# Presentation: 102164

##  Heavy quark energy loss:       radiative v.s. collisional

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

## Quark Gluon Plasma

**Form, observe and understand Quark-Gluon Plasma (QGP).****    **

**Heavy quarks (charm and beauty, M>1 GeV) are widely recognized as the cleanest probes of QGP.**

**High Energy Heavy Ion Physics**

**Heavy mesons not yet available, but they are expected soon!**

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

## Indirect probe- single electron suppression – is available

**Significant reduction at high pT suggests sizeable heavy quark energy loss!**

**Indirect probe- single electron suppression – is available**

**V. Greene, S. Butsyk, QM2005 talks**

**J. Dunlop, J. Bielcik; QM05 talks**

**Can this be explained by the energy loss in QGP? **

## Outline

**Discuss the heavy quark energy loss mechanisms:**
**Radiative energy loss. **
**Collisional energy loss.**
**Single electron suppression results that come from the above mechanisms.**

## Radiative heavy quark energy loss 

**Thre****e important medium effects**** control the radiative energy loss:**** **
**Ter-Mikayelian effect ****(M.L.Ter-Mikayelian (1954); Kampfer-Pavlenko (2000);  Djordjevic-Gyulassy (2003))**** **
**Transition radiation ****(Zakharov (2002); Djordjevic (2006)).**** **
**Medium induced radiative energy loss                                          ****(Djordjevic-Gyulassy (2003); Zhang-Wang-Wang (2004); Armesto-Salgado-Wiedemann (2004))**

**                    ****1)                                         2)                                         3)**

## Transition & Ter-Mikayelian effects on 0th order radiative energy loss

**Transition & Ter-Mikayelian effects on 0****th**** order radiative energy loss**

**Transition & Ter-Mikayelian effects approximately ****cancel**** each other for heavy quarks.**

**M.D., Phys.Rev.C73:044912,2006 **

**CHARM**

**BOTTOM**

## Medium induced radiative energy loss 

**Medium induced radiative energy loss **

**To compute medium induced radiative energy loss for heavy quarks we generalize GLV method, by introducing both       quark *****M***** and gluon mass *****m******g******.***

**Neglected in further computations.**

**Caused by the multiple interactions of partons in the medium.**

## This leads to the computation of the fallowing types of diagrams:

**Final Result to Arbitrary Order in Opacity (L/********)**** with M****Q ****and m****g****> 0**

**M. D. and M. Gyulassy, Phys. Lett. B 560, 37 (2003); Nucl. Phys. A 733, 265 (2004)**

##          LHC, dNg/dy=3000

**         ****LHC, dN****g****/dy=3000**

**        ****RHIC, dN****g****/dy=1000**

**Numerical results for 1****st**** order in opacity induced radiative energy loss**** **

## Can single electron suppression  be explained by the radiative energy loss in QGP? 

**M. D., M. Gyulassy, R. Vogt and S. Wicks, Phys. Lett. B 632, 81 (2006) **

**Can single electron suppression  be explained by the radiative energy loss in QGP? **

**Radiative energy loss predictions with dN****g****/dy=1000**

**Disagreement!**

## Is collisional energy loss also important?

**E. Braaten and M. H. Thoma,   ****Phys. Rev. D 44, 2625 (1991). **
**M. H. Thoma and M. Gyulassy, ****Nucl. Phys. B 351, 491 (1991).**

**Collisional energy loss is negligible!**

**Conclusion was based on inaccurate assumptions (i.e. they used ****α****=0.2), and assumed that dE/dL<0.5 GeV/fm is negligible.  **

**Early work:**

**Recent work:**

**Is collisional energy loss also important?**

**Collisional and radiative energy losses are comparable!**
**M.G.Mustafa,Phys.Rev.C72:014905,2005**
**A. K. Dutt-Mazumder et al.,Phys.Rev.D71:094016,2005 **

**Will collisional energy loss still be important once ****finite size**** effects are included?**

**Above computations are done in an ideal ****infinite**** QCD medium. **

## 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 which there are more outgoing than incoming particles:**

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

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

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

## Collisional energy loss in a finite size QCD medium

**The 0****th**** order collisional energy loss is determined from:**

**Collisional energy loss in a finite size QCD medium**

**Consider a medium of size L in thermal equilibrium at temperature T.**

**M.D., nucl-th/0603066**

## Comparison between computations of collisional energy loss in finite and infinite QCD medium

**Comparison between computations of collisional energy loss in finite and infinite QCD medium**

**Finite size effects are not significant, except for very small path-lengths.**

**M.D., nucl-th/0603066**

## Comparison between charm and bottom collisional energy loss

**Bottom quark collisional energy loss is significantly smaller than charm energy loss.**

**M.D., nucl-th/0603066**

**Comparison between charm and bottom collisional energy loss**

## Collisional v.s. medium induced radiative energy loss

**Collisional v.s. medium induced radiative energy loss**

**M.D., nucl-th/0603066**

**Complementary approach by A. Adil *****et al.*****, nucl-th/0606010: consistent results obtained.**

## Most up to date single electron prediction    (collisional + radiative)

**Most up to date single electron prediction    (collisional + radiative)**

**Inclusion of collisional energy loss leads to better agreement with single electron data, even for dN****g****/dy=1000.**

**(****S. Wicks****, W. Horowitz, M.D. and M. Gyulassy, nucl-th/0512076)**

**Radiative energy loss alone is not able to explain the single electron data, as long as realistic gluon rapidity density dNg/dy=1000 is considered.**

