Gamma-Gamma Physics Tutorial

Light interacting with Light

A small tutorial in gamma-gamma Physics

By Jan A. Lauber, UCL, last updated 18. July 1997

Below you'll find a little introduction to two-photon physics - porbabely more than you ever wanted to know about it.

Photon-Photon couplings

From classical electrodynamics we know that EM waves pass through each other without any interference. From Quantum Electro Dynamics (QED) we know that Photons cannot couple directly to each other, since they don't carry charge, but they can interact through higher order processes:

A photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion/ anti-fermion pair, to either of which the other photon can couple. This fermion pair can be leptons or quarks. In the latter case, we distinguish several cases:

Direct or pointlike: The photon couples directly to a quark inside the target photon. At this small scale, alpha_s is small and this process can be calculated in perturbative QCD.
Single resolved: The quark pair of the target photon form a vector meson. The probing photon couples to a constituent of this meson.
Double resolbed: Both targed and probe photon have formed a vector meson. This results in an interactions between two hadrons. For the latter two cases alpha_s is large, and this Vector Meson Dominance (VDM) process has to be modelled in non-perturbative QCD.

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The Photon Cross-section

The cross-section of the photon-scattering of visible light is phenomenally small and can't be measured experimentally. But photons with higher energies, such as produced copiously at an electron-positron synchrotron interact with each other more often.

While the cross-section of e+e- annihilation falls with the center-of-mass energy, the cross-section of the photon scattering rises logarithmically ( green curve)

When such a scattering process takes place, the electrons that emmited the photons get scattered out of their trajectory. If this scattering angle is large enough, the electron is "seen" inside the the detector, and is called a tag.

The momentum transfer or the virtuality of the photon is expressed as Q^2 . The scaling variable tells us what fraction of the photon momentum was carried by the struck fermion inside the photon. P^2 is the virtuality of the target photon and is very small. W is the invariant mass of the hadrons coming from the interaction.

So, this is what a typical event looks like in the Opal detector: A tagged electron in the Forward Detector (right side) and some hadrons from the gamma-gamma collision.

The cross section of the process can be written in terms of the photon structure functions: q^2