Third Moments of Conserved Charges in Phase Diagram of QCD

Third Moments of Conserved Chargesin Phase Diagram of QCD

Masakiyo Kitazawa(Osaka Univ.)

M. Asakawa, S. Ejiri and MK,PRL103, 262301 (2009).

Baryons’10, Dec. 9, 2010, Osaka U.

Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD

T

0

HadronsColor SC

Quark-Gluon Plasma

?

RHIC, LHCla

ttic

e

QCD Critical Point QCD Critical Point QCD Critical Point QCD Critical Point

Where is the QCD critical point? And, how many?

Stephanov, ’07

MK, et al.,2002

MK, et al.,2002

QCD Critical Point QCD Critical Point QCD Critical Point QCD Critical Point

Where is the QCD critical point? And, how many?

Stephanov, ’07

GL analysisinduced by axial anomaly

Yamamoto, et al. ’06

Zhang, et al., ’09

Basler, Buballa, ’10

Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD

T

0

HadronsColor SC

Quark-Gluon Plasma

?

RHIC, LHCla

ttic

e

•non-uniform states?•quarkyonic state?•BEC/pseudogap region?

QCD Thermodynamics on the Lattice QCD Thermodynamics on the Lattice QCD Thermodynamics on the Lattice QCD Thermodynamics on the Lattice

Phase diagram for =0 Equation of States

Hot QCD, 2009

physical?

Ultra-Relativistic Heavy Ion Collisions Ultra-Relativistic Heavy Ion Collisions Ultra-Relativistic Heavy Ion Collisions Ultra-Relativistic Heavy Ion Collisions

from PHENIX collaborationObservables:

•collective flow•photon / dilepton production rates•jet / particle correlations•event-by-event fluctuations and higher order moments•and etc…

NOTE: Experimental data @ LHC is available! ALICE, 1011.3913/3914

Dilepton Production Rate Dilepton Production Rate Dilepton Production Rate Dilepton Production Rate

PHENIX, 2009

•Most direct probes of the QGP.•They are produced in all stages of time evolution.

e+

e-

Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD Phase Diagram of QCD

T

0

HadronsColor SC

?

RHIC, LHCla

ttic

e

RHIC energy scan

Fluctuations at QCD Critical Point Fluctuations at QCD Critical Point Fluctuations at QCD Critical Point Fluctuations at QCD Critical Point

2nd order phase transition at the CP.

divergences of fluctuations of

•pT distribution•freezeout T•baryon number, proton, chage, …

Stephanov, Rajagopal, Shuryak ’98,’99

baryon # susceptibility

However,•Region with large fluctuations may be narrow.•Fluctuations may not be formed well due to critical slowing down. •Fluctuations will be blurred by final state interaction.

(Net-)Charge Fluctuations (Net-)Charge Fluctuations (Net-)Charge Fluctuations (Net-)Charge Fluctuations

2( )4

Q

ch

ND

N

D-measure:

Asakawa, Heinz, Muller, ’00Jeon, Koch, ’00

When is experimentally measured D formed?•Conserved charges can remember fluctuations at early stage, if diffusions are sufficiently slow.

NQ

NQ: net charge # / Nch: total # y

0

0

us

s

d

duu

d

gg

g g

g

hadrons:hadrons: quark-gluon:quark-gluon:

D ~ 3-4 D ~ 1largesmall

values of D:

Experimental Results for Experimental Results for DD-measure -measure Experimental Results for Experimental Results for DD-measure -measure

RHIC results: D ~ 3

PHENIX ’02, STAR ’03

•hadron gas: D ~ 3-4•free quark-gluon gas: D ~ 1

STAR, ’10

Experimental Results for Experimental Results for DD-measure -measure Experimental Results for Experimental Results for DD-measure -measure

•Failure of QGP formation?•Is the diffusion so fast?

NO! The result does not contradict these statements.Large uncertainty in Nch. Bialas(’02), Nonaka, et al.(’05)

RHIC results: D ~ 3

PHENIX ’02, STAR ’03

•hadron gas: D ~ 3-4•free quark-gluon gas: D ~ 1

STAR, ’10

Take a Derivative of Take a Derivative of BB Take a Derivative of Take a Derivative of BB

B has an edge along the phase boundary

B

B

changes the sign at QCD phase boundary!

