High energy factorization in nucleus-nucleus collisions. I

Abstract

We derive a high energy factorization theorem for inclusive gluon production in $\mathrm{A}+\mathrm{A}$ collisions. Our factorized formula resums (i) all-order leading logarithms $({g}^{2}\mathrm{ln}(1/{x}_{1,2}){)}^{n}$ of the incoming parton momentum fractions, and (ii) all contributions $(g{\ensuremath{\rho}}_{1,2}{)}^{n}$ that are enhanced when the color charge densities in the two nuclei are of order of the inverse coupling---${\ensuremath{\rho}}_{1,2}\ensuremath{\sim}{g}^{\ensuremath{-}1}$. The resummed inclusive gluon spectrum can be expressed as a convolution of gauge invariant distributions $W[{\ensuremath{\rho}}_{1,2}]$ 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 wave functions 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.