Jet coherence in QCD media: the antenna radiation spectrum
Yacine Mehtar-Tani
1
Konrad Tywoniuk
0
0
Department of Astronomy and Theoretical Physics, Lund University
, Solvegatan 14A, SE-22 362 Lund,
Sweden
1
Institut de Physique Tehorique
, CEA Saclay, F-91191 Gif-sur-Yvette,
France
We study the radiation of a highly energetic partonic antenna in a colored state traversing a dense QCD medium. Resumming multiple scatterings of all involved constituents with the medium we derive the general gluon spectrum which encompasses both longitudinal color coherence between scattering centers in the medium, responsible for the well known Landau-Pomeranchuk-Migdal (LPM) eect, and transverse color coherence between partons inside a jet, leading, in vacuum, to angular ordering of the parton shower. We discuss shortly the onset of transverse decoherence which is reached in opaque media. In this regime, the spectrum consists of independent radiation o the antenna constituents.
Contents
1 Introduction 2 3 4
Decoherence in opaque media
A The reduction formula eq. (3.7)
Color coherence phenomena in a few words
Emission amplitude from classical Yang-Mills equations
The antenna spectrum in the presence of a medium
Introduction
One of the key objectives of the heavy-ion program at the LHC is to investigate
properties of the quark-gluon plasma (QGP) using hard probes. In particular, one addresses
in-medium modications of the fragmentation properties of nal state energetic particles
that depart from the well-known fragmentation pattern in vacuum, for instance in e+e
annihilation, proton-proton collisions etc., where no dense medium is formed. These
modications are assumed to be sensitive to local medium properties, such as the density, as well
as their spatiotemporal evolution. Indeed, strong medium eects are observed in heavy-ion
collisions for both single-inclusive leading particle spectra [1{3] and two-particle
correlations [4, 5]. While such measurements have reached a high level of sophistication, shedding
light on qualitative aspects of the quark-gluon plasma, studies of intrajet distributions in
heavy ion collisions have recently been initiated both at RHIC [6{8] and LHC [9{11] with
many promising results and prospects for the future.
The increased experimental capabilities at these high energies have also triggered
several eorts to improve the theoretical understanding of gluon radiation in the presence
of a colored medium. Until recently, only the leading order one-gluon medium-induced
emission spectrum o a highly energetic quark or gluon, which will be denoted
BDMPSZ throughout, was known [12{15]. Equivalent formulations were also derived in [16{24].
This spectrum measures radiative parton energy loss in the QGP and accounts for
momentum broadening of the radiated gluon which undergoes multiple scattering in the medium.
The characteristic broadening of the transverse momenta of such gluons, arising due to
coherence eects between medium rescatterings, sets an upper bound on the energy of the
induced radiation which, nevertheless, can be quite sizable in relatively opaque media.
Regrettably, since the process under consideration does not deal with interference
effects between emitters, see section 2, the extension to multi-gluon emissions is bound to
rely on ad hoc conjectures. In order to study the importance of these radiative
interferences, lately the gluon emission spectrum o a time-like quark-antiquark ( qq) antenna was
calculated. In [25, 26] we considered an antenna traversing a relatively thin medium, i.e.,
assuming only one scattering in the medium background potential. In [27], on the other
hand, we resummed multiple scatterings in the limit of soft gluon emission. The aim of
the present work is to generalize the latter results to arbitrary number of rescatterings of
the quark, antiquark and gluon, thus extending the validity of our previous ndings to
arbitrarily opaque media and up to large gluon energies. We also briey discuss the main
dierence between the direct and interference contributions which relates to the physics of
decoherence of QCD radiation, thus making contact with our previous work [25, 27].
The key result of this work is the derivation of the interference spectrum, cf. eq. (4.16),
while a complete and detailed discussion of the emerging physical picture is presented
in [26, 28], see also [29] for a complementary discussion. The paper is structured as follows.
At the outset, in section 2, we discuss briey the known coherence phenomena relevant for
high-energy physics and heavy-ion collisions. Then, in section 3, we present and solve the
classical Yang-Mills equations for the qq antenna, thus obtaining a compact expression for
the medium-induced gluon eld. Medium averages for the total spectrum are described in
section 4 where we also present the novel interference spectrum J , given in eq. (4.16), which
encodes the new ingredients of transverse coherence in medium. The general properties
of this spectrum are also outlined in brief. In particul (...truncated)