University of Catania INFN-LNS. Heavy flavor in medium momentum evolution : Langevin vs Boltzmann. Santosh Kumar DaS

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1 University of Catania INFN-LNS Heavy flavor in medium momentum evolution : Langevin vs Boltzmann Santosh Kumar DaS In collaboration with: Vincenzo Greco Francesco Scadina Salvatore Plumari

2 Introduction OUTLINE OF MY TALK.. Heavy Quars and Langevin dynamics Boltzmann aroach to heavy quars dynamics Similarities and differences between the two aroaches in a static medium (Langevin and Boltzmann) 1) Sectra ) Momentum sreading ) Bac to bac azimuthal correlation Comarison with the exerimental observables (RAA and v) Effect of hadronic medium on heavy quar observables Summary and outloo

3 Heavy Quar & QGP SPS to LHC s 17.3GeV to. 76TeV ~100 times T i 00 MeV to 600 MeV ~3 times M c, b M c, b c, b QGP T 0 QCD Produced by QCD rocess (out of Equil.) They go through all the QGP life time No thermal roduction

4 Heavy flavor at RHIC At RHIC energy heavy flavor suression is similar to light flavor Simultaneous descrition of RAA and v is a tough challenge for all the models.

5 Heavy Flavors at LHC Again at LHC energy heavy flavor suression is similar to light flavor Is the momentum transfer really small! Can one describe both RAA and v simultaneously?

6 Boltzmann Kinetic equation col t f x E P t t x f,, F. f f d t f t R col,,, 3 f f f f j i j i 1. ), (, q q v q q f q d g,,, 3 3 ) ( ) ( ), ( is rate of collisions which change the momentum of the charmed quar from to - f B f A t f ij j i i i 3 i ) ( d A, j i 3 ij ) ( d B, where we have defined the ernels, Drag Coefficient Diffusion Coefficient B. Svetitsy PRD 37(1987)484 The lasma is uniform,i.e., the distribution function is indeendent of x. In the absence of any external force, F=0

7 f f f f j i j i 1. ), (, Boltzmann Equation Foer Planc It will be interesting to study both the equation in a identical environment to ensure the validity of this assumtion at different momentum transfer and their subsequent effects on RAA and v.

8 where dx j d j E j dt j dt Langevin Equation dtc j ( t, d) is the deterministic friction (drag) force C ij is stochastic force in terms of indeendent Gaussian-normal distributed random variable ), P( ) ex( ) ( x, y, z 1 3 With ( t) ( t) ( t t) i j H. v. Hees and R. Ra arxiv: the re-oint Ito interretation of the momentum argument of the covariance matrix.

9 Langevin rocess defined lie this is equivalent to the Foer-Planc equation: the covariance matrix is related to the diffusion matrix by With B and B 0 1 D A i j C l C ij l Relativistic dissiation-fluctuation relation

10 For Collision Process the A i and B ij can be calculated as following : i i c q q i q f q q M E d E q d E q d E A ) ( j i ij B ) ( 1 Elastic rocesses gc gc We have introduce a mass into the internal gluon roagator in the t and u-channel-exchange diagrams, to shield the infrared divergence. B. Svetitsy PRD 37(1987)484 Mustafa, Pal and Srivastava, PRC, 57,889(1998) 1 1 m D t t T m s D 4

11 Transort theory f ( x, ) C We consider two body collisions Collision s t 0 3 x 0 Exact solution Collision integral is solved with a local stochastic samling [ Z. Xhu, et al. PRC71(04)] [VGreco et al PLB670, 35 (08)]

12 Cross Section gc > gc 1 t The infrared singularity is regularized introducing a Debyescreaning-mass D 1 m T t D 4s m D L. Combridge, Nucl. Phys. B151, 49 (1979)] [B. Svetitsy, Phys. Rev. D 37, 484 (1988) ]

13 Boltzmann vs Langevin (Charm) Angular deendence of Mometum transfer vs P Decreasing m D maes the more anisotroic Smaller average momentum transfer Hees, Mannarelli,Greco,Ra, PRL100(008) Hees,Greco,Ra. PRC73 (006) Das, Scardina, Plumari and Greco arxiv:

