Gluon radiation from a classical point particle. II. Dense gluon fields

Abstract

The goal of this paper is to extend the results of Ref. [1], where formulae were derived for gluonic radiation for a high energy nucleus colliding with a classical colored particle. In Ref.[1], we computed the amplitudes for radiation in the fragmentation region of the particle for a dilute gluonic field. In this paper, we compute the radiation by solving the fluctuation equations of the dense background field in a specific gauge which makes it simple to solve the asymptotic radiation from an initial condition immediately after the passage of the nucleus. We identify and compute two components of gluon radiation, a bulk component which extends to the central region and bremsstrahlung, which may give rise to an experimentally observable intensity peak in the target fragmentation region.

Classical Yang-Mills observables from amplitudes

“…Indeed it is in this context that the classical theory has its main application, as a tool to model transport phenomena in non-Abelian plasmas in the very high temperature regime [113][114][115][116][117][118]. The equations of motion also provide a successful approximation for calculating the gluon distribution functions from deeply inelastic, ultrarelativistic ion collisions [119][120][121], and radiation from classical particles has recently been calculated in this regime [122,123].…”

Gluon bremsstrahlung in relativistic heavy ion collisions

“…As noted in Ref. [12], the classical treatment of the particle computation breaks down in this region. This result should allow a proper matching onto the high transverse momentum region of the emitted gluon, as in this region one can compute the radiation perturbatively, and the contribution we present should be of leading order.…”

“…In previous works, Kajantie, McLerran, and Paatelainen [11,12], proceeding in this spirit of classical Yang-Mills equations, took steps towards calculating small-k ⊥ gluon radiation in the fragmentation region of nucleus-nucleus collisions. We now give a very brief overview of their key results, highlighting the issues we wish to address.…”

“…Specifically, the problem considered in Refs. [11,12] is that of gluon radiation produced when a sheet of colored glass interacts with a classical particle that has an associated colorcharge vector T. One then finds two sources of radiation: the first is electrodynamics-like (ED-like) bremsstrahlung of a charged particle getting a momentum kick from p to p ; the second, which they term the bulk contribution, is from interaction of a gluon emitted by the target quark with the sheet of colored glass, with a term with no reinteraction subtracted. The former is calculated from the following radiation current,…”

“…Indeed the calculation as done in Refs. [11,12] was only meant to be valid for small k ⊥ , i.e., when the gluon does not carry away a significant fraction of the quark's momentum.…”