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HQ Collisional energy loss at RHIC & Predictions for the LHC

This study focuses on the collisional energy loss of heavy quarks in Au+Au collisions at RHIC, with predictions for the LHC. It examines the applicability of the Fokker-Planck equation and the need to increase 22 cross-sections in order to reproduce the RAA and v2 observables. The heavy quark evolution in the Quark-Gluon Plasma (QGP) is investigated using the Boltzmann equation with improved cross-sections. The model explores the thermalization, coalescence, and fragmentation of heavy quarks, as well as quarkonia formation and hard production in initial NN collisions.

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HQ Collisional energy loss at RHIC & Predictions for the LHC

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  1. HQ Collisional energy loss at RHIC & Predictions for the LHC P.B. Gossiaux SUBATECH, UMR 6457 Université de Nantes, Ecole des Mines de Nantes, IN2P3/CNRS Collaborators J. Aichelin, A. Peshier, R. Bierkandt

  2. 1 GOAL of the STUDY Recent revival of the collisional energy loss in order to explain the large "thermalization" of heavy quarks in Au+Au collisions at RHIC at low and intermediate pT Most often, however: 1) No "real" pQCD implemented No running as (cf. previous work of Peshier), "crude" IR regulator 2) Fokker – Planck equation… Might not be applicable : "hard" transfers, # of collisions not systematically large at the periphery … or detailed balance not satisfied (just E loss, no E gain )

  3. 2 From a more phenomenological point of view: 3) Need to crank up the 22 cross sections in order to reproduce the RAA 4) Difficulty (« challenge to the models ») to reproduce both the RAA and the v2 without "exotic" processes, like in-QGP resonances. Our approach: consider heavy-Q evolution in QGP according to Boltzmann equation with improved 22cross sections and look whether this helps solving points 3) and 4) If yes: consider other observables and make predictions for LHC

  4. 3 Global Model Evolution of heavy quarks in QGP (thermalization) D/B formation at the boundary of QGP through coalescence of c/b and light quark + fragmentation Quarkonia formation in QGP through c+cY+g fusion process (hard) production of heavy quarks in initial NN collisions

  5. 4 Ri Heavy quarks in QGP In pQGP, heavy quarks are assumed to interact with partons of type "i" (massless quarks and gluons) with local 22rate: Associated transport coefficient (drag, energy loss,…) depend on the QGP macroscopic parameters (T, v, m) at a given 4-position (t,x). These parameters are extracted from a "standard" hydro-model (Heinz & Kolb: boost invariant) We follow the hydro evolution of partons and sample the rates Ri "on the way", performing the QqQ'q' & QgQ'g' collisions: MC approach

  6. Oldies

  7. 5 Cross sections We start from Combridge (79) as a basis: However, t-channel is IR divergent => modelS

  8. 6 With m(T) or m(t) 1 1 Naïve regulating of IR divergence: Models A/B: no as - running m2(T) = mD2 = 4pas(1+3/6)xT2 as(Q2) 0.3 (mod A) as(2pT) (mod B) ( 0.3) Customary choice … of the order of a few % !

  9. 7 Other hypothesis / ingredients of the model • Au–Au collisions at 200 AGeV: 17 c-cbar pairs in central collisions • Q distributions: adjusted to NLO & FONLL • Cronin effect (0.2 GeV2/coll.). • No force on HQ before thermalization of QGP (0.6 fm/c) • Evolution according to Bjorken time until the beginning or the end of the cross-over • Q-Fragmentation and decay  e as in Cacciari, Nason & Vogt 2005. • No D (B) interaction in hadronic phase

  10. 8 Results for model B: c b all Evolution  beginning of cross-over : Cranking factor N.B.: Overshoot due to coalescence One reproduces the RAA shape at the price of a huge cranking K-factor The end of coll Eloss in pQGP ?

  11. 9 1 1 HTL m2(T) = mD2 ?Model C: remembering of HTL (but still no as–running vs Q2) Low |t| Idea:Take m2(T) in the propagator of Combridge in order to reproduce the "standard" Braaten – Thoma Eloss With m(T) calibrated on BT

  12. 10 HTL -dmn Braaten-Thoma: (provided g2T2<< |t*| << T2 ) (Peshier – Peigné) Low |t| Large |t|: Bare propagator + SUM: Indep. of |t*| !

