arXiv:1106.5231v1 [nucl-th] 26 Jun 2011
QUANTUM SPECTRUM OF CHERENKOV GLUE
M. N. Alfimov∗, A. V. Leonidov†
P.N. Lebedev Physical Institute
119991 Leninsky pr. 53, Moscow, Russia
Full quantum calculation of Cherenkov gluon radiation by quark and gluon currents and a
Cherenkov decay of a gluon into a pair of Cherenkov gluons in transparent media is performed.
Energy losses due to Cherenkov gluon radiation in high energy nuclear collisions are calculated. The
angular distribution of the energy flow due to the radiation of Cherenkov gluons is analyzed.
∗Also at the Moscow Institute of Physics and Technology.
†Also at the Institute of Theoretical and Experimental Physics.
Experimental observation of the two-humped structure of dihadron angular correlations in ultrarel-
ativistic heavy ion collisions at RHIC [1, 2, 3, 4, 5, 6] bearing a remarkable likelihood to the angular
distribution of Cherenkov photons  has brought into the focus of attention a possible existence of the
phenomenon of Cherenkov radiation of gluons, an idea formulated in [8, 9] and applied to the analysis
of ring-like structures in cosmic ray events in .
Interpretation of the experimental data in terms of the Cherenkov radiation of gluons is not unique.
Theoretical descriptions aiming at describing the double-humped angular pattern of two-particle az-
imuthal correlations include that in terms of the Mach cone generated by jets propagating in dense
medium, see e.g. the recent analysis in , as well as in terms of originating from dynamical fluctu-
ations of the expanding hot and dense fireball . From the experimental point of view it has been
demonstrated  that in the case of large rapidity interval between the two particles and for one specific
choice of transverse momenta bins for trigger and associated particles the resulting angular pattern can
be completely described by the azimuthal asymmetries of the collective flow. In the case of narrow
rapidity interval the situation looks different, see a detailed argumentation in , and the problem of
finding an appropriate description for the experimental data at the level of detalization of  is, in our
opinion, still open.
The Cherenkov radiation of gluons is a manifestation of nontrivial properties of nonabelian medium
created in ultrarelativistic heavy ion collisions .
Cherenkov gluon radiation and a summary of earlier work was presented in . The analysis of 
was based on a straightforward generalization of the classical Tamm-Frank theory . A simple field-
theoretical model of two interacting scalar fields leading to Cherenkov excitations was considered in .
A model taking into account the opacity of the medium and rescattering of Cherenkov gluons consid-
ered in  was shown to successfully reproduce the experimental data on double-humped correlations
[1, 2, 3, 4, 5, 6]. A new line of studies was started in [19, 20] where a theory of Cherenkov radiation of
mesons was constructed in the framework of holographic approach to strong interactions.
To develop a more reliable theoretical picture for Cherenkov radiation of gluons one has to generalize
the classical approach of [8, 9, 15] and the simple scalar field model of  to a quantum field theory
description based on in-medium QCD. The main goal of the present paper is to develop such an approach
to Cherenkov gluon radiation of quark and gluon currents1. Our consideration is essentially based on
the quantum theory of electromagnetic Cherenkov radiation developed in , see also . Recently
the approach of  was generalized to the case of a moving medium .
The calculation of Cherenkov gluon radiation by quark currents presented below is a straightforward
generalization of the abelian case considered in . The calculation of Cherenkov radiation of gluon
currents and of the gluon decay into a pair of Cherenkov gluons are new. The corresponding expressions
and the resulting qualitative picture of the pattern of energy loss related to the Cherenov radiation
present the main results of the present paper.
The plan of the paper is as follows.
In the paragraph 2.1 we give some general remarks on the physics of Cherenkov radiation.
In the paragraph 2.2 we compute the rate of the single Cherenkov decay of the quark current.
In the paragraph 2.3 we compute the rate of the single Cherenkov decay of the gluon current.
In the paragraph 2.4 we compute the rate of the double Cherenkov decay of the gluon current.
In the Appendix A we describe a simple field-theoretical model justifying the Feynman rules for
in-medium QCD used in the paper.
The interpretation of RHIC data in terms of
2Single and double Cherenkov decays
In this section we compute the spectra of Cherenkov gluons radiated by quark and gluon currents
and the spectrum of Cherenkov gluons created in the decay of a free gluon into two Cherenkov gluons.
1Some preliminary results were discussed in .
and, therefore, the following decomposition for Aai:
Aai(x) = Aai
(1)(x) + Aai
(λ)(k), |k| = k0;
(λ)(k), |k| =√εk0;(A.14)
It is easy to check that in order to be consistent with the commutation relations for the vector potential
the gluon polarization vectors should be normalized as follows: (ei
and ε(? ei
(1,2)(k))2= 1 for the ”ordinary” gluons
(1,2)(k))2= 1 for in-medium gluons.
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