Abstract
We study the effects of adding the Coulomb interactions to the harmonic oscillator (HO) approximation of the heavy parton propagating through the quark–gluon plasma (the extension to QCD of the Molliere theory). We explicitly find the expression for the transverse momentum distribution of the gluon radiation of the heavy quark propagating in the quark gluon plasma in the framework of the Moliere theory, taking into account the BDMPSZ radiation in the HO approximation, and the Coulomb logarithms described by the additional logarithmic terms in the effective potential. We show that these Coulomb logarithms significantly influence the HO distribution, derived in the BDMPSZ works, especially for the small transverse momenta, filling the dead cone, and reducing the dead cone suppression of the heavy quark radiation (dead cone effect). In addition we study the effect of the phase space constraints on the heavy quark energy loss, and argue that taking into account of both the phase space constraints and of the Coulomb gluons reduces the dependence of the heavy quark energy loss on its mass in the HO approximation.
Highlights
The energy loss of a quark propagating in the quark–gluon plasma (QGP) was extensively studied in recent years in different approaches. in particular in the harmonic oscillator approximation, developed by BDMPSZ [1,2,3,4,5,6,7], and in the GLV opacity expansion formalism [8,9,10]
The heavy quark energy loss can be studied in different formalisms, like opacity expansion, harmonic oscillator approximation, ADS/CFT
We see that compared with the BDMPS spectrum calculated with the same boundary conditions, the corrections increase the energy loss and is rather close to GLV energy loss. Note that this is just the qualitative estimate since, as we remarked above, the angular distributions were calculated in soft gluon approximation, and precise phase space constraints are beyond the accuracy of this approximation [15,46]
Summary
The energy loss of a quark propagating in the quark–gluon plasma (QGP) was extensively studied in recent years in different approaches. in particular in the harmonic oscillator approximation, developed by BDMPSZ [1,2,3,4,5,6,7], and in the GLV opacity expansion formalism [8,9,10]. The Moliere theory was extended to the case of heavy quarks in [45] The latter works did not include the study of the transverse momenta distributions, and the energy loss calculated without taking into account the proper phase constraints on the radiated gluons. It is of great interest to include the effects of Coulomb Logarithms in the transverse distributions in the BDMPSZ approach This problem arises the special interest in the case of heavy quarks where the important role of phase constraints was first stressed in [15]. The detailed comparison to the experimental data needs additional model dependent inputs like inclusion of the expansion, correct phase constraints
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