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Evolution of Heavy Quarks in Quark-Gluon Plasma: A Study on Dragging and Diffusion

This study investigates the evolution of heavy quarks in quark-gluon plasma through Fokker-Planck equations and explores the drag and diffusion coefficients of these quarks. It examines the pre-equilibrium and thermal phases, as well as the interaction with light quarks and gluons. The study also compares the Langevin/FP approach with the Boltzmann equation.

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Evolution of Heavy Quarks in Quark-Gluon Plasma: A Study on Dragging and Diffusion

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  1. Dragging Heavy Quarks by Quark Gluon Plasma DAE-BRNS 2nd Heavy Flavour Meet, February 3 - 5, 2016, SINP, Kolkata

  2. Plan: • Introduction • HQs evolution through Fokker-Planck Eqs • Drag/Diffusion coefficients of HQs • Pre-equilibrium phase • Thermal phase • Hot hadrons • Do the HQs follow the flow of LQs/gluons? • Langevin/FP vs Boltzmann • Summary

  3. Relativistic hydrodynamics is a tool to describe the space-time evolution of the matter formed in heavy ion collisions. The relevant Eqs are: Initial Conditions Equation of State Freeze-out Condition

  4. HQs thermalize later than gluons and light quarks. Thermalization time for HQ ~ (MHQ/T)× Thermalization time for light quarks (G. Moore & D. Teaney, PRC 2005) JA, S. Raha and B. Sinha, PRL 1994. • Gluons & light quarks thermalize and provide an expanding thermal background • for the non-equilibrated HQs. Interactions between equilibrated and • non-equiliobrated degrees of freedom. • Evolution of the • expanding background is governed by the hydrodynamics, • HQs is governed by Fokker-Plank Equation.

  5. Motion of heavy quarks in Quark Gluon Plasma ~ Pollen Grains (HQs) in Water (QGP). Fokker-Planck Equation can be used to describe the evolution of the HQs in the QGP B. Svetitsky, PRD 1988; S. Chakraborty and D. Syam, Lett. Nuovo Cim. 1984

  6. Dragging heavy flavours in QGP Why HQ? – Early Production - Do not decide bulk properties Evolution of HQs in QGP

  7. Landau Kinetic equation. replaced reduced where we have defined the kernels , → Drag Coefficient → Diffusion Coefficient (Physical Kinetics, Lifshitz & Pitaevskii) Non -equilibrium Equilibrium Distribution Function Distribution Function Landau Kinetic Equation Fokker Planck Equation

  8. Inputs: • Initial heavy quark distributions: from pp collisions (Mangano, Nason & Ridolfi NPB 1992). • Dissipatative process: collisional, radiative • c and b fragmentation functions to D, B mesons (C. Peterson et. al. PRD 1983) • Decay of heavy mesons to single e- (M. Gronau et. al., NPB 1977)

  9. Drag of Heavy Quarks Collisional Radiative Q+q->Q+q+g Wang et al, PRD 1995 Mustafa et, PLB 1998; Abir et al 2011, Bhattacharyya et al 2012 Dead cone effects Insert thermal mass into the internal gluon propagator in the t-channel exchange diagrams to shield the infrared divergence.

  10. Drag/Diffusion due to collisional and radiative losses R. Abir et al, PRD 2012 Drag, p= 5GeV p=5 GeV T=525 MeV T=525 MeV

  11. Diffusion due to collisional and radiative losses

  12. Do the HQs follow the distribution of the bath particles? FP Eq. can be written as: In statistical equilibrium the flux = 0 (Physical Kinetics, Lifshitz & Pitaevskii)

  13. For Tsallis distribution: Walton & Rafelski, PRL 2000. T=725 MeV T=525 MeV Shear viscosity vs diffusion S. Mazumder et al, PRD 2014 Majumder et al, PRL 2007

  14. Momentum space Diff. coeff. =Drag coeff. Ti=300 MeV RHIC and Spatial diff. coeff Compare with Mazumder, Bhattacharyya, Alam & Das 2012

  15. Role of hadrons in the suppression of heavy flavours Diffusion coefficient, D-meson Drag, D-meson D-meson Diffusion coefficient, B-meson Solid line calculated. Dashed line estimated from Einstein relation.

  16. Role of hadrons Das, Ghosh, Sarkar, JA , PRD 2013; PRD 2012; PRD 2011. LHCC RHICC Hadronic suppression is marginal Useful to characterize QGP using HF suppression

  17. Shear viscosity to entropy ratio: eta/s: of QGP (RHIC data) ~of Li6 atoms [Temperature difference ~1019 density differnece 1025 with QGP] ~of finite nuclei (Auerbach & Shlomo PRL 2009) ~(1-5)/4pi

  18. How fast is the thermalization? Classical Yang-Mills (CYM) & Kharzeev-Levin-Nardi (KLN) gluon distributions LHC RHIC Schenke et al., PRC 2014; Drescher & Nara, PRC 2007.

  19. Evolution of HQs in pre-equilibrium stage Das et al, JPG 2015 QGP , Ti=340 MeV Drag and Diffusion of Charm quark mD ~

  20. Drag and diffusion coefficients of bottom quark QGP , Ti=340 MeV QGP , Ti=510 MeV

  21. Evolution: Boltzmann vsLangevin (Charm) Momentum evolution starting from a  (Charm) in a Box Boltzmann Langevin In case of Langevin the distributions remain Gaussian. In case of Boltzmann the charm quarks follow the ~ Brownian motion at Low Momentum. Das, Scardina, Plumari and Greco, PRC,90,044901(2014)

  22. Evolution: Boltzmann vsLangevin (Charm) Momentum evolution starting from a  (Charm) in a Box Boltzmann Langevin mD=0.83 GeV In case of Langevin the distributions are Gaussian as expected. In case of Boltzmann the charm quarks does not follow the Gaussian shape at high momentum.

  23. Momentum evolution starting from a  (Bottom) Boltzmann Langevin P=10 GeV P=10 GeV P=5 GeV For bottom quarks it works better.

  24. Boltzmann vsLangevin Charm Charm mD=0.4 GeV mD=0.83 GeV Bottom Bottom T= 400 MeV mD=0.4 GeV T= 400 MeV mD=0.83 GeV Das, Scardina, Plumari and Greco PRC,90,044901(2014)

  25. Summary • Radiative loss plays dominant role at RHIC/LHC energies • HQs do not follow the LQs/gluon distributions • Pre-Equilibrium phase important for low energy collisions • Hadrons play marginal role at LHC makes HF suppression very effective for characterizing QGP • Improvements? • Non-perturbative QCD inputs, initial conditions for expanding background, EoS; initial conditions for the probe (HQs) suffer from some degree uncertainities.

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