2 nd Heavy Flavour Meet - 2016, Kolkata, February 02 - 05, 2016

1. Nuclear modification and Azimuthal anisotropy of heavy flavour decay muons in ultra relativistic heavy-ion collisions UmmeJamil Department of Physics, D. R. College, Golaghat, Assam In collaboration with: RaktimAbir Aligarh Muslim University, aligarh. Somnath De Institute of Physics, Bhubaneswar. MunshiGolam Mustafa Saha Institute of Nuclear Physics , Kolkata. Dinesh K. Srivastava Variable Energy Cyclotron Centre, Kolkata. 2nd Heavy Flavour Meet - 2016, Kolkata, February 02 - 05, 2016 Here comes your footer  Page 1

2. Outline: • Motivation. • Initial distribution of production of heavy quarks. • Energy loss of heavy flavour. • Initial conditions and evolution of plasma. • RAA of muons from heavy flavour at forward rapidity at • LHC. • Azimuthal anisotropy of heavy flavour decay muons at • LHC. • Summary.

3. Motivation At extremely high energy densities, QCD predicted formation of a new form of matter (QGP), consisting of deconfined (anti)quarks and gluons. Heavy quarks (charm and bottom, M>1 GeV) are widely recognized as the excellent probes of QGP: t=1/2MQ << 0.1 fm/c  Heavy flavours can be produced only during the early stage of collision. Produced mainly during the time t=1/2MQ << 0.1 fm/c. Means it is nearly negligible at later times. Early stage No heavy quark production  Due to their large mass, the production of heavy quarks is small making them special as a probe for QGP.  Experimentally easy to observe, through Semi-leptonic decays. Heavy flavours produced at the initial time of system evolution will pass through the QGP, colliding with quarks and gluons and radiating gluons. Thus the heavy flavours will loose energy while passing through the QGP.

4. Initial distribution FONLL calculation. M. Cacciari, S. Frixione, N. Houdeau, M. L. Mangano, P. Nason and G. Ridolfi, JHEP 1210 (2012) 137 UJ and Dinesh K Srivastava , J. Phys. G: Nucl. Part. Phys. , 37 (2010) 085106

5. Collisional energy loss for heavy quarks: • Peigne and Peshier (PP) formulation • In Braatan and Thoma formalism, it was assumed that the momentum exchange q<<E. PP pointed out that this is not reliable in the energy regime E>>M2 /T , and corrected it in the QED case while calculating the collisional energy loss of a muon in the QED plasma. This work in QED is then used to calculate the collisional energy loss of a heavy quark through QGP. • A fixed coupling approximation is used. Stephane Peigne and Andre Peshier, PRD 77 (2008) 114017

6. Small-angle/collinear gluon emission • There are couple of model implementations in the literature viz., DGLV, ASW-SH, HT, • AMY, that aim to quantify jet quenching and energy loss (mainly radiative) related • phenomena within perturbative QCD. • All this generally used formalisms currently available for energy loss of a high • momentum parton through gluon radiations, have few common technical approximations. • One of the main approximations that involved at the level of single emission kernel calculations and related to kinematics is: Small-angle/collinear gluon emission : • Energy of the emitted gluon is much larger than its transverse momentumk ┴ i.e. w >> k ┴ and w k||. For the process qQ  qQg, without loss of generality, one can take k ┴ = w sin q and k|| = w cos q , where q being angle between direction of propagation of leading partons and direction of emitted gluons. This particular approximation therefore implies q = 0. • In the Present (AJMS) formalism, We DO NOT have taken this approximation. RaktimAbir, UJ, Munshi G. Mustafa, Dinesh K. Srivastava, Physics Letters B 715 (2012) 183

7. Energy Loss of Heavy Flavour Present (AJMS) radiative energy loss formalism RaktimAbir, UJ, Munshi G. Mustafa, Dinesh K. Srivastava Physics Letters B 715 (2012) 183

