QGP Meet Institute of Physics Bhubaneshwarsgupta/talks/04bhubaneshwar.pdf · 2009. 3. 25. · QCD...

Predictions for QCD matter

Sourendu Gupta (TIFR, Mumbai)

October 6, 2004

QGP Meet

Institute of Physics

Bhubaneshwar

Plan of the talk

1. Aspects of high T QCD

2. The speed of sound and specific heat

3. Electrical conductivity and viscosity

4. Fluctuations and chemistry

5. Jet quenching crabwise; no J/ψ suppression

Collaborators: Saumen Datta (Bielefeld), Rajiv Gavai (TIFR), Robert Lacaze(Saclay), Manu Mathur (SNBNCBS), Swagato Mukherjee (TIFR), Rajarshi Ray(TIFR).

Machines: 486, Pentiums, SGI Origin, DEC α, NEC SV5, CRAY X1

QCD Matter/S. Gupta: Bhubaneshwar, 2004 plan, the plasma, c2s and cV , η/S and σ/T , fluctuations, summary 1

The Indian Lattice Gauge Theory Initiative


Aspects of high T QCD matter

It is a plasma

Overall charge/colour neutrality— Debye screening, Landau damping.Probes: all quantitative— need to measure correlations between fluctuations andviscosities or other dissipative response functions.

It is a strongly dissipative fluid

Large viscosity, small correlation lengths.Consequences: many qualitative— probes lose momentum quickly (jetquenching?), early thermalization, independent fluctuations.Caution: May mimic ideal fluids— independent fluctuations, speed of sound, etc.


The phase diagram of QCD (1)

T

Tc(T , )µ∗∗

m

µ0

s=0

s>0

1

2

1. Fodor and Katz (2000) mπ/mρ = 0.185(2), mρ/Tc = 5.372(5), Lmπ = 3.1–3.9

2. Allton et al (2003) mπ/mρ = 0.70(1), mρ/Tc = 5.5(1), Lmπ = 15.4(5)

Compensation between mπ dependence and L dependence: accidental?

Berges and Rajagopal, Halasz, Jackson, Shrock, Stephanov and Verbaarschot: (1998)



T

Tc(T , )µ∗∗

m

µ0

s=0

s>0

2

1. Fodor and Katz (2000) mπ/mρ = 0.185(2), mρ/Tc = 5.372(5), Lmπ = 3.1–3.9

2. Allton et al (2003) mπ/mρ = 0.70(1), mρ/Tc = 5.5(1), Lmπ = 15.4(5)

Compensation between mπ dependence and L dependence: accidental?

Berges and Rajagopal, Halasz, Jackson, Shrock, Stephanov and Verbaarschot: (1998)



T

Tc(T , )µ∗∗

m

µ0

s=0

s>0

Parameters in Nf = 2: T , µ0 = (µu + µd)/2 = µB/3, µ3 = (µu − µd)/2 = µI,m = (mu +md)/2, ∆m = mu −md.

Parameters in Nf = 2 + 1: T , µB, µI, µY (µs), m, ∆m, ms.



p>0

s=p=0

s >0uLOFF

Τ

µ3

µ0

A

(T , )µ∗ ∗

s>0

p

s

A

sp

A

Son and Stephanov (2000), Klein Toublan and Verbaarschot (2003), Nishida (2003),

Barducci, Casalbuoni, Pettini and Ravagli (2004)

(T ∗, µ∗)— penta-critical point (earlier called tri-critical: only for mu = md =)A— tri-critical point (remains for arbitrary mu and md).

SG and R. Ray, in progress



p>0

s=p=0

s >0uLOFF

Τ

µ3

µ0

s>0

A

(Τ ,µ )∗ ∗p=0

p>0

T

µ0

µ3

All is not lost— there are critical points and phase transitions to be discoveredeven in the real world of strong interactions.


Beyond EOS: speed of sound and specific heat

In a relativistic theory: P (T, µ), i.e., pressure adjusts itself if T is changed. Hencecompressibility is not well defined for µ = 0. As a result there are only two secondderivatives of the free energy—

c2s =1V

∂E

∂P

∣∣∣∣S

, cV =1V

∂E

∂T

∣∣∣∣V

.

