Nuclei colliding at very high energy create a strong, quasiclassical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromoelectric and chromomagnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. For example, we find that the ratio of longitudinal to transverse pressure very early in the system behaves as pL/pT=-[1-32a(Qτ)2]/[1-1a(Qτ)2]+O(Qτ)4, where τ is the longitudinal proper time, Q is related to the saturation scales Qs of the two nuclei, and a=ln(Q2/m2) with mascale to be defined later. Our results are generally applicable if τ 1/Q. As already discussed in a previous paper, the transverse energy flow Si of the gluon field exhibits hydrodynamiclike contributions that follow transverse gradients of the energy density . In addition, a rapidity-odd energy flow also emerges from the non-Abelian analog of Gauss' law and generates nonvanishing angular momentum of the field. We discuss the space-time picture that emerges from our analysis and its implications for observables in heavy-ion collisions.
Bibliographical noteFunding Information:
This work was supported by the Office of Science, U. S. Department of Energy, and by the U. S. National Science Foundation.
R.J.F. and G.C. thank L. McLerran for discussion and encouragement, and R.J.F. and J.I.K. thank L. Csernai for comments on the manuscript. We are grateful to M. Li for checking many equations in the manuscript for errors and typos. R.J.F. and G.C. were supported by the U.S. National Science Foundation through CAREER Grant No. PHY-0847538 and by the JET Collaboration and Department of Energy Grant No. DE-FG02-10ER41682. G.C. also acknowledges partial support from the US Department of Energy Grant No. DE-FG02-87ER40371. J.I.K. and Y.L. were supported by the Department of Energy Grant No. DE-FG02-87ER40328. We thank F. Gelis for the numbers used to reproduce the results from Ref.  in Fig. 5.