8. K. Saraswat, P. Shukla, V. Singh, Nuclear Physics A 943 (2015), 83

9. Energy Loss of Heavy Flavor Radiative energy loss for heavy quarks: • Djordjevic, Gyulassy, Levai, and Vitev (DGLV) formulation • For massless case Gyulassy, Levai and Vitev (GLV) computed the induced radiation to an arbitrary order in opacity χn (χ=L/λ) of the plasma . • DGLV generalize the GLV opacity expansion method to compute the first order induced energy loss including the kinematic effect due to heavy quark mass. Wicks et al. present a simplified form of the DGLV formalism for the average radiative energy loss of heavy quarks. S. Wicks et.al, Nuclear Physics A 784(2007)426

10. Energy Loss of Heavy Flavor

11. Initial conditions and evolution of plasma. The initial conditions: • The energy loss depends on: • Path length of the heavy quarks in the plasma. • Temperature evolution of the plasma and • The energy and mass of the heavy quark. • Neglect the transverse expansion of the plasma. • Bjorken cooling is assumed to work locally. S. Wicks et.al, Nuclear Physics A 784 (2007) 426 N. Armesto et. al, Nuclear Physics A 00 (2014); K. Aamdot et al. (ALICE Collaboration) 105 (2010) 252301 • The critical temperature Tc for existence of QGP is taken as 170 MeV.

12. Initial conditions and evolution of plasma. Average path length: f L(f,r) • The distance covered by the heavy quark will vary from 0 to 2R. • For central collisions the results for <L> will not depend on f R r F • For non-central collisions the results for <L> will depend on the azimuthal angle

13. Initial conditions and evolution of plasma. Average path length: Now, vT =pT /mT L = <L>/vT. tL • If c ≥ L tL • If c < L the heavy quark would be inside • QGP only while covering the distance vT × c. tc We approximate <> = <L>eff / 2, where <L>eff =min [<L>, vT × c ].

14. Nuclear modification factor The nuclear modification factor at impact parameter b is: TAA is calculated using Glauber model. Suppression = Final momentum distribution of heavy quarks/Initial momentum distribution of heavy quarks • We perform the calculations in the frame in which the rapidity of the heavy quark is the same as the fluid rapidity. • So, energy of the heavy quark • After loosing energy ∆E, the heavy quark new energy: • The fragmentation of heavy quarks in to mesons is governed by Peterson fragmentation function. The parameters used are ec= 0.06 and eb= 0.006.

15. Comparison of energy loss predicted by radiative and collisional energy loss formalisms.

16. RAA at LHC RAA of D mesons at 2.76 ATeV and 5.5 ATeV. RaktimAbir, UJ, Munshi G. Mustafa, Dinesh K. Srivastava Physics Letters B 715 (2012) 183

17. RAA at LHC RAA of muons at forward rapidity at 2.76 ATeV. Comparison of RAA of muons at forward rapidity at 2.76, 5.5 and 39 ATeV. ALICE Collaboration, Phys. Rev. Lett. 109, 112301 (2012).

18. Azimuthal Anisotropy The differential azimuthal anisotropy is measured in terms of the parameter V2 (pT) : V2 (pT) of muons at forward rapidity at 2.76 ATeV. And prediction for 39 ATeV at FCC. GraziaLuparello for the ALICE Collaboration, arXiv:1411.2442v1 [nucl-ex] 10 Nov 2014 ALICE Collaboration, arXiv:1507.03134v1 [nucl-ex] 11 Jul 2015

19. Summary • The nuclear modification factor RAA predicted by present(AJMS) and DGLV formalisms are • quite different. But in case of elliptic flow we observe that both shows similar trend. • We have noted that the suppression of muons at LHC is well supported by the • present(AJMS) formalism. • The nuclear modification factor of muons at 0-10% centrality predicted by the present • formalism has shown very good agreement with the ALICE data. However the • prediction shows more suppression while we take account the collisional energy loss. • We expect that the consideration of Wood-Saxon density distribution for the colliding • nuclei will improve the scenario. • It is necessary to obtain both radiative and collisional energy loss from the same • formalism to minimize the various uncertainties. • Moreover, data at high pT region with improved statistics are required to remove • prejudice on different energy loss and jet quenching models. Thank you