•m3(BBB) can be measured by event-by-eventanalysis if NB in y is determined for each event.

33

33 2

( )1(BB )B

B

B B

B mVT

N

V

: third moment of fluctuations (skewness)

22

2

( )1 B

BB V VT

N

y

NB

Impact of Negative Third Moments Impact of Negative Third Moments Impact of Negative Third Moments Impact of Negative Third Moments

Once negative m3(BBB) is established, it is evidences that

(1) B has a peak structure in the QCD phase diagram.(2) Hot matter beyond the peak is created in the collisions.

•No dependence on any specific models.•Just the sign! No normalization (such as by Nch).

Third Moment of Electric Charge Third Moment of Electric Charge Third Moment of Electric Charge Third Moment of Electric Charge

•net baryon # in y : difficult to measure•net charge # in y : measurable!

Experimentally,

3 3

3 2 3

(( QQ

1Q

))

Q

Q

mV

N

T V

Q : chemical potential associated to NQ

Under isospin symmetry,

3

1 1( )

8 2QQQ

7 B IB

m

singular @CEP isospin susceptibility(nonsingular)

Hatta, Stephanov ’02

Third Moment of Electric Charge Third Moment of Electric Charge Third Moment of Electric Charge Third Moment of Electric Charge

•net baryon # in y : difficult to measure•net charge # in y : measurable!

Experimentally,

3 3

3 2 3

(( QQ

1Q

))

Q

Q

mV

N

T V

Q : chemical potential associated to NQ

B

I/9

The “Ridge” of Susceptibility The “Ridge” of Susceptibility The “Ridge” of Susceptibility The “Ridge” of Susceptibility

= 0 at B=0 (C-symmetry)

m3(BBB) is positive for small B (from Lattice QCD)

Region with m3(BBB)<0 is limited near the critical point:

~ B at B>>QCD (since ~B4 for free Fermi gas)

T

The “Ridge” of Susceptibility The “Ridge” of Susceptibility The “Ridge” of Susceptibility The “Ridge” of Susceptibility

Analysis in NJL model:

= 0 at B=0 (C-symmetry)

m3(BBB) is positive for small B (from Lattice QCD)

Region with m3(BBB)<0 is limited near the critical point:

~ B at B>>QCD (since ~B4 for free Fermi gas)

T

m3(BBB)<0

m3(QQQ)<0

Derivative along Derivative along TT Direction Direction Derivative along Derivative along TT Direction Direction

Signs of m3(BBE) and m3(QQE) change at the critical point, too.

T

T

ˆT T T

ˆ /T

2

3 3ˆ

2

3 3ˆ

( ) ( )1( )

( ) ( )1

E

EQQ( )

BBB B

QQ

Tm

VT T T

Tm

VT

N

N

T

E

T

E

E : total energy in a subvolume measurable experimentally

More Third Moments More Third Moments More Third Moments More Third Moments 3 2

ˆ3 5 3

ˆ

2ˆ

3 4

2ˆ

3 4

( ) ( )1( )

( ) 1( )

(

B

EEE

EE

EE) 1

(2

Q )Q

B

B

B

E

E

T Cm

VT T T

Cm

VT T

Cm

VT T

N

N

E

T

T

ˆT

ˆ /T

22

ˆ 2 2ˆ

( )TC

V T V

E

T

“specific heat” at constant ̂•diverges at critical point•edge along phase boundary

More Third Moments More Third Moments More Third Moments More Third Moments 3 2

ˆ3 5 3

ˆ

2ˆ

3 4

2ˆ

3 4

( ) ( )1( )

( ) 1( )

(

B

EEE

EE

EE) 1

(2

Q )Q

B

B

B

E

E

T Cm

VT T T

Cm

VT T

Cm

VT T

N

N

E

Signs of these three moments change, too!