Recall the definition of the trace of the stress-energy tensor—

∆T 4

=E/V − 3P

T 4.

∆ = 0 is a conformal field theory (i.e., scale symmetric). In QCD ∆ 6= 0.

Breaking of scale symmetry implies c2s 6= 1/3 and cV /T 3 6= 4E/V T 4.


Speed of sound

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

1 1.5 2 2.5 3 3.5 4

C s2

T/Tc

Ideal gas/CFT

Black: re-analysis of Bielefeld’s Nt = 4 data (SG, QCD 2002: IIT-K)Red: new results for continuum limit (Mukherjee, Gavai, SG, in progress)Coming soon: closer to Tc and below Tc, continuum limit.


Specific heat

0

5

10

15

20

25

1.5 2 2.5 3 3.5T/Tc

Ideal gas

4E/T4

Cv/T3

Results are far from ideal gas (6–8σ), but close to CFT (1–2σ).Gavai, SG. Mukherjee, in progress

Experimental question: is it feasible to measure event-to-event ∆T/T in thefireball?


Transport coefficients: Shear Viscosity

1. AdS/CFT gives η/S ≥ 1/4π. (Son, Starinets et al.)

2. Perturbation theory contains a log(1/g) factor which is negative for T/Tc ≤ 7.(Arnold, Yaffe and Moore)

3. 2 → 2 collisions with constant cross section, σ0 = 10 mb gives η = 1.264T/σ0.(Gyulassy and Molnar)

4. RHIC data can be fitted in blast wave model with η/S ≈ 0.14. (Teaney)

5. Lattice? Direct computation difficult but another method possible. Computeelectrical conductivity and extract thermalization time scale from it usingσ = 〈e2〉nqτq/m, where nq ' S/V , m is thermal mass. τq = 0.3 fm. Assumeτg ' τq/2. Then η/S ≈ 0.2. (SG, [PL B597 57, 2004])


Electrical conductivity and photon production

The differential photon emissivity is given by—

ωdΩd3p

=〈e2〉8π3

nB(ω;T )ρµµ(ω,p;T ) where 〈e2〉 = 4πα∑

f

e2f ≈121.

In terms of the DC electrical conductivity (j = σE)

σ(T ) =〈e2〉6

∂

∂ωρii(ω,0;T )

∣∣∣∣ω=0

,8π3ω〈e2〉T 2

dΩd3p

= 6σ

T.

Since kµρµν = 0, we have ρ00 = 0 along the line p = 0. Formally,

ρ00(ω,0;T ) = 2πχQωδ(ω),

where χQ is the charge susceptibility.


Perturbation theory: pinch singularities

There are pinch singularities at small external energy, ω, from ladder diagrams—corresponding to multiple scatterings off particles in the plasma.

ρ(ω

)

ω/Τgg ln(g)2

2π T

2π T Nt= 2π/a

Arnold, Moore and Yaffe,

G. Aarts and J.M.M. Resco JHEP 0204:053,2002


The spectral function

Since the problem is linear, work with

∆G(ω,p;T ) = Gfull(ω,p;T )−Gideal(ω,p;T ) =∫ ∞

0

dωK(ω, τ ;T )∆ρ(ω,p;T ).

This gets rid of a ω2 divergence at infinity and shows a bump at small ωcorresponding to Landau damping.

1

10

100

0 0.2 0.4 0.6 0.8 1

G

/3T

3V

∆

tT





0



-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2

aa

V2 ∆

ρ (

ω)

Tω/π





0



-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2

aa

V2 ∆

ρ (

ω)

Tω/π

integration method





0



-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2

aa

V2 ∆

ρ (

ω)

Tω/π

integration method+ bin size





0



-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2

aa

V2 ∆

ρ (

ω)

Tω/π


+ integration limits





0



-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2

aa

V2 ∆

ρ (

ω)

Tω/π


+ integration limits+ Bayesian prior





0



-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2

aa

V2 ∆

ρ (

ω)

Tω/π

(

) X 3


+ integration limits+ Bayesian prior


Electrical Conductivity and damping of low frequency photons

0

25

50

75

1 1.5 2 2.5 3 3.5

d

C

Td

p2

3 =

p=0

EM3

8π ω

Ωω

T/T c

Estimate Landau damping at ωL ≈ 200 MeV, and τq ≈ 0.3 fm. Mean free path ofphotons with E ≤ ωL is τq/〈e2〉 ≈ 20× 0.3 = 6 fm. (Another approach: plugσ ≈ 1/7T into Maxwell’s equations and find skin depth)

Question to experimentalists: can you see this independent check of the shearviscosity? Connect hydrodynamics to photons— single source of dissipation.