14 Boltzmann vs Langevin (Charm) md=0.4 GeV md=0.83 GeV Das, Scardina,Plumari and Greco arxiv: (PRC, In ress) md=1.6 GeV

15 Bottom: Boltzmann = Langevin T= 400 MeV m D =0.83 GeV T= 400 MeV m D =0.4 GeV Bottom Bottom md=1.6 GeV roximation Boltzmann But Larger M b /T ( 10) the better Langevin aroximation wors

16 Nuclear Suression Factor (R AA ) : R AA N d coll dn d T dy dn T Au dy Au If R AA = 1 No medium If R AA < 1 Medium A direct measure of the energy loss

17 Ellitic Flow : T dn d dyd T dn d T T dy 1 v1 cos( ) v cos( )... v HF ( T ) cos( ) x x y y Polar Plots : y y 1+v 1 cosφ 1+v cos(φ) x x 1+v Overall shift Major axis = 1+v Minor axis = 1-v

18 Imlication for observable, R AA? md=0.83 GeV The Langevin aroach indicates a smaller R AA thus a larger suression. However one can moc the differences of the microscoic evolution and reroduce the same R AA of Boltzmann equation just changing the diffusion coefficient by about a 30 %

19 Momentum evolution starting from a (Charm) in a Box Langevin dn 10GeV 3 d initial Boltzmann md=0.83 GeV In case of Langevin the distributions are Gaussian as exected by construction In case of Boltzmann the charm quars does not follow the Brownian motion Das, Scardina, Plumari and Greco arxiv: (PRC, In ress)

20 Momentum evolution starting from a (Bottom) dn 10GeV 3 d initial In a Box Langevin Boltzmann T=400 MeV Mc/T 3 Mb/T 10 [S. K. Das, F. Scardina, V. Greco arxiv: ]

21 Momentum evolution for charm vs temerature Boltzman dn 10GeV 3 d initial T= 400 MeV Boltzmann T= 00 MeV Charm Charm At 00 MeV Mc/T= 6 > start to see a ea with a width

22 Bac to Bac correlation in a Box Initialization: x=z=0, y=10 GeV x=z=0, y=-.5 fm md=0.83 GeV The larger sread of momentum with the Boltzmann imlicates a large sread in the angular distributions of the Away side charm

23 R AA at RHIC for different <> The Langevin aroach indicates a smaller R AA thus a larger suression. One can get very similar R AA for both the aroaches just reducing the diffusion coefficent The smaller averege transfered momentum the better Langevin wors

24 v at RHIC centrality 0-30 % Also for v the smaller averege transfered momentum the better Langevin wors Boltzmann is more efficient in roducing v for fixed R AA

25 R AA and v at RHIC at md=1.6 GeV Our results can be further imroved by imlementing Coalescence + Fragmentation for hadronisation. Das, Scadina,Plumari and Greco arxiv: With isotroic cross section one can describe both RAA and V simultaneously within the Boltzmann aroach!

26 Using inuts from quasi article model Plumari, Alberico, Greco and Ratti PRD,84, (011) Berrehrah,Bratovsaya,Cassing,Gossiaux, Aichelin, Bleicher PRC,89, (014) Berrehrah, Gossiaux, J. Aichelin, W. Cassing, Bratovsaya arxiv:

27 R centrality 30 50% m D =0.4 GeV (BM) 60% of LV m D =0.83 GeV (BM) 50% of LV R AA 0.8 R AA T (GeV) T (GeV) 1. m D =1.6 GeV (BM) 40% of LV R AA One can get very similar R AA for both the aroaches just reducing the diffusion coefficent T (GeV)

28 LHC centrality 30 50% Also for v the smaller averege transfered momentum the better Langevin wors Boltzmann is more efficient in roducing v for fixed R AA