**See talk by S. Wicks, parallel session I**

## Conclusions

** ****Radiative energy loss mechanisms alone are not able to explain the recent single electron data. **
**Collisional and radiative energy losses are comparable, and both contributions are important in the computations of jet quenching. **
** **
**Inclusion of the collisional energy loss lead to better agreement**** with the experimental results. **

## Acknowledgements:

**Miklos Gyulassy**
**(Columbia University)**
**Simon Wicks**
**(Columbia University)**
**Ramona Vogt**
**(LBNL, Berkeley and University of California, Davis)**
**William Horowitz**
**(Columbia University)**

## Ter-Mikayelian effect

**This is the ****non-abelian analog**** of the well known ****dielectric plasmon effect**** ********(k************pl********~ gT.**
**In pQCD**** ****vacuum**** ****gluons are massless and**** ****transversely polarized****. ****However, in a ****medium**** the gluon propagator has both****       ****transverse**** ****(****T****)**** ****and**** longitudinal**** ****(****L****)**** ****polarization parts. **

**T**

**L**

**vacuum**

## In order to compute the main order radiative energy loss we calculated |Mrad|2, where Mrad is given by Feynman diagram:

**We used the optical theorem, i.e.:**

**Where *****M***** is the amplitude of the following diagram:**

**Dielectric**
**Effect**

## This computation was performed assuming a static medium.

**This computation was performed assuming a static medium.**

**To compute the effect we start from work by**** ****B.G. Zakharov,**** ****JETP Lett.76:201-205,2002****.**

## Single electron suppression

**2) Heavy quark energy loss**
**3) c and b fragmentation functions into D, B mesons **
**4) Decay of heavy mesons to single e****-****.**

**Single electron suppression**

## Initial heavy quark pt distributions

**Initial heavy quark pt distributions**

**High quark mass, i.e. M****»****Λ****QCD**

**Perturbative calculations of heavy quark production possible.**

**M. Cacciari, P. Nason and R.Vogt, Phys.Rev.Lett.95:122001,2005;  **
**MNR code**** ****(M. L. Mangano, P.Nason and G. Ridolfi*****,***** Nucl.Phys.B373,295(1992)).****                    **
**R.Vogt, Int.J.Mod.Phys.E 12,211(2003).**

## Pt distributions of charm and bottom before and after quenching at RHIC

**M. D., M. Gyulassy and S. Wicks, Phys. Rev. Lett. 94, 112301 (2005).**

**Pt distributions of charm and bottom before and after quenching at RHIC**

**M. Gyulassy, P. Levai and I. Vitev, Phys.Lett.B538:282-288 (2002).**

## Single electrons pt distributions

**Panels show ****single e****-**** from ****FONLL**** **
**M. Cacciari, P. Nason and R. Vogt, ****Phys.Rev.Lett.95:122001,2005**
**M. D., M. Gyulassy, ****R. Vogt**** and ****S. Wicks****, Phys.Lett.B632:81-86,2006**

**Single electrons pt distributions**

**Before quenching**

**After quenching**

**Bottom dominate**** the single**** e****-**** ****spectrum above**** 4.5 GeV****!**

## Single electron suppression as a function of pt 

**Single electron suppression as a function of pt**

**At pt~5GeV, ****R****AA****(e****-****)**** ******** 0.7****±****0.1**** ****at RHIC.**** **

## Are there other energy loss mechanisms?

**Are there other energy loss mechanisms?**

**Collisional and radiative energy losses are comparable!**
**M.G.Mustafa,Phys.Rev.C72:014905,2005 **

**Finite size effects significantly lower collisional energy loss**
**S. Peigne, P.-B. Gossiaux, T. Gousset,     hep-ph/0509185**

**The paper, however, did not make separation between elastic and part of radiative energy loss effects.**** **

## The numerical results can be understood from:

**The numerical results can be understood from:**

**1****st**** order energy loss can ****not ****be characterized only by a “Dead-cone” effect!**

**LPM**** effects are ****smaller**** for ****heavy**** than for light quarks!**

**Results confirmed by two independent groups:                                                               ****B. W. Zhang, E. Wang and X. N. Wang, ****Phys.Rev.Lett.93:072301,2004;****                           N. Armesto, C. A. Salgado, U. A. Wiedemann, ****Phys.Rev.D69:114003,2004. **

## Suppose that pions come from light quarks only and single e-from charm only. 

**Why, according to pQCD, pions have to be at least two times more suppressed than single electrons?**

**Suppose that pions come from light quarks only and single e****-****from charm only.**** **

**Pion and single e****-**** suppression would really be the same. **

**However,**
**Gluon contribution to pions increases the pion suppression****, while**

**2) Bottom contribution to single e****-**** decreases the single e****-**** suppression**
**leading to ****at least factor of 2 difference**** between pion and single e****-**** R****AA****.**

## Comparison with other models

**Ideal infinite QCD medium case:**

- Thoma-Gyulassy (1990) (linear response approach).
- Braaten-Thoma (1991) (quantum-mechanical approach).
- Romatasche-Strickland (2003) (anisotropic medium).

**Finite QCD medium case:**

- Peigne-Gossiaux-Gousset (hep-ph/0509185, 2005) (linear response approach): Finite size effects significantly reduce the collisional energy loss.
- Wang (nucl-th/0604040, 2006) (quantum-mechanical approach):                                                             interference effects exist at 0th order energy loss level.
- Adil-Gyulassy-Horowitz-Wicks (nucl-th/0606010, 2006) (linear response approach): obtained consistent results.