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Two Photon Physics

As already mentioned in the introduction, the photon can be described as a superposition of a number of virtual states. Each state represents the probability to fluctuate into a quark-antiquark or lepton-antilepton pair and can be represented by a wave-function. Due to theoretical difficulties the quark-antiquark pair is subdivided into high and low virtuality fluctuations, with a cutoff-limit (p_T) in the transverse momenta of the quarks. The high virtuality part can be calculated by perturbative QCD, whereas the low-virtuality part is described in a non-perturbative phenomenological model involving the summation over vector meson states. In mathematical form the photon therefore is described as the bare photon plus three summation terms [24]:

$$\gamma \gamma_{bare}^{} \sum_{V=\rho^0,\omega,\phi,J/\psi}^{} \sum_{q=u,d,s,c,b,t}^{} \overline{q} \sum_{l=e,\mu,\tau}^{}$$ (6.1)

The last term describes the fluctuation into a lepton-antilepton pair and is calculable to high precision by QED and is in this scenario of less interest and will be discarded from the analysis. The two other terms describe the hadronic part of the photon wave-function and photon-photon collision studies will help to improve our understanding of QCD.