Fluctuations and chemistry

Taylor coefficients of various quantities in µ—

1. of free energy gives charge and baryon number fluctuations

2. of chiral condensate gives correlation volume of charge fluctuations (R. Ray’stalk)

3. ratio of QNS gives ratio of production rates of quarks of different mass(Wroblewski parameter)

-0.18

-0.16

-0.14

-0.12

-0.10

-0.08

-0.06

-0.04

-0.02

0

0.02

0.5 1.0 1.5 2.0 2.5

χ

/Τ2

11

T/Tc

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.5 1.0 1.5 2.0 2.5

χ

/Τ2

20

T/Tc


Correlation volume of baryon number fluctuations (1)

Correlations between baryon number fluctuations (flavour singlet, C = −1) arecarried by pure glue operators. Correlation lengths are given by the screening massof the glue operator A30.

Bödeker and Laine [JHEP 0109 029, 2001]

Leading order pertubative evaluation performed recently, agrees with latticemeasurements of χ11 for T ≥ 2Tc.

Gavai and SG [PR D64 074506, 2001], Blaizot, Iancu and Rebhan [PL B523 143, 2001]



0

1

2

3

4

5

6

1 2 3

1/T

L(T

)

pert

T/Tc

Debye (colour) screening: A1++

Baryon number screening: A2--

Glueball-like screening masses

Baryon number screening length increases near Tc.Probably drops again below Tc.Diffusion rate expected to decrease near Tc.Datta and SG [PR D67 054503, 2003]



1.0

1.5

2.0

2.5

3.0

3.5

1.0 1.5 2.0 2.5 3.0

T=0

Perturbative

L(A

)

/L(A

)

12

++

- -

T/Tc

Ratio of Debye screening length to baryon number correlation length increasesnear Tc. Evidence for non-perturbative physics.Datta and SG [PR D67 054503, 2003]


Strange quark production rate

0.2 0.4 0.6 0.8 1

[ ]

λs

AGS Si-Au

AGS Au-Au

SpS Pb-Pb

SpS S-Ag

SpS S-S

RHIC Au-Au

Quenched QCD (T )c

0.2

0.4

0.6

0.8

1.0

0.5 1 2 3

sλT/T c

m /T =0.1, m /T =1.0cscu

N =0fN =2f

Ratio of production rates for heavy and light quarks equals the ratio of the QNSfor the two quarks. Agrees with data on Wroblewski parameter extracted fromexperiments.

Gavai and SG (2002), Cleymans (2002), Gavai and SG in preparation.

More in talk by R. Ray


Summary

1. No phase transition at µ = 0 when mπ > 0, but many phases reachable inheavy ion collisions by tuning T , µB and µq. Many different critical points maybe within reach— need intense new lattice computations.

2. Speed of sound may be compatible with ideal gas or CFT. Specific heat liftsthe degeneracy, and shows QCD is close to CFT and far from ideal gas.

3. Viscosity inferred from lattice data is not far from the CFT limit, and agreeswith value obtained by fitting to experimental data. Consequence is that softphotons feel a skin-depth in the plasma. Like jet quenching can experimentssee also soft photon dimming?

4. Theory of fluctuations now very firm. Fluctuation length scales and timeconstants are computable on the lattice. How much fluctuation survives thequark-hadron cross over? Need a firmer estimate of the critical end point to pinthis down.


StartPlanIntroPhase diagram

Sound and specific heatSpeed of soundSpecific heat

TransportLinear ResponsePinch singularitiesSpectral functionPhoton damping

Fluctuations and chemistryCorrelation volumeStrange quarks

Summary

QGP Meet Institute of Physics Bhubaneshwarsgupta/talks/04bhubaneshwar.pdf · 2009. 3. 25. · QCD...

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