Heavy quark production and elliptic flow at RHIC and LHC

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1 Heavy quark production and elliptic flow at RHIC and LHC Jan Uphoff with O. Fochler, Z. Xu and C. Greiner Institute for Theoretical Physics Hirschegg January 20, 2010

2 Outline Motivation Charm processes in BAMPS Box calculation: chemical equilibration Heavy quark production in heavy-ion collisions Elliptic flow of charm Summary 1

3 Motivation Large heavy quark mass >> Λ QCD Charm: M c 1.5 GeV Bottom: M b 4.75 GeV _ D D charm production at early stage of collision ideal probe for this c _ c Pre-equil. phase stage 2

4 BAMPS BAMPS: Boltzmann Approach of MultiParton Scatterings Transport algorithm solving the Boltzmann equations for on-shell partons with pqcd interactions Implemented processes: Z. Xu & C. Greiner, Phys. Rev. C 71 (2005) (no light quarks yet) 3

5 BAMPS Rapid thermalization eq 1fm/c Z. Xu & C. Greiner, Phys. Rev. C 76 (2007) /s extraction / s 0.08 Z. Xu, C. Greiner & H. Stöcker, Phys. Rev. Lett. 101 (2008) 4

6 BAMPS Hydro Solving the Riemann problem Shock waves by F. Lauciello & I. Bouras I. Bouras et al., Phys. Rev. Lett. 103 (2009) 5

7 Time scale of chemical equilibration Toy model: consider box of gluons with just two processes Initial conditions: thermally distributed gluons Rate equation: with Matsui, Svetitsky, McLerran, Phys. Rev. D (1986) Biro, van Doorn, Müller, Thoma, Wang, Phys. Rev. C (1993) 6

8 Box calculation T 0 = 400 MeV 7

9 Box calculation T 0 = 400 MeV 8

10 Box calculation T 0 = 800 MeV 9

11 Initial charm in hard parton scatterings Two approaches: 1. LO pqcd: mini-jets depend on renormalization scale μ R depend on factorization scale μ F both very sensitive on parton distribution functions factorization scale renormalization scale charm mass 2. PYTHIA Monte Carlo Event Generator for nucleon-nucleon collisions 10

12 Initial charm in hard parton scatterings Total initial charm yield in central Au+Au RHIC: PYTHIA: 8 14 charm pairs LO pqcd: 2 4 charm pairs PYTHIA closer to data Jan Uphoff, Goethe University Frankfurt Charm quark production DPG Spring Meeting, March 19,

13 Initial gluon distribution for parton cascade PYTHIA scaling to heavy-ion collisions with Glauber model (considering shadowing) and energy conservation hard partons ~ N bin : number of binary collision Minijets (low p T cut-off at 1.4 GeV) soft partons ~ A: number of nucleons in one nuclei Color glass condensate H.J. Drescher & Y. Nara, Phys. Rev. C75 (2007) 12

14 Charm production in the QGP BAMPS simulation of QGP phase at RHIC 13

15 charm pairs Charm production in the QGP at RHIC RHIC PYTHIA initial conditions BAMPS Only 0.3 charm pairs are produced during the QGP phase 3 % of total charm M charm = 1.5 GeV PHENIX data, Phys. Rev. Lett. 94 (2005) 14

16 charm pairs Charm production in the QGP at RHIC RHIC BAMPS Different initial conditions factor 2.5 difference in charm production during QGP phase M charm = 1.5 GeV 15

17 charm pairs Charm production in the QGP at RHIC RHIC BAMPS K factor or different charm mass factor 2 difference in charm production during QGP phase 16

18 charm pairs Charm production in the QGP at RHIC RHIC Maximum charm production of 3.4 pairs 27 % of total charm 17

19 charm fugacity Charm production in the QGP at RHIC RHIC Extract temperature, compute n eq Number of charm quarks in center of collision far above equilibrium value 18

20 charm pairs Charm production in the QGP at LHC LHC BAMPS charm pairs are produced in the QGP % of total charm 19

21 charm fugacity Charm production in the QGP at LHC LHC RHIC 20

22 bottom pairs Bottom production in the QGP at LHC LHC BAMPS 0.01 bottom pairs are produced in the QGP 0.2 % of total bottom 21

