# Presentation: 102170

## Heavy Quarks as a Probe of a New State of Matter:Theory 

- Heavy Quarks and Transport Coefficients
- 			Emil Mottola, T-8
- Energy Loss and Flow of Heavy Quarks
- 			Ivan Vitev, T-16 & P-25
- Lattice QCD Calculations of Tc and EOS
- 			Rajan Gupta, T-8

## What we would like to know about the QGP

- Has RHIC created the non-abelian plasma of ***QCD ***?
- Is ***Chiral Symmetry*** restored in this state?
- What are the ‘right’ ***quasi-particle*** degrees of 	freedom above Tc?
- What are the equilibration ***processes/time scales***?
- What are the detailed mechanisms of ***energy loss***?
- What is the ***viscosity*** of the QGP, and why is it so 	small?

## Heavy (c and b) quarks produced early in the collision, 	survive throughout plasma formation, expansion, 
		     and decay
Large masses (~1.5, 5 GeV) allow more precise, weak 	coupling pQCD methods possible
Yields of heavy quark bound states can be compared with 	lattice QCD simulations to measure Temperature
Mass dependence of heavy quark diffusion allows 	disentagling of QGP relaxation time scales, 	properties  energy loss, viscosity

- 		     and decay
***Large*** ***masses*** **(~1.5, 5 GeV)** allow more precise, weak 	coupling pQCD methods possible
- Yields of heavy quark bound states can be compared with 	lattice QCD simulations to measure** *****Temperature***
***Mass dependence*** of heavy quark diffusion allows 	***disentagling*** of QGP relaxation time scales, 	properties ****** ****energy loss, viscosity**

***Heavy Quarks are a Key Probe***

## Heavy Quark Mass Dependence of Elliptic Flow

## Transport Coefficients and Heavy Quarks

- Transport Coefficients – Fundamental Characterization 	of the Quark-Gluon fluid
- Computing Transport Coefficients in QCD
- Boltzmann Eq.
- Spectral Functions in Lattice QCD
- Real Time Resummations
- Damping Rate of Fermions in a Hot Plasma
- Non-Equilibrium QFT – QCD
- Progress to date and Future Plans

## Slide 6

## Transport CoefficientsViscosity

- Dissipative Parameters of ***Hydrodynamic Flow***
- 		Eg. ***Viscosity***
- 	  Energy-Momentum-Stress Tensor of a Fluid
- 	   *T******p)* *v**** **v**** **** p g***      (perfect fluid)
- [                                                ]  (shear)
- 		+  *g******v**** v***)           (bulk)
- Measure energy cost of spatio-temporal _gradients_
- Dimensions  (~ (***p*)  c(cis collision time)

## Transport Coefficients in Hot Gauge Theories

- Collision Time *********c**** = *******Decay Width of e in Plasma)
- Decay Width ******Imag. Part of Self-energy ******* * ***vanishes*** at any finite order of perturbation theory
***Consistent Resummation*** of perturbation 	required, even for weak coupling
- Technical Problems of infrared divergences and 	gauge dependence had been roadblocks,
- 		***now resolved ***(Debye screening + damping)

## Transport Coefficients:Boltzmann Approach

- Solve Boltzmann eq. by expanding about equilibrium
- 		*f ( ***x**, **p** ; t*)*  classical distribution fn.
- 		 		= Collision integral
- Then compute <***j ***> or <***T***> with this ***f*
- Assumes ***hard*** quasi-***classical*** scattering only
- Not relativistically covariant
- Good only if quantum coherence effects can be neglected  		(coherence length << c )

## Linear Response

- Expresses Transport coefficients in terms of Equilibrium _***Real Time***_ Correlation Functions
***	******	******Egs.****** Electrical Conductivity*** determined by:
- 	 **k**, <j(**x**, t) j(**y**, 0)> ei**k**(**x-y**) e-it  d3x dt
- 			DC =
***	******	******      ******Viscosity***  Coefficients determined by:
- **k**, <T (**x**, t) T(**y**, 0)> ei**k**(**x-y**) e-it  d3x dt
***	******	***First Principles, Fluctuation-Dissipation Relation
- _General_, hard **+** soft, _***quantum***_, _***covariant***_*** ***

## Lattice Spectral Functions

- Measure Finite Temperature Correlation Functions on 	a ***Euclidean Time*** Lattice
***Hard + soft, quantum, covariant, non-perturbative***
- But ***difficult*** (because real time response as *** 0* 	poorly determined by noisy, finite data set on ***n*)
- 	    	Bigger lattices, better statistics needed
- 		— No firm, quantitative results yet...

## Real Time Resummation 

- Avoids continuation from Euclidean lattice
- Gives physical quasi-particles, hard + soft 	scattering, and finite mean free path *********c***
- Fully quantum (coherence effects included), 	relativistic
- Amenable to ***systematic*** analytic 	approximation in weak coupling limit
- Collaborators- M. E. Carrington (Brandon U., Manitoba)
-  &  Z. Szep (Budapest)

## HTLs in Hot Gauge Theory

- Basic Framework is Hard Thermal Loop 	(HTL) Expansion of Braaten, Pisarski, ...
- One-loop, Leading Order (LO) in ***T/p***
- Takes account LO Collective Effects–
- 		Debye Screening, Landau damping
- But Quasi-particles still treated as 	***collisionless:***
- 			***Imag. ************ ******HTL  ******=  0 ***
- Next-to-Leading Order ? Gauge dependence?

## NLO Fermion Self-Energy

- HTL Resummed Fermion Propagator** ****G**
**	****	****G****-1**** ****= ****G****-1****  ****+ *********HTL****                       *
- HTL Photon Propagator** ****D**** **
**	****	****D****-1******** ****= ****D****-1********  ****+ *********HTL***** **********
- HTL Corrected Vertex
**	****	*************HTL **********************HTL                      ******     ***
- Next-to-Leading Order HTL Self-Energy
- *********NLO*************G ************D********D******** **
******************G**************

## Conductivity 

- 	Next step is to input the fermion damping rate and NLO self-energy into Schwinger-Dyson eq. for a NLO resummed vertex
-                  =                 +
- Then Polarization  * **G ****HTL****G *

## Progress to Date

- NLO Resummation beyond Hot Thermal 	Loops (HTL’s) proven correct, gauge 	invariant method in QED & ***QCD***
- Fermion Damping Rate / Mean Free Path of e- 	in hot QED plasma calculated:
- 		     Im NLO = T (2.70)
- 			**Phys. Rev. D 75, 045019 (2007)**
-   → Method is general---relaxation processes of 	QGP determined from microscopic QCD

## Non-Equilibrium QCD

- Viscosity calculation is similar
- Input parameters for non-ideal (viscous) 	hydrodynamics
- Dressed Quasi-particles (Debye screened 	***finite ************c*** quarks, gluons) identified
- First Principles Method works also at finite 	baryon density (neutron stars)
- Effective Action gives both Free Energy (EOS)
***	******and real time*** evolution of soft fields + QGP

## Future Plans

- Complete Calculation of Conductivity in QED
- Damping Rates and Viscosity in QCD
- EOS and evolution eqs. for soft mean fields + hard 	scattering processes
- Comparison with Langevin Diffusion Coefficient,
- 		Energy Loss Calculations & Parameters
- Comparison with Lattice EOS & Spectral Fns.
- Heavy Quark Mass Dependence (***b, c***) of ***p******t***  	distribution in ***elliptic flow ***