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Third Moments of Conserved Charges in Phase Diagram of QCD

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### Third Moments of Conserved Chargesin Phase Diagram of QCD

Baryons’10, Dec. 9, 2010, Osaka U.

Masakiyo Kitazawa

(Osaka Univ.)

M. Asakawa, S. Ejiri and MK,

PRL103, 262301 (2009).

MK, et al.,2002

Zhang, et al., ’09

Basler, Buballa, ’10

GL analysis

induced by axial anomaly

QCD Critical PointAnd, how many?

Where is the QCD critical point?

Stephanov, ’07

Phase Diagram of QCD

RHIC, LHC

Quark-Gluon Plasma

T

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

lattice

Hadrons

Color SC

m

0

Ultra-Relativistic Heavy Ion Collisions

from PHENIX collaboration

Observables:

- 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

g

e+

e-

PHENIX, 2009

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

- 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.

Stephanov, Rajagopal, Shuryak ’98,’99

2nd order phase transition at the CP.

baryon # susceptibility

divergences of fluctuations of

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

(Net-)Charge Fluctuations

Asakawa, Heinz, Muller, ’00

Jeon, Koch, ’00

D-measure:

NQ

NQ: net charge # / Nch: total #

Dy

hadrons:

quark-gluon:

values of D:

D ~ 3-4

largesmall

D ~ 1

When is experimentally measured D formed?

- Conserved charges can remember fluctuations
- at early stage, if diffusions are sufficiently slow.

Experimental Results for D-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 D-measure

RHIC results: D ~ 3

PHENIX ’02, STAR ’03

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

STAR, ’10

- 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)

Dy

Take a Derivative of cBcB has an edge along the phase boundary

changes the sign at

QCD phase boundary!

: third moment of

fluctuations (skewness)

- m3(BBB) can be measured by event-by-event
- analysis if NB in Dy is determined for each event.

NB

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

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

(1) cB has a peak structure in the QCD phase diagram.

(2) Hot matter beyond the peak is created in the collisions.

mQ : chemical potential

associated to NQ

Third Moment of Electric ChargeExperimentally,

- net baryon # in Dy : difficult to measure
- net charge # in Dy : measurable!

mQ : chemical potential

associated to NQ

Third Moment of Electric ChargeExperimentally,

- net baryon # in Dy : difficult to measure
- net charge # in Dy : measurable!

cB

cI/9

Under isospin symmetry,

isospin susceptibility

(nonsingular)

singular @CEP

Hatta, Stephanov ’02

The “Ridge” of Susceptibility

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

= 0 at mB=0 (C-symmetry)

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

~ mB at mB>>LQCD (since W~mB4 for free Fermi gas)

T

m

m3(BBB)<0

m3(QQQ)<0

The “Ridge” of SusceptibilityRegion with m3(BBB)<0 is limited near the critical point:

= 0 at mB=0 (C-symmetry)

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

~ mB at mB>>LQCD (since W~mB4 for free Fermi gas)

Analysis in NJL model:

T

m

E : total energy in a subvolume

measurable experimentally

Signs of m3(BBE) and m3(QQE)

change at the critical point, too.

Derivative along T DirectionT

m

- diverges at critical point
- edge along phase boundary

T

m

- diverges at critical point
- edge along phase boundary

T

m

Signs of these three moments change, too!

G=5.5GeV-2, mq=5.5MeV, L=631MeV

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

- on the lattice
- at RHIC and LHC energies

c4

c6

Cheng, et al. ‘08

Trails to the Edge of Mountainsm3(EEE) on the T-axis

- Experimentally: RHIC and LHC

- On the lattice:

m3(QQQ), etc. at mB>0

- Experimentally: energy scan at RHIC

- On the lattice: ex.) Taylor expansion

Summary

Seven third moments

m3(BBB), m3(BBE), m3(BEE), m3(EEE),

m3(QQQ), m3(QQE), and m3(QEE)

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.

Negative moments would be measured and confirmed both

in 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

STAR, 1004.4959

Measurement of the skewness

of proton number @STAR

shows that

for 19.6-200GeV.

Proton # Skewness @STAR

STAR, 1004.4959

Measurement of the skewness

of proton number @STAR

shows that

for 19.6-200GeV.

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

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

Higher Order Moments

Ratios between higher order moments (cumulants)

RBC-Bielefeld ’09

Ejiri, Karsch, Redlich, ’05

Gupta, ’09

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

Quarks:1/32

Hadrons:1

Higher order moments increase much faster near the CP.

Stephanov, ’09

Rajagopal, et al., ’10

Derivative along T direction

simple T-derivative:

E : total energy in a subvolume

measurable experimentally

mixed 3rd moments:

Problem: T and m can not be determined experimentally.

Quark # Scaling of v2

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

How to interpret?

Nonaka, et al., ’03

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