23 Elliptic flow v 2 22

24 Elliptic flow v 2 for gluons O. Fochler, Z. Xu & C. Greiner, Phys.Rev.Lett.102 (2009) Z. Xu & C. Greiner, Phys. Rev. C 79 (2009) central Au+Au 23

25 Elliptic flow v 2 for charm at RHIC gc gc K gc gc only elastic charm processes 24

26 Elliptic flow v 2 for charm at RHIC gc gc K gc gc only elastic charm processes 25

27 Elliptic flow v 2 for charm at RHIC gc gc K gc gc only elastic charm processes 26

28 Elliptic flow v 2 for charm at RHIC 27

29 Elliptic flow v 2 for charm at RHIC Debye mass with a prefactor κ = 0.2, proposed by A. Peshier, arxiv: [hep-ph] P.B. Gossiaux, J. Aichelin, Phys.Rev.C78 (2008) only elastic charm processes gc gc K gc gc 28

30 Conclusion & outlook Chemical equilibration time for charm very large Huge uncertainty on initial charm yield due to PDF and scale dependencies LO calculations cannot explain data Full space-time evolution of charm and bottom quarks Small charm yield during QGP phase RHIC: 3-27 % of final charm are produced in QGP LHC: % of final charm are produced in QGP Negligible bottom yield during QGP phase at LHC LO gluon charm scattering is not sufficient to build up collective flow Future tasks: Light quarks Higher order corrections, gluon radiation for charm scattering Energy loss of charm quarks R AA 29

31 Thank you for your attention. 30

32 Backup 31

33 BAMPS 3+1 dimensional Monte Carlo cascade Divides collision zone into cells Z. Xu & C. Greiner, Phys. Rev. C 71 (2005) Using stochastic method: Testparticles to increase statistics 32

34 Partonic cross sections Dominant process for charm production: Other possible process: 33

35 Charm quark scattering LO pqcd: Debye screening 34

36 Partonic cross sections Back reaction through detailed balance gluons identical kinematical factor particles color averaging 35

37 Solution of rate equation Number of charm quarks for fixed temperature and fixed number of particles: 36

38 Box calculation T 0 = 800 MeV 37

39 Time scale of chemical equilibration 38

40 Time scale of chemical equilibration Considering all processes No change of chemical equilibration time scale 39

41 PYTHIA PYTHIA simulates only nucleon-nucleon collisions Distinguish between particles from soft and hard events 40

42 PYTHIA 41

43 Initial conditions for parton cascade 42

44 Initial conditions for cascade at LHC Pb+Pb Pb+Pb 43

45 Initial conditions for cascade at LHC In agreement with most of LHC predictions (cf. N. Armesto, J.Phys.G35 (2008) 44

46 Charm yield from PYTHIA Total initial charm yield in central Au+Au RHIC: PYTHIA: 3 14 charm pairs LO pqcd: 2 4 charm pairs Choose CTEQ6l as standard parton distribution function, although its charm yield is farer from data than CTEQ6m Reason: Designed for LO event generators 45

47 Temperature at RHIC and LHC RHIC, PYTHIA LHC, PYTHIA LHC, mini-jets 46

48 Charm scales with number of bin. coll. STAR data arxiv: [nucl-ex] 47

49 Charm quark scattering LO pqcd: Cross section: 48

50 Charm quark scattering LO pqcd: Cross section: divergent for t=0 49

51 Charm quark scattering Solutions: 1. Cut-off for t max 2. Debye screening 50

52 Charm quark scattering Solutions: 1. Cut-off for t max 2. Debye screening Total cross section: 51

53 Charm quark scattering 52

54 LO pqcd: mini-jets p+p Sqrt(s)= 200 GeV 53

55 Comparison with Hydro A. El, Z. Xu and C. Greiner, arxiv: [hep-ph] 54

56 55 ] [ ] [ 1 ) ( dw C f f R E n n tr E p E p NS z z ZX and C.Greiner, PRL 100, , (2008) sin ~ ) 3 1 ( ] [ ] [ d d d n n E p n dw C f E p C f E p dw R tr z z z tr transport rate 4 nln n s Eta/s extraction

57 Partonic cross sections 56

58 Partonic cross sections 57