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Open charm at RHIC and LHC

Open charm at RHIC and LHC. J. Aichelin in collaboration with M. Bluhm, P.B. Gossiaux, T. Gousset, (A.Peshier). Why heavy quarks are interesting? Interaction of heavy quarks with the plasma - collisional - radiative

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Open charm at RHIC and LHC

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  1. Open charm at RHIC and LHC J. Aichelin in collaboration with M. Bluhm, P.B. Gossiaux, T. Gousset, (A.Peshier) Why heavy quarks are interesting? Interaction of heavy quarks with the plasma - collisional - radiative - Landau Pomeranschuk Migdal (LPM) effect Results for RHIC and LHC open charm at RHIC and LHC

  2. What makes heavy quarks (mesons) so interesting? - produced in hard collisions (initial distribution: FONLL) - no equilibrium with plasma particles (information about the early state of the plasma) - not very sensitive to the hadronisation process Ideal probe to study properties of the QGP during its expansion Caveat: two major ingredients: expansion of the plasma and elementary cross section (c(b)+q(g) ->c(b)+q(g)) difficult to separate (arXiv:1102.1114 ) Introduction

  3. Elastic heavy quark – q(g) collisions Collisional energy loss in elementary coll is determined by the elementary elastic scattering cross sections. Q+q -> Q+q : Neither g2= 4α(t) nor κ mD2= are well determined Literature: α(t) =is taken as constant or as α(2πT) mDself2 (T) = (1+nf/6) 4πas( mDself2) xT2 (hep-ph/0607275) But which κ is appropriate? κ =1 and α =.3:large K-factors are necessary to describe data Is there a way to get a handle on α and κ ? Collisional Energy Loss

  4. A) Debye mass PRC78 014904, 0901.0946 mD regulates the long range behaviour of the interaction Loops are formed If t is small (<<T) : Born has to be replaced by a hardthermal loop (HTL) approachlike in QED: (Braaten and Thoma PRD44 (91) 1298,2625) For t>T Born approximation is ok QED: the energy loss ( = E-E’) Collisional Energy Loss Energy loss indep. ofthe artificial scale t* which separates the 2 regimes .

  5. HTL in QCD cross sections is too complicated for simulations Idea: - Use HTL (t<t*) and Born (t>t*) amplitude for dE/dx make sure that result does not depend on t* -thenuse Born approx with a μ which gives same dE/dx Extension to QCD In reality a bit more complicated: Phys.Rev.C78:014904 Result smaller than standard value Collisional Energy Loss : μ ≈ 0.2 mD

  6. B) Running coupling constant • Effective as(Q2) (Dokshitzer NPB469,93, Brodsky 02) “Universality constraint” (Dokshitzer 02) helps reducing uncertainties: Our choice Peshier 0801.0595 Our choice V=F Collisional Energy Loss Comp w lattice results PRD71,114510 IR safe. The detailed form very close to Q2 = 0 is not important does not contribute to the energy loss Large values for intermediate momentum-transfer

  7. The matching gives   0.2 mD for running S for Debye mass and   0.15 mD not running! Large enhancement of cross sections at small t Little change at large t Largest energy transfer from u-channel gluons Collisional Energy Loss

  8. Inelastic Collisions Low mass quarks : radiation dominantes energy loss Charm and bottom: radiation of the same order as collisional 4 QED type diagrams Commutator of the color SU(3) operators Radiative Energy Loss M1-M5 : 3 gauge invariant subgroups 1 QCD diagram MQCD dominates the radiation

  9. MSQCD in light cone gauge In the limit the radiation matrix elements factorize in kt , ω = transv mom/ energy of gluon E = energy of the heavy quark DQCD = color factor leading order: no emission m=0 -> Gunion Bertsch from light q Emission from g Emission from heavy q Radiative Energy Loss

  10. Landau Pomeranschuk Migdal Effekt (LPM) reduces energy loss by gluon radiation Heavy quark radiates gluons gluon needs time to be formed Collisions during the formation time do not lead to emission of a second gluon Coherent g scattering with N plasma part. during form. time Landau Pomeranschuck Migdal effect leads to the emission of one gluon ( not N as Bethe Heitler)

  11. Formation time (Arnold (hep-ph/0204343) qt for energetic particles momentum conserved (energy conservation (BDMPS) similar) g g using LPM Formation time: increases by subsequent gq,gg coll

  12. single scattering multiple scattering single collision Multiple collision =ω/EHQ LPM single multiple scatt. single At intermediate gluon energies formation time is determined by multiple scattering

  13. For x>xcr=mg/M, gluons radiated from heavy quarks are resolved in less time then those from light quarks and gluons =>radiation process less affected by coherence effects. For x<xcr=mg/M, basically no mass effect in gluon radiation [fm] λ(T) LPM important for intermediate x where formation Time is long = ω/E Landau Pomeranchuck Migdal Effect Most of the collisions Dominant region for average E loss