  13. 11 m2(T)  0.2 mD2(T) Comparing with dE/dx in our model: In QGP: g2T2> T2 !!! provided g2T2<< |t*| << T2 BT: Not Indep. of |t*| ! We introduce asemi-hard propagator --1/(t-n2) -- for |t|>|t*| to attenuate the discontinuities at t* in BT approach. Recipy: n2 in the semi-hard prop. is chosen such that the resulting E loss is maximally |t*|-independent. This allows a matching at a sound value of |t*| T

  14. 12 as(2pT) Model C: no Q2 – running, optimal m2 Also Refered as mod C THEN: Optimal choice of m in our OBE model: m2(T)  0.15 mD2(T) with mD2 = 4pas(2pT)(1+3/6)xT2 … factor 2 increase w.r.t. mod B

  15. 13 Results for model C: Evolution  beginning of cross-over Evolution  end of cross-over Rate chosen “as at Tc” : Cranking factor One reproduces the RAA shape at the price of a large cranking K-factor (8-5)

  16. More recently (2-3 years  now)

  17. 14 Model D: running as m2(T) mDself2 (T2) = (1+nf/6) 4pas( mDself2) xT2 Self consistent mD Cf Peshier hep-ph/0607275 Indeed reduction of log increase… …not much effect seen on the RAA

  18. 15 semi-hard propag. Model E : running as AND optimal m2 • Effective as(Q2) (Dokshitzer 95, Brodsky 02) • Bona fide “running HTL”: as  as(Q2) same method as for model C: m2(T)  0.2 mDself2(T)

  19. E E E Reminder: C C C At large velocity 16 drag "A" of heavy quarks Conclusion:including running asand IR regulator calibrated on HTL leads to much larger values of coll. Eloss as in previous works

  20. 17 Central RAA for model E & interm. conclusion: I. One reproduces RAA for K=1.5-2 (<<20 with naïve model 1) on all pT rangeprovided one performs the evolution  end of mixed phase II. Despite the unknowns (b-c crossing, precise kt broaden.,…), unlikely that collisional energy loss could explain it all alone Our present framework III. It is however not excluded that the "missing part" could be reproduced by some conventional pQGP process (radiative Eloss)

  21. 18 Min. bias Results for model C &E : mixed phase responsible for40% of the v2 irrespectively of the model ?! “Characterization of the Quark Gluon “Plasma with Heavy Quarks” ?

  22. Could other observables help ?

  23. 19 Initial correlation (at RHIC); supposed back to back here Azimutal Correlations for Open Flavors Transverse plane What can we learn about "thermalization" process from the correlations remaining at the end of QGP ? D/B Q Q-bar How does the coalescence - fragmentation mechanism affects the "signature" ? Dbar/Bbar -

  24. (Q and produced back to back in trans. Plane) 20 Azimutal correlations at RHIC: * Intermediate pT: both pT>1GeV/c and < 4GeV/c  no correlation left for central collisions 10-20 % correlation left for min bias collisions magnify Similar width for the 2 upper curves (smaller dE/dx) Mexican hat (?) for model E Possible discrimination ?

  25. 21 Probing the energy loss with RAA at large pT: * large pT: mostly corona effect (?) * Naïve view (b=0): Opaque Thickness: a x l(Tc,s) Transparent * More quantitatively: let us focus – within the model E – on c-quarks produced at transverse position < rcrit Fin. vs init. distribution of c Path-length dependence (of course, built in, but survives the “rapid” cooling) “some” Q produced at center manage to come out rcrit = 4fm rcrit = 2fm larger thermalization for inner quarks rcrit = 9fm rcrit = 6fm

  26. 22 More theoretical cuts: Decreasing for central Q Translucid Opaque Transparent Creation dist to the center (fm)  cst at periphery * Challenge: tagging on the “central” Q, i.e. getting closer to the ideal “penetrating probe” concept:

