Away-Side Angular Correlations Associated with Heavy Quark Jets

Transcription

1 Away-Side Angular Correlations Associated with Heavy Quark Jets Jorge Noronha Presented by: William Horowitz The Ohio State University Based on: J.N, Gyulassy, Torrieri, arxiv: [hep-ph] and Betz, Gyulassy, J.N, Torrieri, arxiv: [hep-ph] Workshop on Heavy Quark Physics in Nucleus-Nucleus Collisions, UCLA 2009

2 Outline I Motivation: Di-Jets in HIC II Holographic Description of Heavy Quarks III Cooper-Frye Freeze-out IV Di-Jet Correlations in pqcd x AdS/CFT V Conclusions & Outlook 2

3 I Motivation: Di-Jets in HIC 200 GeV Shoulder peak position nearly independent of: - Centrality - System size - Orientation of the trigger particle w.r.t. to reaction plane PHENIX, ArXiv: v1 [nucl-ex] 3

4 Signature of conical emission? Mach's law H. Stoecker, Nucl.Phys.A750: ,2005. J. Casalderrey-Solana, E. Shuryak, D. Teaney, Nucl.Phys.A774: ,2006. near-side For light partons v ~ 1 then from EOS!!!! However, recent measurements indicate that the peaks are not substantially affected by flow. Mach cones SHOULD be affected by it!!! Is the conical flow observed in the experiment really due to nice and well defined Mach cones? away-side 4

5 - There's still huge theoretical uncertainty to what these peaks correspond to... See, for instance: I. Vitev, PLB 630, 78 (2005). V. Koch, A. Majumber, X-N Wang, PRL 96, (2006). J. Jia, R. Lacey, arxiv: [nucl-th]. TBNG, arxiv: [nucl-th]. If the peaks really correspond to Mach cones, one should be able to see experimentally that the location of the peaks changes with the velocity of the away-side jet according to Mach's law. Current data is for light partons that move with v ~ 1. Thus, away-side correlations associated with tagged heavy quark jets (in which the velocity v can be determined) will provide a direct test of the Mach cone hypothesis. 5

6 However, heavy quark energy loss in the QGP can be a tricky business... See, for instance: Wicks, Horowitz, Djordjevic, Gyulassy, NPA 784, 426 (2007). Due to the uncertainties regarding how large the coupling in the QGP is, we tried to find predictions for the away-side angular correlations involving heavy quarks using two completely different models for the jet+medium interactions: - Strongly-coupled plasma described by the AdS/CFT correspondence Ref: Gubser, Pufu and Yarom, PRL 100, (2008) JN, Gyulassy, Torrieri, arxiv: [hep-ph] - pqcd-based source term in 3+1 ideal hydro Ref: Betz,Gyulassy, JN, Torrieri, arxiv: [hep-ph] 6

7 III Holographic Description of Heavy Quarks Heavy quark mass Exact solution for plasma on Herzog et al, Gubser, Friess et al., PRD 75, (2007). 7

8 Drag force in SYM plasma Heavy quark's velocity Non-expanding, infinite plasma Gubser, PRD 74, (2006). Herzog et al, JHEP 0607, 013 (2006). Casalderrey-Solana and Teaney, PRD 74, (2006). - The total of the strongly-coupled plasma can be computed from the metric fluctuations induced by the trailing string. Friess et al., PRD 75, (2007). - This tensor describes the response of the medium due to the presence of the heavy quark. It includes all the contributions: classical Coulomb, non-equilibrium Neck, hydrodynamic far zone with Mach cones and diffusion wakes. - One can use it to study how the strong color fields created by the heavy quark affect the strongly coupled plasma. 8

9 From the numerical calculations of Gubser, Pufu and Yarom, PRL 100, (2008) Mach wake Note the strong transverse component in the Neck region!!! Diffusion wake JN, Gyulassy, Torrieri, arxiv: [hep-ph] 9

10 Thus, we can divide spacetime around the heavy quark as follows: 1) The highly Lorentz-contracted Head zone: region very close to the quark where the coherent fields dominate and any sort of hydrodynamics is certainly not valid. 2) The Neck region: a transition region between the head and far zones that is still strongly affected by the coherent Coulomb field. 3) The far zone: where hydrodynamics is certainly a good approximation and Mach, as well as diffusion wakes, can be found. Now we need to compute the angular distribution coming from these regions... However, we first need to understand some details of this calculation... 10

11 Checking the details... EOS: CFT Head+ Neck+ Mach+ Diff. Wake background However, note that the disturbances caused by the string (fluctuations are neglected) Thus, the relative disturbance w.r.t. to background is (very small number) 11

12 Interesting consequence: Linearized Navier-Stokes hydrodynamics provides a good description of heavy quark's wake down to distance scales of away from the heavy quark. Noronha, Torrieri, Gyulassy, PRC 78, (2008). Chesler, Yaffe, PRC 78, (2008). How big are the flow and temperature fluctuations created by the heavy quark? Flow One can show that We obtain that the local temp. 12

