# Presentation: 542580

## Heavy quark energy loss in a dynamical QCD medium

**Magdalena Djordjevic**
**The Ohio State University**

**M. Djordjevic and U. Heinz, arXiv:0705.3439 [nucl-th] **

## Heavy flavor (charm and beauty) suppression is widely recognized as the excellent probes of QGP at RHIC and LHC. 

**N. Brambilla et al., e-Print hep-ph/0412158 (2004)**.

**High pt suppression is a consequence of the energy loss.**

**Reliable computations of energy loss mechanisms are needed.**

## Radiative energy loss

**Collisional energy loss**

**Collisional energy loss comes from the processes which have the same number of incoming and outgoing particles:**

**Radiative energy loss comes from the processes in which there are more outgoing than incoming particles:**

**0****th**** order**

**1****st**** order**

**0****th**** order**

## This motivated an approximation by which a medium is composed of static constituents (modeled by Yukawa potential). This model was used in all heavy flavor radiative energy loss calculations by now.

**This motivated an ****approximation**** by which a ****medium is composed of static constituents**** (modeled by Yukawa potential). This model was used in all heavy flavor radiative energy loss calculations by now.**

**Approximation consequence: ****In such a medium, collisional energy loss has to be ****exactly equal to zero****!**

**Until recently, a generally held belief was that the radiation is the dominant energy loss mechanism.**
** ****(Based on early computations by Braaten and Thoma 1991; Thoma and Gyulassy 1991, BDMPS 1995.)**

**Apparently consistent**

## However, recent collisional energy loss computations showed that collisional and radiative energy losses are comparable.

**However, recent collisional energy loss computations showed that ****collisional and radiative energy losses are comparable****.**

**M.G.Mustafa,Phys.Rev.C72:014905,2005**

**M.Djordjevic,Phys.Rev.C74:064907,2006**

**Collisional energy loss results are ****inconsistent ****with static approximation!**

**Can static medium approximation be used in radiative energy loss calculations?**

## Our goal

**We want to compute the heavy quark radiative energy loss in ****dynamical medium**** of thermally distributed massless quarks and gluons. **

**Why?**

** ****To address the ****applicability**** of static approximation in radiative energy loss computations. **
** ****To compute collisional and radiative energy losses within a ****consistent ****theoretical framework. **

**M. Djordjevic and U. Heinz, arXiv:0705.3439 [nucl-th] **

## Radiative energy loss in a dynamical medium

**Radiative energy loss in a dynamical medium**

**We compute the medium induced radiative energy loss for a heavy quark to first (lowest) order in number of scattering centers. **
**To compute this process, we consider the radiation of one gluon induced by one collisional interaction with the medium. **

**To simplify the calculations, we consider the Bethe-Heitler limit.                           The calculations were performed by using two Hard-Thermal Loop approach.**

## For exchanged gluon, cut 1-HTL gluon propagator cannot be simplified, since both transverse (magnetic) and longitudinal (electric) contributions will prove to be important.

**For ****exchanged gluon****, cut 1-HTL gluon propagator cannot be simplified, since ****both transverse**** (magnetic) ****and longitudinal ****(electric)**** ****contributions will prove to be ****important****.**

**For ****radiated gluon****, cut 1-HTL gluon propagator can be**** simplified**** to ****(M.D. and M. Gyulassy, PRC 68, 034914 (2003).**

## 1st group of diagrams presents contributions where both ends of the exchanged gluon q are attached to the heavy quark, i.e. no 3-gluon vertex is involved:

**1****st**** group of diagrams presents contributions where both ends of the exchanged gluon *****q***** are attached to the heavy quark, i.e. no 3-gluon vertex is involved:**

**Logarithmic ****divergence**** is a consequence of the ****absence**** ****of magnetic mass.**

**M. D. and U. Heinz, arXiv:0705.3439 [nucl-th] **

## 2nd group of diagrams presents contributions where only one end of the exchanged gluon q is attached to the heavy quark:

**3****rd**** contribution presents a diagram where both ends of the exchanged gluon *****q *****are attached to the radiated gluon *****k*****:**