29 D D DK DK D D Hadronic Phase Using scattering length obtained from Heavy Meason Chiral Perturbation Theory B B BK BK B B γ(fm 1 ) D B B 0 (GeV /fm) D (GeV/fm) B D T(GeV) T(GeV) Das,Ghosh, Sarar and Alam M. Laine,JHEP,04, 14 (011) Phys Rev D 85, (01 ) He, Fries,Ra, Phys. Let.B701, 445(01) Ghosh, Das, Sarar, Alam, PRD84, (011) Abreu, Cabrera, Llanes-Estrada,Torres-Rincon, Annals Phys. 36, 737 (011) Torres-Rincon, Tolos, Romanets, PRD,89, (014)

30 Hadronic Phase Das, Scardina, Greco, Alam Under Prearation Das, Ghosh,Sarar,Alam, PRD,88,017501, (013) He, Fries, Ra, arxiv:1401:3817 Ozvenchu, Torres-Rincon, Gossiaux, Aichelin, Tolos, arxiv:

31 Heavy Baryon to Meson Ratio M, K, Z. Liu, S. Zhu, PRD 86, (01); NPA 914,494 (013 Ghosh, Das, Greco, Sarar and Alam PRD,90, (014)

32 J J J / J / / J / / N J / N J/Psi in Hadronic Phase c c c c N N c c Yooawa, Sasai, Hatsuda and Hayashigai PRD 74, (006) Mitra, Ghosh, Das, Sarar and Alam arxiv:

33 Summary & Outloo Both Langevin and Boltzmann equation has been solved in a box for heavy quar roagating in a thermal bath comosed of gluon at T= 400 MeV as well as for a exanding medium at RHIC and LHC energies. We found charm quars does not follow the Brownian motion at RHIC and LHC energies. Langevin dynamics overestimate the suression than the Boltzmann aroach. For a given RAA Boltzmann aroach develo larger v. With isotroic cross-section one can reroduce RAA and v simultaneously within the Boltzmann aroached at RHIC energy. We have also highlighted the significance of the hadronic hase. Imlementation of radiative rocess is under rogress.

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35 Momentum evolution starting from a (Charm) in a Box Langevin dn 10GeV 3 d initial Boltzmann md=0.83 GeV In case of Langevin the distributions are Gaussian as exected by construction In case of Boltzmann the charm quars does not follow the Brownian motion Das, Scadina,Plumari and Greco arxiv:

36 With FDT With QCD

37 J/Psi in Hadronic Phase V,, J J J / J / / J / / N J / N c c c c N N c c Haglin,Gale, PRC 63, 06501(001). Yooawa, Sasai, Hatsuda and Hayashigai PRD 74, (006) Effective Lagrangian Scattering Length Mitra, Ghosh, Das, Sarar and Alam arxiv:

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41 10 4 dn/d t=t0 t=4 (md=0.4 GeV) t=0 fm (md=gt) Thermal (GeV)

42 Bac to Bac correlation The larger sread of momentum with the Boltzmann imlicates a large sread in the angular distributions of the Away side charm

43 Momentum evolution for charm vs temerature Boltzman dn 10GeV 3 d initial T= 400 MeV Boltzmann T= 00 MeV Charm Charm At 00 MeV Mc/T= 6 > start to see a ea with a width Such large sread of momentum imlicates a large sread in the angular distributions that could be exerimentally observed studying the bac to bac Charm anticharm angular correlation

44 Charm evolution in a static medium Simulations in which a article ensemble in a box evolves dynamically Bul comosed only by gluons in thermal equilibrium at T=400 MeV C and Cbar are initially distributed: uniformily in r-sace, while in - sace fm Due to collisions charm aroaches to thermal equilibrium with the bul

45 I) LPM effect : Suression of bremsstrahlung and air roduction. l f q Formation length ( ) : The distance over which interaction is sread out 1) It is the distance required for the final state articles to searate enough that they act as searate articles. ) It is also the distance over which the amlitude from several interactions can add coherently to the total cross section. As q increase l f reduce Radiation dros roortional S. Klein, Rev. Mod. Phys 71 (1999)1501 (II) Dead cone Effect : Suression of radiation due to mass 1 d dzd 1 z x E / 1 q s x E / s q ~ C s 4 where z x x F 1 Where and the energy fraction of the final state quar and anti-quar. and m s Radiation from heavy quars suress in the cone from θ =0 (minima) to θ= γ (maxima)