Electron–positron pair production in ultrarelativistic heavy ion collisions
Section snippets
Introduction, overview and purpose
Quantum electrodynamics (QED) is the best-tested theory we have [1], [2], [3], [4]. It is a quantum field theory which describes the gauge invariant interaction of charged particles with photons. With this theory one is able to describe high precision experiments like the Lamb shift and the magnetic moments of the electron and muon with great accuracy. In the present review we are dealing with the fundamental process of particle production in high energy scattering processes. Experiments up to
Lepton pair production by a high energy photon in the strong Coulomb field of a heavy nucleus
In this chapter we recall the well known theoretical treatment of the Bethe–Heitler process, the pair production by a photon in the Coulomb field of a nucleus. This is simpler than the problem of pair production in the field of two nuclei, but shows already many of the important aspects of the nucleus–nucleus case. It corresponds to the cases (i)–(iii) (see Section 1), where only one photon is attached to one of the nuclei. Case (iv) is the one, which is specific to the nucleus–nucleus
Lepton pair production in relativistic heavy-ion collisions using Feynman diagrams
In this paragraph we want to briefly review the work on pair production in relativistic heavy ion collisions based on the summation of Feynman graphs in the high energy limit. The problem is formulated in [51]. The process to be studied iswhere the corresponding four-momenta are given in the brackets.
In the paper [51] the first terms in the amplitude of pair production in the Coulomb field of two relativistic heavy ions are calculated. The
Exact solution of the one-particle Dirac equation in the ultrarelativistic limit and what one can conclude from that
An interesting topic is the solution of the (single-particle) Dirac equation for two countermoving ions and how this relates to the process of pair production. This was strongly triggered by the observation, that in the limit of ultrarelativistic nuclei and using an appropriate gauge, the expression for the electromagnetic interaction simplifies and the Dirac equation can be solved analytically in a closed form [56].
Before we discuss this specific solution of the Dirac equation, it is useful to
Coulomb corrections for the heavy ion case, based on the Bethe–Maximon approach
In the last section the exact solution of the one-particle Dirac equation in the high energy limit was discussed. Using the eikonal/sudden approximation at high energies it was claimed in several publications that Coulomb corrections are not present. This claim must be wrong, since one has to reproduce the Bethe–Maximon results for photoproduction, see Section 2, in the limit where the charge of one nucleus is small, i.e. . In Section 3 we dealt with pair production in the “usual”
Higher order effects in electron pair production: multiple pair production and bound-free pair production
In the previous sections we have mainly dealt with one special kind of higher order effects, the so-called Coulomb corrections. By definition they describe the effect of higher order Coulomb interactions on the one-pair production. They are well understood in terms of the Bethe–Maximon theory, or, equivalently, the approach of summing Feynman diagrams [34]. Higher order interactions can also lead to a second kind of process: Multiple pair production is the most important process of this type
Transition from the adiabatic to the sudden regime
The physics of pair production in fast () and slow () heavy ion collisions () is very different: for the slow collisions there is spontaneous pair production in supercritical fields, a non-perturbative effect. For fast collisions we can apply perturbation theory. Two-photon production dominates, as was discussed above. Let us first mention the corresponding situation of atomic ionization and electron–positron-pair production in a time-varying spatially constant
Comparison to experiment and outlook on LHC
Since our last review of this subject in [18], the heavy ion collider RHIC has come into operation. Both the STAR and the PHENIX collaborations have published measurements on pair production. In the case of STAR the data was taken for events accompanied by nuclear breakup. In this way one is able to measure pair production at small impact parameters. Due to the high Lorentz factor , the electromagnetic fields are stronger than at SPS or AGS energies. For a discussion of experiments at
Conclusion
In April 1990 a workshop took place in Brookhaven with the title ‘Can RHIC be used to test QED?’ [101]. We think that after about 17 years the answer to this question is ‘no’. However, many theorists were motivated to deal with this topic. The gradual progress, which was sometimes quite tortuous, is described in this report.
In this review we studied electron–positron pair production in heavy ion collisions at relativistic energies. There were quite a few papers in the last years approaching
Acknowledgments
We are grateful to A. Alscher, A. Aste, C.A. Bertulani, U. Dreyer, S.R. Klein, H. Meier, E.A. Kuraev, P. Stagnioli, V. Serbo for their collaboration on various topics of this review. We are indebted to U.G. Meißner and V. Serbo for their valuable comments on an earlier version of this review. Furthermore we wish to acknowledge very interesting and helpful discussions with many people, we would like to mention especially A. Baltz, J.B. Jeanneret, J.M. Jowett, A. Milstein, N.N. Nikolaev, W.
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