Time-dependent observables in heavy ion collisions. Part I. Setting up the formalism
- 36 Downloads
We adapt the Schwinger-Keldysh formalism to study heavy-ion collisions in perturbative QCD. Employing the formalism, we calculate the two-point gluon correlation function G 22 aμ,bν due to the lowest-order classical gluon fields in the McLerran-Venugopalan model of heavy ion collisions and observe an interesting transition from the classical fields to the quasi-particle picture at later times. Motivated by this observation, we push the formalism to higher orders in the coupling and calculate the contribution to G 22 aμ,bν coming from the diagrams representing a single rescattering between two of the produced gluons. We assume that the two gluons go on mass shell both before and after the rescattering. The result of our calculation depends on which region of integration over the proper time of the rescattering τ Z gives the correct correlation function at late proper time τ when the gluon distribution is measured. For (i) τ Z ≫ 1/Q s and τ − τ Z ≫ 1/Q s (with Q s the saturation scale) we obtain the same results as from the Boltzmann equation. For (ii) τ − τ Z ≫ τ Z ≫ 1/Q s we end up with a result very different from kinetic theory and consistent with a picture of “free-streaming” particles. Due to the approximations made, our calculation is too coarse to indicate whether the region (i) or (ii) is the correct one: to resolve this controversy, we shall present a detailed diagrammatic calculation of the rescattering correction in the φ4 theory in the second paper of this duplex.
KeywordsPerturbative QCD Quark-Gluon Plasma
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- L. Kadanoff and G. Baym, Quantum Statistical Mechanics, W.A. Benjamin Inc., New York U.S.A. (1962).Google Scholar
- M.L. Bellac, Thermal field theory, Cambridge University Press, Cambridge U.K. (2011).Google Scholar
- Y.V. Kovchegov and B. Wu, Time-dependent observables in heavy ion collisions II: in search of pressure isotropization in the φ 4 theory, in preparation (2017).Google Scholar
- M.E. Peskin and D.V. Schroeder, An Introduction to quantum field theory, Addison-Wesley, Reading U.S.A. (1995).Google Scholar