T

T

ˆT

ˆ /T

22

ˆ 2 2ˆ

( )TC

V T V

E

T

“specific heat” at constant ̂•diverges at critical point•edge along phase boundary

Model Analysis Model Analysis Model Analysis Model Analysis

•Regions with m3(*EE)<0 exist even on T-axis. This behavior can be checked

2-flavor NJL; G=5.5GeV-2, mq=5.5MeV, =631MeV

•on the lattice•at RHIC and LHC energies

Trails to the Edge of Mountains Trails to the Edge of Mountains Trails to the Edge of Mountains Trails to the Edge of Mountains

m3(EEE) on the T-axis

2 3

3 3 3

1 ( ) 1E( )E E

C S

T

T Tm

T T T T

•Experimentally: RHIC and LHC

•On the lattice:

Trails to the Edge of Mountains Trails to the Edge of Mountains Trails to the Edge of Mountains Trails to the Edge of Mountains

m3(EEE) on the T-axis

2 3

3 3 3

1 ( ) 1E( )E E

C S

T

T Tm

T T T T

•Experimentally: RHIC and LHC

•On the lattice:

•Experimentally: energy scan at RHIC

•On the lattice: ex.) Taylor expansion

2 4 62 4 6B B Bc c c

3 4 63( ) ~BBB 5B Bm c c

Cheng, et al. ‘08

c4 c6

m3(QQQ), etc. at >0

Summary Summary Summary Summary

Seven third moments

all change signs at QCD phase boundary near the critical point.

To create a contour map of the third moments on the QCD phase diagram should be an interesting theoretical subject.

m3(BBB), m3(BBE), m3(BEE), m3(EEE), m3(QQQ), m3(QQE), and m3(QEE)

Negative moments would be measured and confirmed bothin heavy-ion collisions and on the lattice. In particular,

(1) m3(EEE) at RHIC and LHC energies,(2) m3 (QQQ)=0 at energy scan,

are interesting!

Proton # Skewness @STAR Proton # Skewness @STAR Proton # Skewness @STAR Proton # Skewness @STAR STAR, 1004.4959

Measurement of the skewnessof proton number @STARshows thatfor 19.6-200GeV.

3( ) 0PN

Proton # Skewness @STAR Proton # Skewness @STAR Proton # Skewness @STAR Proton # Skewness @STAR

Remark: Proton number, NP, is not a conserved charge.

No geometrical connection b/w 2nd & 3rd moments.3 2

2

( ) ( )P P

PVT V

N

T

N

Measurement of the skewnessof proton number @STARshows thatfor 19.6-200GeV.

STAR, 1004.4959

3( )BBB B

B

m

3( ) 0PN

Higher Order Moments Higher Order Moments Higher Order Moments Higher Order Moments

Ratios between higher order moments (cumulants)

Higher order moments increase much faster near the CP.

Ejiri, Karsch, Redlich, ’05Gupta, ’09

Stephanov, ’09Rajagopal, et al., ’10

RBC-Bielefeld ’09

Hadrons:1 Quarks:1/32

4th/2nd at =0 reflects the charge of quasi-particles

Derivative along Derivative along TT direction direction Derivative along Derivative along TT direction direction

simple T-derivative:2 3 2

3

2 3 2

3

( ) ( ) ( )

( ) ( ) ( )Q

B

I

B

Q Q

B BT

T VT

E

E T

T V

N

T

N N

N N N

E : total energy in a subvolume

2 2

3 33 3

( ) ( )( ) , ( )BQEQ EB

Q ENm m

VT VT

E EN

measurable experimentally

Problem: T and can not be determined experimentally.

mixed 3rd moments:

Elliptic Flow 1 Elliptic Flow 1 Elliptic Flow 1 Elliptic Flow 1

reactionplane

beam axis

x

z

Ｙ

Elliptic flow v2

reactionplane

v2>0 v2<0

3

3~ 1 2 cosn

n

d NE v n

dp

Quark # Scaling of Quark # Scaling of vv22 Quark # Scaling of Quark # Scaling of vv22

Nonaka, et al., ’03

•Divide by quark number.•Clear quark number scaling!

How to interpret?

Elliptic Flow @ ALICE Elliptic Flow @ ALICE Elliptic Flow @ ALICE Elliptic Flow @ ALICE

Heavy ion collisions have been performed at LHC!

ALICE, 1011.3914

new data