  27. * Reversing the argument: selecting 23 Q-Qbar correlations (at RHIC):  back to back while might bias the data in favor of “central” pairs Possible caveat:  Need for a numerical study 

  28. 24 Q-Qbar correlations (at RHIC): Average dist. to center Privilege of simulation: retain Q and Qbar from the same “mother” collision (exper.: background substraction) 5fm Indeed some (favorable) bias for init pT > 5GeV/c 4fm 3fm Some hope to discriminate between “running” and “non running” models (From the theorist point of view at least) 2 part

  29. 25 Rcb ratio of c to b RAA(pT)(at RHIC): 5fm Horowitz (SQM 07): large mass dependence of AdS/CFT transp coefficient – scaling variable:pl1/2T2/2Mq L-- ≠ moderate dependence in rad pQCD -- log(pT/M) --. 4fm 3fm RCB  1 for pQCD rad Collisional Energy loss sets upper limit on Rcb. Clear possibility to discriminate between various models.

  30. Towards… LHC

  31. 26 D & B mesons at LHC Rescaled collisional E loss • RAA  1 at asymptotic pT values, mostly seen in running as models. • medium at LHC relatively less opaque that at RHIC RHIC < LHC

  32. 27 RCB at LHC Taken from Horowitz SQM07 Clear distinction between various Eloss mechanisms: LHC will reveal it !

  33. 28 Azimutal B-Bbar correlations at LHC: Despite E loss, Large signal/background for pT>10 GeV/c Prediction for the transverse broadening of the Q-jet, related to the B transport coefficient

  34. K=1.8 RHIC < LHC 29 Electrons (D&B) @ LHC Rescaled collisional E loss Same trends as for open flavors

  35. 30 v2 for Electrons (D&B) @ LHC v2 LHC < v2 RHIC (in agreement with “smaller” relative opacity at LHC) and turns over for smaller pT (under study).

  36. 31 Conclusions – Prospects: I. One reproduces all known HQ observables at RHIC with Collisional energy loss rescaling factor of K=1.5-2 (<<20 with naïve model 1) on all pT rangeprovided one performs the evolution  end of mixed phase II. Conservative predictions for LHC, found to be relatively less opaque than at RHIC, due to harder HQ initial distributions III. LHC will permit to distinguish between various E loss mechanisms (pure collisional, mixed rad + collisional, sQGP AdS/CFT) IV. Q-Jet broadening in azimutal correlation will permit to test B transport coefficient and better constrains the medium. Need MC@NLO for better description of initial Q-production and e+ - e- correlations.

  37. Back up

  38. Boltzmann vs Fokker-Planck T=400 MeV as=0.3 Collisions with quarks & gluons

  39. Model B / 1

  40. 7 Results for model 1: Evolution  beginning of cross-over Evolution  end of cross-over : Cranking factor One reproduces the RAA shape at the price of a huge cranking K-factor  The end of coll Eloss in pQGP ?

  41. 8 With such cranking, the model I can be considered at most as an effective one calibrated on RAA(why not ?). Considering (nevertheless) v2: Conclusions: • v2 of Q still increases considerably during the cross-over (contrarily to the one of thermalized quarks) • Reasonnable agreement with the data

  42. Model C / 2

  43. 14 Minimum bias case Similar conclusions as for model 1: • v2 of Q still increases considerably during the cross-over (contrarily to the one of thermalized quarks) • Reasonnable agreement with the data

  44. Model E / 4

  45. 16 Model 4 (and 4bis): running as AND optimal m2 m2(T)  0.2 mD2 (T2)= (1+nf/6)4pas(mD2) xT2 & as(Q2) same method as for model 2:

  46. Mesoscopic aspects of the model

  47. 18 : Large deviations at small and intermediate moment transfer : hard transfer due to u-channel Differential cross section of c-quark in the different variations of the model With gluons With quarks

  48. 19 : Large deviations at small and intermediate energy transfer : hard transfer due to u-channel Probability P(w) of energy loss per fm/c: With gluons With quarks

  49. v2

  50. RHIC

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