Elsevier

Physics Reports

Volume 453, Issue 1, November 2007, Pages 1-27
Physics Reports

Electron–positron pair production in ultrarelativistic heavy ion collisions

https://doi.org/10.1016/j.physrep.2007.09.002Get rights and content

Abstract

In recent years, a large number of papers have appeared that dealt with e+e- pair production in heavy ion collisions at high energies. To a large extent these studies were motivated by the existence of relativistic heavy ion accelerators all over the world. There pair production can be studied in so called “ultra-peripheral collisions”, where the ions do not come close enough to interact strongly with each other. Various different methods have been used and it is the purpose of this review to present a unified picture of the present status of the field. The lowest order Born result has been known for more than seven decades. The interest and focus is now on higher order effects for values of Zα1, where Z is the charge number of the ion. A similar problem appears for the Bethe–Heitler process, the production of e+e- pairs in photon–nucleus collisions. It was solved essentially some five decades ago by Bethe and Maximon. The result of Bethe and Maximon can also be recovered by summing over a class of Feynman diagrams to infinite order. These results can be used for a study of Coulomb corrections in nucleus–nucleus collisions. Indeed, the major part of these corrections have a structure closely related to the Bethe–Maximon solution. There are additional terms which give a small contribution to the total cross section at high energies. Their importance can be enhanced by concentrating on small impact parameters. An interesting exact solution of the one-particle Dirac equation in the high-energy limit was found independently by several authors. This led to some discussion about the interpretation of these results within quantum electrodynamics (QED) and the correct regularization necessary to get the correct result. The dust of previous debates has settled and, indeed, a consistent picture has emerged. Another interesting higher order effect is multiple pair production, which we also discuss. We compare experimental results obtained recently at relativistic heavy ion collider (RHIC) for free and bound-free pair production with theoretical results. We also make some more remarks on the physics of strong electric fields of longer duration. A new field is opened up by ultra-intense laser pulses. We argue that due to the short interaction time in ultraperipheral heavy ion collisions pair production can be well understood in the frame of QED perturbation theory.

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 e+e-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 e+e- 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 isA(p1)+B(p2)e+(q+)+e-(q-)+A(p1)+B(p2),where the corresponding four-momenta are given in the brackets.

In the paper [51] the first terms in the amplitude of e+e- 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 Z1 is small, i.e. Z1α1. 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 e+e- pair production in fast (vc) and slow (v0) heavy ion collisions (Zunitedatom>137(173)) 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 e+e- 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 γ, 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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