1. Jet energy loss at RHIC and LHC including collisional and radiative and geometric fluctuations Simon Wicks, QM2006 Work done with Miklos Gyulassy, William Horowitz, Magdalena Djordjevic Institut für Theoretische Physik

2. 2 Simon Wicks Sunday 19 th November 2006 pQCD and energy loss At RHIC and LHC: Radiative mechanisms are important, but not ‘dominant’ SW, W. Horowitz, M. Djordjevic M. Gyulassy ( WHDG ) nucl-th/0512076 M. Mustafa, Phys. Rev. C72:014905 (2005)

3. 3 Simon Wicks Sunday 19 th November 2006 Integration over production positions Integrals over the initial geometry just have to be done.

4. 4 Simon Wicks Sunday 19 th November 2006 WHDG extended theory ~IdealOur model Production All orders pQCD NLO pQCD (FONLL for LHC spectra) (large uncertainty in normalization, small uncertainty in the power law) Geometry Propagate through evolving hydro simulation Realistic Woods-Saxon nuclear density Jets produced ~ T AA Propagate through Bjorken expanding ρ part αsαs Running Fixed α s =0.3 (large uncertainty as energy loss strongly dependent on α s ) Energy loss mechanism Collisional and radiative in same theoretical framework Incoherent addition of DGLV radiative and leading log TG / BT collisional NOTE however: we use physical dN g /dy~1000

5. 5 Simon Wicks Sunday 19 th November 2006 The results – RHIC Important consistency check: Compare predictions to both pion and electron data (WHDG = nucl-th/0512076v3) Result: inclusion of collisional+geometry ~fits pion data, and improves the heavy quark quenching, but still underpredicts pT~4-8 data with FONLL b/c ratio. (B/D ratio or direct D measurement very important to reduce uncertainties) STAR: nucl-ex/0607012, PHENIX (QM2006): nucl-ex/0611018

6. 6 Simon Wicks Sunday 19 th November 2006 The results – More RHIC Integrated RAA v2

7. 7 Simon Wicks Sunday 19 th November 2006 The results - LHC See William Horowitz’s poster for more details about LHC and comparison to other predictions. Here: estimate dNg/dy=2900 via CGC Note the slope of our pion predictions. Light jetsHeavy jetsPions

8. 8 Simon Wicks Sunday 19 th November 2006 Improving the model 1) Toward a better description of collisional fluctuations. 2) Effects of running QCD coupling.

9. 9 Simon Wicks Sunday 19 th November 2006 Collisional fluctuations in WHDG (Fokker-Planck-like) Fokker-Planck: Characterised by 2 numbers / functions: (drag, diffusion) Small ε approx (used in WHDG): Gaussian, centered at average energy loss (given by BT or TG), width (in WHDG) given by fluctuation-dissipation theorem, σ 2 = 2T (Green curve = collisional fluctuations in WHDG)

10. 10 Simon Wicks Sunday 19 th November 2006 A model of elastic energy loss Use this model in order to study fluctuations: Jet interacts with a medium modified HTL propagator with initially static medium particles which recoil. Mass of medium particle tuned to give ΔE~ ΔE TG or BT Gives mean free path of quark jet ~ 2.5fm m eff ~0.3 GeV E,M

11. 11 Simon Wicks Sunday 19 th November 2006 Bottom jets – extreme 10 collisions (L~25fm) Multiple collisions: Poisson weighted convolution of single collision distribution (ie independent collisions) Bottom, for 10 collisions: Full distribution (red) is wider than the Gaussian (black). Full distribution is still slightly skew even at 10 collisions. Gaussian gives R AA =0.19 vs 0.20 FP good in this case

12. 12 Simon Wicks Sunday 19 th November 2006 Bottom jets – typical 2 collisions (L~5fm) Multiple collisions: Poisson weighted convolution of single collision distribution (ie independent collisions) Bottom, for 2 collisions: Full distribution (red) is wider than the Gaussian (black). Full distribution is very skewed for 2 collisions. Gaussian (FP) approx misses the physics, BUT gets R AA close!

13. 13 Simon Wicks Sunday 19 th November 2006 Light jets – 2 and 5 collisions For small numbers of collisions, the Gaussian / FP-like approximation over predicts the quenching by ~0.1 (similar result for charm quarks)

14. 14 Simon Wicks Sunday 19 th November 2006 Elastic fluctuations: Summary After all the elastic+geometric fluctuations, we expect: All R AA predictions move up, charm, light quarks, gluons (by ~0.1). Bottom quarks stay ~ same place. At  R AA ~0.1 level there are other effects that need to be taken into account: 1) Large theory uncertainty in electron prediction is bottom/charm ratio. 2) … (next slide)

15. 15 Simon Wicks Sunday 19 th November 2006 Effect of running the QCD coupling  (Q 2 )

16. 16 Simon Wicks Sunday 19 th November 2006 Running the QCD coupling I A.Peshier hep-ph/0607275 Braun & Pirner hep-ph/0610331

17. 17 Simon Wicks Sunday 19 th November 2006 Running the QCD coupling II Peshier = Running α, infinite energy jet (black dashed) Running α = finite energy jet “Fixed α (1)”= α at t=(2πT) 2 “Fixed α (2)”= α fixed at 0.3 Model: Bjorken estimate, 1/t 2, cutoff at t=μ 2 1-loop running α, Λ QCD = 0.2GeV. Result: 1)Running alpha results similar to fixed alpha For T< 1GeV except in unphysical E=Infty limit Further investigation needed to determine: R AA prediction including full geometry and elastic fluctuations (in progress)

18. 18 Simon Wicks Sunday 19 th November 2006 Extended WHDG Theory Status 1) WHDG shows that elastic energy loss cannot be neglected in jet tomography. 2) Full geometry path fluctuations must be included. 3) Our extended theory with collisional + radiative +geom comes close to a consistent explanation of both pion and electron data at RHIC. 4) Large uncertainty from bottom/charm ratio,  R AA ~0.2-0.3. 5) Fokker-Planck formalism misses the physics of small collision number distributions. 6) For light quarks and gluons, WHDG with FP elastic fluctuations probably overestimates the influence of collisional by  R AA ~0.1. However: for bottom quarks, the WHDG result for R AA is insensitive to (5)). (=> Bottom quark R AA moves closer to light quark R AA ) 7) Running alpha increases the collisional quenching. Resulting R AA predictions: calculation in progress.