  14. .. And if the medium is absorptive (PRL 107, 265004) Damping Ter-Mikaelian with Γ1 single multipl New timescale 1/Γ damping Γ2 damping dominates radiation spectrum Γ3

  15. Influence of LPM and damping on the radiation spectra LPM, damping, mass: Strong reduction of gluon yield at large ω LPM: increase with energy decrease with mass Weak damping strong damping radiation spectrum BH Mult. Scatter HQ mass

  16. RHIC 200 AGeV and LHC 2.76 TeV • . c,b-quark transverse-space distribution according to Glauber • c,b-quark transverse momentum distribution as in d-Au (STAR)… very similar to p-p (FONLL)  Cronin effect included. • c,b-quark rapidity distribution according to R.Vogt (Int.J.Mod.Phys. E12 (2003) 211-270) and priv comm. • QGP evolution: 4D / Need local quantities such as T(x,t)taken fromhydro dynamical evolution (Heinz & Kolb) • D meson produced via coalescence mechanism. (at the transition temperature we pick a u/d quark with the a thermal distribution) but other scenarios possible. • No damping yet Model

  17. Too large quenching (but very sensitive to freeze out) • Radiative Eloss indeed dominates the collisional one • Flat experimental shape is well reproduced • RAA(pT) has the same form for radial and collisional energy loss (at RHIC) All non-photonic electrons as[0.2,0.3] Results RHIC I Results RHIC as[0.2,0.3] separated contributions e  D and e B. 26

  18. Results RHIC II arXiv 1005.1627 (PHENIX) theory collisional K= 2 RAA centrality dependence (PHENIX) well reproduced v2 of heavy mesons depends on where fragmentation/ coalescence takes place end of mixed phase beginning of mixedphase Results RHIC

  19. Collisional + radiative energy loss + dynamical medium : compatible with data • To our knowledge, one of the first model using radiative Eloss that reproduces v2 Results RHIC III For the hydro code of Kolb and Heinz: K = 1 compatible with data K = 0.7 best description Results RHIC

  20. Results LHC I Same calculations as at RHIC only difference: initial condition dN/dy (central) = 1600 Results LHC Centrality and pt dependence of RAA reasonably well reproduced

  21. Results LHC II v2 very similar at RHIC and LHC B and b flow identical D and c 20% difference (hadronization) RHIC Results LHC Difference between B and D can validate the model (only difference is the mass) LHC

  22. Results LHC III Ratio charm/bottom (Horowitz et al.) JPG 34, S989 Wicks et al NPA743,493 LHC 5.5 ATeV Is AdS/CFT still valid? Results LHC Charm/bottom ratio will show whether pQCD or AdS/CFT is the right theory to describe HI reactions

  23. Conclusions All experimental data are compatible with the assumption that QCD describes energy loss and elliptic flow v2 of heavy quarks. RHIC and LHC described by same program (hydro ini is diff) Special features running coupling constant adjusted Debye mass Landau Pomeranschuk Migdal Description of the expansion of the medium (freeze out, initial cond.) can influence the results by at least a factor of 2(1102.1114 ) Refinements still necessary: Running coupling constant for gluon emission vertex gluon absorption Expansion scenario (fluctuating initial conditions :EPOS) Conclusion

  24. Energy loss per unit length: dE/dz dE/dz Eq = 20 GeV, T=300 MeV mg=300MeV radiative For large quark masses: Collisional and radiative energy loss of the same order Small q masses: radiative dominante Radiative Energy Loss Collisional (Peigne & Smilga) arXiv:0810.5702 Rad: ΔE E Coll: ΔE ln E

  25. Landau Pomeranschuk Migdal (LPM) Effect: A second gluon can only be emitted after the first is formed In leading order no gluon emission from light quarks Formation time for a single collision Landau Pomeranschuk Migdal Effect x=ω/E At qt = kt =0:

  26. For x>xcr=mg/M, gluons radiated from heavy quarks are resolved in less time then those from light quarks and gluons =>radiation process less affected by coherence effects. For x<xcr=mg/M, basically no mass effect in gluon radiation [fm] λ(T) LPM important for intermediate x = ω/E Landau Pomeranchuck Migdal Effect Most of the collisions Dominant region for average E loss

  27. Presumably at RHIC and LHC a plasma (QGP) is formed • which is, however, not directly visible. One has to conclude • on its existence from decay products • This is all but easy: • - The multiplicity of almost all particles coincides with the • expectation of a statistical model • for given μ ≈0 and T≈160 MeV =Tc • Consequence: loss of memory of the history of the QGP • may measure simply freeze out condition • Spectra distorted by final state hadronic interactions • -> most of single particle obs. do not elucidate the enigma Introduction • collective variables • Jets • heavy mesons (containing a c or b quark and • which do not come to equilibrium)

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