Radiative heavy quark energy loss in QCD matter Magdalena Djordjevic and Miklos Gyulassy Columbia University

 Motivation  Radiative heavy quark energy loss - Ter-Mikayelian effect - Medium induced radiative energy loss  Is there heavy quark suppression at RHIC?  Conclusion 1

One of the most important goals of high energy heavy ion physics is the formation and observation of a quark-gluon Plasma (QGP). What is a good probe for QGP? In 1978 Shuryak has proposed dileptons as an excellent “thermometer” for QGP. The problem with this probe is that QGP is not the only source for the production of dileptons. ** PHENOMENOLOGY OF CHARM AND BOTTOM PRODUCTION. R. Vogt Z.Phys.C71: ,1996 Other important sources for dilepton production: 1) Pion annihilation and resonance decays 2) Open charm contribution 3) Drell-Yan may dominate, respectively, at low, intermediate and high ranges of invariant dilepton mass M. Motivation: 2

*In 1997 Shuryak proposed that open charm background could be reduced if charm quarks suffered a large energy loss when propagating through a high opacity plasma. *ENERGY LOSS EFFECTS ON CHARM AND BOTTOM PRODUCTION IN HIGH-ENERGY HEAVY ION COLLISIONS. Zi-Wei Lin, Ramona Vogt, Xin-Nian Wang Phys.Rev.C57: ,1998 *However, recently (2001) Dokshitzer and Kharzeev proposed that the “dead cone” effect of gluon radiation by a heavy quark may reduce again the hope for reducing open charm background due to energy loss. *PHENIX single e data seem to see no charming nuclear effect ! 3

DOES THE CHARM FLOW AT RHIC? S. Batsouli, S. Kelly, M. Gyulassy, J.L. Nagle Phys.Lett.B 557 (2003) 26 First Au+Au->e X data show no hint of Charm energy loss ! ?? PHENIX Collaboration (K. Adcox et al.) Phys.Rev.Lett.88:192303,2002 At least moderate pT charm is not Suppressed. 4 The motivation for studying heavy quark energy loss in a dense QCD medium: 1. To compute quantitatively the magnitude of radiative energy loss by heavy quarks. 2. And to compute the single and pair lepton observables at RHIC WHERE IS THE CHARM QUARK ENERGY LOSS AT RHIC? M. Djordjevic, M. Gyulassy Phys.Lett.B 560 (2003) 37

Radiative heavy quark energy loss There are two important medium effects that control the radiative energy loss in a QGP. 1)Ter-Mikayelian effect (the plasmon effect) 2)Energy loss due to the interaction with the medium  pl ~gT k gg g c 5

Ter-Mikayelian effect This is a non-abelian analog of a well known Ter- Mikayelian effect in electrodynamics. Effect is connected with the fact that plasma modifies gluon self energy. In perturbative QCD vacuum gluons are massless and transversely polarized partons. However, in the medium gluon propagator has both transverse and longitudinal polarization parts. We compute both longitudinal and transverse contribution to the 0 th order in opacity, by taking into account the momentum dependence of gluon self energy (one-loop (HTL) polarization tensor). 6 The Ter-Mikayelian effect on QCD Radiative Energy Loss M. Djordjevic, M. Gyulassy nucl-th/

 Longitudinal contribution is negligible.  The plasmon effect on transverse contribution is important, since for charm it leads to ~30% suppression of the vacuum radiation. The Ter-Mikayelian effect thus enhances the yield of high transverse charm quarks relative to the vacuum case. 7 Comparison between medium and vacuum 0 th order in opacity fractional energy loss is shown on Fig. 1:

Fig.2 shows the one loop transverse plasmon mass m g (k)  √(  2 -k 2 ). We see that m g starts with the value  pl =µ/√3 at low k, and that as k grows, m g asymptotically approaches the value of m  =µ/√2, in agreement with Rebhan A, Lect. Notes Phys. 583, 161 (2002). We can conclude that we can approximate the Ter-Mikayelian effect by simply taking m g  m . 8

gg g c Energy loss due to the interaction with the medium The second important effect on the energy loss is the induced gluon radiation caused by the multiple interactions of partons in the medium. To compute medium induced radiative energy loss for heavy quarks we have used Gyulassy-Levai-Vitev (GLV) method, in which we now introduced both quark m q and plasmon mass m g =m . 9

The computation was done so far only up to the first order in opacity. The numerical results for induced radiative energy loss are shown on Fig.2 for charm and bottom quark. According to Levai et al. (Levai et al., Nucl. Phys. A 698, 2002), effective static plasma opacity is 3~4 fm. The energy loss plotted on Fig.3 is for effective opacity 4 fm. Fig. 5 10

Fig.4 shows the fractional charm quark energy loss for 10GeV jet as a function of opacity Medium thickness L. Yellow region represents the energy loss which will contribute to the extra pt suppression of charm quark in the medium comparing to the vacuum case. According to the results obtained until now, we can assume that RHIC conditions belong somewhere in the shaded region of this figure. 11 Is there heavy quark suppression at RHIC?

We see that in this region additional energy loss is small, and thus it would lead to small suppression of high pt charm yield comparing to the vacuum case. Therefore, this may be the reason why the charm yield suppression has not been observed at RHIC. 12

Conclusion Ter-Mikayelian Radiation due to multiple interactions of partons in the medium 13 Single e 10% Central Au-Au data can be explained by two different approaches: Hydro PYTHIA pQCD Decisive test between these two approaches would be the measurement of v2 for charm at RHIC.  Observation of the elliptic flow would means that charm flows at RHIC.  However, if no charm elliptic flow is observed, then we propose that nonexistence of significant difference between charm yield in medium and vacuum can be explained by the cancellation of two medium effects: