Abstract
We derive the in-medium gluon radiation spectrum off a quark within the path integral formalism at finite energies, including all next-to-eikonal corrections in the propagators of quarks and gluons. Results are computed for finite formation times, including interference with vacuum amplitudes. By rewriting the medium averages in a convenient manner we present the spectrum in terms of dipole cross sections and a colour decoherence parameter with the same physical origin as that found in previous studies of the antenna radiation. This factorisation allows us to present a simple physical picture of the medium-induced radiation for any value of the formation time, that is of interest for a probabilistic implementation of the modified parton shower. Known results are recovered for the particular cases of soft radiation and eikonal quark and for the case of a very long medium, with length much larger than the average formation times for medium-induced radiation. Technical details of the computation of the relevant n-point functions in colour space and of the required path integrals in transverse space are provided. The final result completes the calculation of all finite energy corrections for the radiation off a quark in a QCD medium that exist in the small angle approximation and for a recoilless medium.
Highlights
By rewriting the medium averages in a convenient manner we present the spectrum in terms of dipole cross sections and a colour decoherence parameter with the same physical origin as that found in previous studies of the antenna radiation
This factorisation allows us to present a simple physical picture of the mediuminduced radiation for any value of the formation time, that is of interest for a probabilistic implementation of the modified parton shower
The dense and hot state of matter produced in heavy ion collisions, commonly referred to as a quark-gluon plasma (QGP), is characterised by the deconfinement of quarks and gluons up to distances much larger than the size of hadrons
Summary
The dense and hot state of matter produced in heavy ion collisions, commonly referred to as a quark-gluon plasma (QGP), is characterised by the deconfinement of quarks and gluons up to distances much larger than the size of hadrons. The large centre-of-mass collision energy per nucleon pair in collider experiments — the Relativistic Heavy Ion Collider (RHIC) at BNL and, above all, the Large Hadron Collider (LHC) at CERN — leads to abundant hard particle production and, to the possibility of measuring a variety of observables with high statistics Among such hard probes, those related to the modification of jets and jet-like properties of particle production resulting from the effects imparted by the hot and dense medium to the propagation dynamics of high-energy particles — what is commonly referred to as jet quenching, see e.g. We find that colour coherence between the outgoing quark and gluon survives longer than in those calculations done in the eikonal limit for all propagators but the one of the softest particle, suppressing the spectrum of radiated gluons All these corrections are found to vanish in the limit of negligible formation time of the produced gluon, where we recover the results known in the literature, in particular those in [37].
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