ar X iv : h ep - e x / 01 12 01 8 v 1 1 3 D ec 2 00 1 ELECTRODYNAMICS AT THE HIGHEST ENERGIES

At very high energies, the bremsstrahlung and pair production cross sections exhibit complex behavior due to the material in which the interactions occur. The cross sections in dense media can be dramatically different than for isolated atoms. This writeup discusses these in-medium effects, emphasizing how the cross section has different energy and target density dependencies in different regimes. Data from SLAC experiment E-146 will be presented to confirm the energy and density scaling. Finally, QCD analogs of the electrodynamics effects will be discussed. Bremsstrahlung and pair production were described by Bethe and Heitler in 1934. 1 In brems-strahlung (braking radiation), an electron with energy E interacts with a target nucleus, and slows down, emitting a photon with energy k in the process. For interactions with an isolated atom, for k ≪ E, the Bethe and Heitler bremsstralung cross section scales as dσ dk ≈ 1 k. (1) In pair production, a photon fluctuates to an e + e − pair. The newly created electron or positron interacts with the electromagnetic field of a target nucleus, and the pair becomes a real e + e − pair. For photon energies k ≫ m e , the pair production cross section is independent of k. Sophisticated calculations of bremsstrahlung and pair production confirm that these energy dependencies hold within a few percent. Bethe and Heitler treated bremsstrahlung and pair production as occuring at a single point in space. With this assumption, the radiation depends on the change in electron velocity ∆ v due to the scattering from the target, independent of the nature of the force that causes the velocity change. For any interaction, one can determine the expected ∆ v distribution, and, from that, find the bremsstrahlung radiation. With this approach, it is relatively easy to generalize from isolated atoms to a dense medium. In 1953, Ter-Mikaelian 2 and Landau and Pomeranchuk 3 pointed out that the assumption that the interaction occurs at a single point fails when the incoming particle has a high enough energy. It is impossible to localize the reaction to a point on the projectile's trajectory. This is true classically as well as quantum mechanically. The pathlength over which the reaction can be localized is the formation length, l f. Classically, the formation length is the distance z over which the phase factor, exp(i[ k·z−ωt]) is roughly constant (k · z − ωt < 1). In a …