High energy factorization in nucleus-nucleus collisions

TL;DR

The paper develops a high-energy factorization for inclusive gluon production in nucleus–nucleus collisions within the Color Glass Condensate framework. It derives a retarded, all-orders leading-log resummation where LL x and ρ-enhanced contributions are absorbed into JIMWLK-evolved weight functionals W_Y[ρ], yielding a convolution of evolved sources with the LO gluon production operator. A novel derivation shows the JIMWLK Hamiltonian can be obtained purely from retarded light-cone Green's functions, enabling a clean factorization proof for A+A that generalizes known results in pA and clarifies the role of inclusivity. The results connect the early-time Glasma dynamics to the later hydrodynamic evolution and highlight paths to include instabilities and subleading effects in future extensions.

Abstract

We derive a high energy factorization theorem for inclusive gluon production in A+A collisions. Our factorized formula resums i) all order leading logarithms (g^2 \ln(1/x_{1,2}))^n of the incoming partons momentum fractions, and ii) all contributions (g ρ_{1,2})^n that are enhanced when the color charge densities in the two nuclei are of order of the inverse coupling-- ρ_{1,2}\sim g^{-1}. The resummed inclusive gluon spectrum can be expressed as a convolution of gauge invariant distributions W[ρ_{1,2}] from each of the nuclei with the leading order gluon number operator. These distributions are shown to satisfy the JIMWLK equation describing the evolution of nuclear wavefunctions with rapidity. As a by-product, we demonstrate that the JIMWLK Hamiltonian can be derived entirely in terms of retarded light cone Green's functions without any ambiguities in their pole prescriptions. We comment on the implications of our results for understanding the Glasma produced at early times in A+A collisions at collider energies.

Figures (9)

• Figure 1: The closed time path used in the Schwinger-Keldysh formalism.
• Figure 2: A locally space-like surface $\Sigma$ used to define the initial value of the color field.
• Figure 3: NLO corrections in the single nucleus case, seen as an initial value problem on the surface $x^-=\epsilon$. The shaded area represents the domain where the nuclear color sources live ($0\le x^-\le\epsilon$). The field fluctuations represented in red continue to evolve in the region $x^->\epsilon$ until they hit the operator we want to evaluate. However, this evolution is entirely hidden in the dependence of the classical field upon its initial value at $x^-=\epsilon$, and we do not need to consider it explicitly.
• Figure 4: Leading logarithmic contribution of the tadpole diagram.
• Figure 5: 2-loop contributions made of products of pieces already encountered at 1-loop. Although we do not make this distinction in the figure, one of the factors is attached at a slightly smaller value of $x^-$, because the two Hamiltonians in eq. (\ref{['eq:tmp1']}) are at different rapidities.