## The divergence is naturally regulated when all the diagrams are taken into account.

**The divergence is naturally regulated when all the diagrams are taken into account.**

## Radiative energy loss in dynamical QCD medium

**Radiative energy loss in dynamical QCD medium**

**M. D. and U. Heinz, arXiv:0705.3439 [nucl-th] **

## Radiative energy loss in static QCD medium

**Assume thermal QCD medium composed of static sacattering centers.**** **

## Comparison of radiative energy loss formulas in dynamical and static medium

**Dynamical medium**

**Static medium**

**Comparison of radiative energy loss formulas in dynamical and static medium**

**M. D. and U. Heinz, arXiv:0705.3439 [nucl-th] **

## Dynamical vs. static radiative energy loss at the RHIC

- dynamic

- static

- static

- static

- dynamic

- dynamic

- s=0.3, L=5fm, T=225 GeV

## Ratio of dynamical and static radiative energy loss at RHIC

**Ratio of dynamical and static radiative energy loss at RHIC**

- 75%

**M. D. and U. Heinz, arXiv:0705.3439 [nucl-th] **

- s=0.3, L=5fm, T=225 GeV

- CHARM

## Dynamical vs. static radiative energy loss at the LHC

**There is ****no jet energy domain**** where the assumptions of static scattering scatterers becomes a valid approximation.**

**Dynamical vs. static radiative energy loss at the LHC**

**Dynamical effects important for ****all types of quarks****!**

- 80%

**M. D. and U. Heinz, arXiv:0705.3439 [nucl-th] **

- s=0.3, L=5fm, T=400 GeV

## What is the origin of such energy loss increase?

**What is the origin of such energy loss increase?**

**electric contribution**

**magnetic contribution**

**In dynamical medium both electric and magnetic contributions from the exchanged (virtual) gluons contribute to the energy loss.**

## Electric v.s. magnetic contribution to the radiative energy loss in dynamical QCD medium

**Electric v.s. magnetic contribution to the radiative energy loss in ****dynamical ****QCD medium**

**Both contributions are equally important!**

**dynamical medium**

## On the other hand, in static medium only electric contribution from the exchanged gluon contribute to the energy loss:

**electric contribution**

**static medium**

## Inclusion of dynamical effects leads to a slight reduction of the electric contribution to the radiative energy loss.

**Inclusion of dynamical effects leads to a ****slight reduction**** of the**** electric ****contribution to the radiative energy loss.**

**Additional ****magnetic contibution**** is the reason for a significant ****increase ****of**** ****the radiative energy loss in dynamical medium.**

## Summary

**We studied the radiative energy loss for both light and heavy quarks, in dynamical medium of thermally distributed massless quarks and gluons. **
**While each individual contribution to the energy loss in a dynamical medium is infrared divergent (due to the absence of magnetic screening), there sum lead to an infrared safe result. **
**The energy loss in a dynamical medium is almost 75% larger than in a static medium. Therefore, the constituents of QCD medium  *****can not*****  be approximated as static scattering centers.**** **
**The increase of the energy loss is exclusively due to the magnetic contribution of the exchanged gluon.**

## Conclusion and future directions

**The dynamical effects are important, and have to be included in the computation of jet energy loss.**
**The observed quark energy loss could be significantly larger than previously thought. **
**The computation of heavy quark energy loss in a finite size dynamical QCD medium is the next important goal to obtain the the reliable quantitative predictions of radiative energy loss and jet suppression in the upcoming RHIC and LHC experiments.**

## backup

## Comment on BDMPS approach

**Static medium:**

**Dynamical medium:**

**0**

** ****Deep LPM regime**
** ****Huge number of scatterings**

**BDMPS does not distinguish between dynamical and static medium!**

## Static medium:

**Static medium:**

**Dynamical medium:**

** ****is not well defined in dynamical medium. There are two possible choices:**

## Radiative energy loss in static QCD medium

**Assume thermal QCD medium composed of static sacattering centers.**** **

## Computational assumptions

*** ******E***** ********* ********* ********* ******k******t*****,***** q******t*****, ****where ******** (*****E*****) is the gluon (jet) energy, and *****k******t****** *****(*****q******t*****)***** *****is the transverse momentum of the radiated (exchanged) gluon.**
**Additional assumptions:**
** ****Spin in the problem is neglected.**
** ****Highly energetic jet, such that we can assume ************************1****              (M is the mass of the heavy quark jet).**

**Computational assumptions**