PROCESSES WITH LARGE IMPACT PARAMETERS AT COLLIDING BEAMS

Abstract

At the collider VEPP-4 a remarkable deviation of the measured bremsstrahlung photons from the standard calculation method has been measured in the reaction e+e−→e+e−γ. The decreasing number of photons is explained by the fact that large impact parameters give the essential contributions to the cross section. These parameters are by several orders of magnitude larger than the transverse beam sizes. In that case the standard definitions of “cross section” and “number of events” are invalid. Similar effects are expected for the single photon bremsstrahlung and the e+e− pair production at existing and planned high energy e±e−, ep and eγ colliders. A calculation scheme for particle production in the interaction of two bunches, which allows one to take into account these effects quantitatively, is presented. In this scheme the colliding bunches are represented as wave packets, and quantum distribution functions are used. The modified definitions of the cross section and the number of events contain the features of “nonlocality” and “interference”. Reasonable approximations which can be easily used are discussed. The results are applied to analyze the influence of the finite beam sizes on reactions which have been proposed for measuring the luminosity and the beam polarization at the colliders LEP and HERA.