Dragging Heavy Quarks by Quark Gluon Plasma

DAE-BRNS 2nd Heavy Flavour Meet, February 3 - 5, 2016, SINP, Kolkata 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 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 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. 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 Dragging heavy flavours in QGP Why HQ? – Early Production - Do not decide bulk properties

Evolution of HQs in QGP

f    ApfBpf  i  ij t pi pj 

Landau Kinetic equation.

f    ApfBpf  i  ij t pi pj 

where we have defined the kernels ,

 3, → Drag Coefficient Ai dk(pk)ki

 3, → Diffusion Coefficient Bij dk(pk)kikj (Physical Kinetics, Lifshitz & Pitaevskii) d3q (p,k)g f(q)v (2)3 q,pp,qpk,qk

Non -equilibrium Equilibrium replaced Distribution Function Distribution Function

reduced Landau Kinetic Equation Fokker Planck Equation 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) Drag of Heavy Quarks

gcgc

Collisional

qcqc

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. 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 Diffusion due to collisional and radiative losses 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) 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 Momentum space Diff. coeff.

=Drag coeff. Ti=300 MeV

RHIC

and

Spatial diff. coeff

Compare with

Mazumder, Bhattacharyya, Alam & Das 2012 Role of hadrons in the suppression of heavy flavours

Diffusion coefficient, Drag, D-meson D-meson D-meson

Diffusion coefficient, B-meson Solid line calculated. Dashed line estimated from Einstein relation. 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 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 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. Evolution of HQs in pre-equilibrium stage Das et al, JPG 2015

QGP , Ti=340 MeV

Drag and Diffusion of Charm quark

mD ~ Drag and diffusion coefficients of bottom quark

QGP , Ti=340 MeV

QGP , Ti=510 MeV Evolution: Boltzmann vs Langevin (Charm)

Momentum evolution starting from a  (Charm) in a Box dN   p  2GeV  d 3 p Langevin initial Boltzmann

In case of Langevin the In case of Boltzmann the charm quarks follow distributions remain Gaussian. the ~ Brownian motion at Low Momentum.

Das, Scardina, Plumari and Greco, PRC,90,044901(2014) Evolution: Boltzmann vs Langevin (Charm)

Momentum evolution starting from a  (Charm) in a Box dN   p 10GeV  d 3 p Langevin initial Boltzmann

mD=0.83 GeV

In case of Langevin the In case of Boltzmann the charm quarks does distributions are Gaussian as not follow the Gaussian shape at high momentum. expected. Momentum evolution starting from a  (Bottom)

Langevin Boltzmann

P=10 GeV P=10 GeV

P=5 GeV For bottom quarks it works better. Boltzmann vs Langevin

Charm Charm

mD=0.4 GeV mD=0.83 GeV

Bottom Bottom

T= 400 MeV T= 400 MeV mD=0.4 GeV mD=0.83 GeV

Das, Scardina, Plumari and Greco PRC,90,044901(2014) 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.