13 IV Cooper-Frye Freeze-out We use the numerical results for and S. Gubser, S. Pufu, and A. Yarom, PRL 100, (2008). Obtain particles Particle spectra Freeze-out hypersurface ( surface of last scattering ) Fluid 13

14 - For a rapidly expanding medium, the density decreases very quickly and the mean free path of the particles grows significantly fast. Thus, there is roughly a transition from strong coupling to free streaming in a very short time interval. - During this short time, one may assume that the phase space distribution does not change significantly and one may approximate Need evaluated on the surface Three straightforward observations: - CF should be ok in the far zone (where hydrodynamics works). - In the Neck zone CF freeze-out may not be the best approximation. - Head zone yield is not taken into account. 14

15 Focusing on the hydrodynamical far zone... For a static medium, we use an isochronous freeze-out Massless particles at mid-rapidity y = 0 Boltzmann approx. Static background Defines far zone 15

16 Note that in the far zone which leads to Viscous corrections to CF are subleading in 1/Nc and are neglected. Global moments The hydrodynamic far zone only gives a broad bump at - The Mach and diffusion wakes that are present in this region do not lead to interesting structures in the supergravity approximation. - A similar result can be derived for a boost invariant expanding medium. 16

17 Since the Coulomb Head has been subtracted, any non-trivial shoulder structure can only come from the Neck region!!!! While we know that CF may not be applicable in the Neck, we hope that some of its features, such as its strong transverse flow, can be roughly described using CF. Neck zone defined by Violates Mach's law! 17

18 IV Di-Jet Correlations in pqcd x AdS/CFT Based on Betz, Gyulassy, JN, Torrieri, arxiv: [hep-ph] (3+1) Ideal hydro pqcd-based source Computed by R. Neufeld, PRD 78, (2008) Neufeld, Muller, Ruppert, PRC 78, (2008). 18

19 A snapshot of the dynamics 19

20 Comparing the Necks in pqcd and AdS/CFT 20

21 Isochronous Cooper-Frye Freeze-out After CF freeze-out, one does not find a double -peak structure in the away-side in pqcd. 21

22 V Conclusions & Outlook - In the Cooper-Frye freeze-out (+supergravity), a double-peak structure in the away-side appears only when we CF the region where hydro may not be a good approximation (Neck region). - Our results indicate that the non-equilibrium transverse flux from the Neck zone could imitate Mach cone-like correlations, without, however, the dependence of the angle on the jet velocity as expected from Mach's law. - Unlike in AdS/CFT, the induced transverse flow in the Neck zone is too weak in pqcd to produce conical correlations after Cooper-Frye freeze-out. Observation of non-mach conical correlations associated with tagged heavy quark jets of different velocities could provide additional support for novel non-perturbative dynamics as suggested by the AdS/CFT string phenomenology. - More realistic setup is needed: expanding medium, phase transition, confinement... However, due to energy-momentum conservation, we expect that the strong transverse flow showed by the Neck should appear in the final away-side angular correlations. 22

23 Back-up slides 23

24 Bulk Freeze-out Based on Betz, Gyulassy, JN, Torrieri, arxiv: [hep-ph] Bulk momentum distribution (Bowling ball freeze-out) 24

25 Bulk momentum distribution 25

26 The AdS/CFT Correspondence Maldacena's conjecture, 1998 SYM is equivalent to string theory on Witten, 1998; Gubser, Klebanov, Polyakov, 1998 Definition of the duality - Lorentz invariance - Match conformal dimension - Use conserved quantities - Gauge invariant observables - Euclidean space Bulk Dynamical gravity Boundary Translational invariant gauge theory 26

27 SU(Nc) Supersymmetric Yang-Mills - 16 supercharges + extra 16 due to conformal invariance. - SU(4) R-symmetry (rotates the scalars and the fermions). - Global SO(6) symmetry. Gauge bosons 4 fermions Scalars All in the adjoint representation of SU(Nc) Nc D3-branes superpartners 27

28 The duality at finite temperature (near extremal black brane) Horizon at Black brane By checking that the Euclidean continuation of the metric is regular at Black hole temperature (plasma temperature) Note that in this case the system is always in the deconfined state. 28

29 Entropy density: The Stefan-Boltzmann limit for What about the limit SYM? Bekenstein-Hawking formula: Note the famous prefactor... 29

30 In the Neck zone the stress perturbation can be comparable to the background!!!! How does one define the Neck region? Extremely close to the quark -> Lorentz boosted Coulomb field stress Head zone J. J. Friess et al., PRD 75, (2007). Hydrodynamics must fail in the Head zone!!! Near field zone: Field effects from the Head are important Computed analytically by Yarom, PRD 75, (2007); Gubser and Pufu, NPB 790, 42 (2008). Hydrodynamics is valid when the Knudsen number We define then 30

31 Knudsen zone Inside this region local equilibrium cannot be maintained. Noronha, Torrieri, Gyulassy, PRC 78, (2008). Head zone can be determined by equating Dominguez et al, NPA 811, 197 (2008). Lorentz contracted pancake 31