown that if the position of the photon is determined, the wave-function property of the photon instantly breaks down.

Figure 1.1: Diffraction of light through a two slit wall. In the classical approach light behaves like a soundwave in air or as a wave on a water surface, and interference of the waves from the two slits makes an amplitude pattern on the rear screen. If the intensity of light is brought down so that only one photon passes through the slit and there is no interference to speak about, the amplitude pattern is however still seen on the screen. This is explained by quantum mechanics telling us that the photon only has a certain probability to either go through the upper or lower slit. Any attempt to determine which path the photon took, will automatically destroy the wave pattern. The experiment (on a different scale though) has the same outcome if electrons instead of photons are used.

The photon is the mediator of the electromagnetic force and as charged particles (like the electron and the proton) couples to this they exchange photons when they interact with each other. The photon itself has no charge and photons do not interact among themselves (nothing will thus happen when you cross two laser beams). The photon does not have any restmass, but as shown by Einstein energy and mass are distinctly connected with his famous formula E = mc².

As shown to the world for the first time at large scale over Hiroshima and Nagasaki in August 1945, mass can be converted into energy. The opposite is however also possible and if the energy of a photon is high enough it can fluctuate into a particle and anti-particle pair. All particles have their corresponding anti-particles with same mass, but opposite quantum numbers (like the charge). In order for any particle transition to be possible all the quantum numbers must be conserved.

By the help of quantum mechanics, the photon can thus be described as a superposition of a number of possible particle pairs. A photon is thus not only a bare photon, it can fluctuate into different virtual states. These states are described by something that is called the photon structure functions, which will be described later (section 6.3). This mechanism makes collisions between photons possible, as they sometimes are something else than photons.

Electrons are surrounded by a cloud of virtual photons, they are called virtual because they only live on the existence of energy borrowed from the electron. Quantum mechanics allows energy to be created out of nothing during a very short period of time as long as it is payed back at the next instant. A cloud of photons is therefore constantly created and eliminated around any charged particle. The higher energy the electron has, the more energy is available to be borrowed and the virtual cloud grows.

If two electrons are close to each other and the energy is large enough, there is thus a distinct probability that two of these virtual photons will collide (if the virtual photon has fluctuated into a charged particle pair). As a photon normally is symbolized by the Greek letter gamma (=$\gamma$) this is referred to as a two photon- or a $\gamma$$\gamma$-collision (Fig. 1.2). By studying such collisions it is possible to probe the structure function of the photon and thereby give us a better understanding of both Quantum Electro Dynamics (QED) and Quantum Chromo Dynamics (QCD).

Figure 1.2: The collision of two virtual photons radiated from the electron and positron in the LEP beam. The invariant mass of the $\gamma$$\gamma$-system ( W_{$\gamma$$\gamma$}) can be extracted from measurments on the outgoing leptons.

The LEP accelerator at CERN has accelerated electrons to the highest energy achieved yet, and this paper is based on $\gamma$$\gamma$ collisions detected with help of the VSAT detector in the DELPHI experiment. The VSAT (Very Small Angle Tagger) detector is, as the name suggest, located at very low angles and can measure both of the leptons coming out from a $\gamma$$\gamma$-collision. A measurement of the full kinematics of the $\gamma$$\gamma$-system can then be obtained. VSAT will, due to the small angles, provide data with a very low Q² (the momentum transfer to the photons), which is a very interesting region to study [1].