Kenji Morita 24 June, 20141 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions,

24 June, 2014 1

Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”

Probing the QCD Phase Boundary Probing the QCD Phase Boundary with Fluctuations of Conserved with Fluctuations of Conserved

Charges Charges

Kenji MoritaKenji Morita

(FIAS)(FIAS)

24 June, 2014 2/19


Search for Phase Transition in Search for Phase Transition in QCDQCD

Fukushima-Hatsuda, Rep.Prog.Phys.74 ‘11

Towards understanding the Towards understanding the origin of the matterorigin of the matter

Chiral transitionChiral transition

ConfinementConfinement

Theoretical Expection

(from lattice QCD and models)

For the statistical system specified by (T, )

Heavy Ion Collisions :

Evidence for high energy density matter (QGP)

Phase Transition ?

1012K

24 June, 2014 3/19


Multiplicity Fluctuations in Heavy Ion Multiplicity Fluctuations in Heavy Ion CollisionsCollisions

O(107) events@RHIC

Counting # of particles within a given circumstance (centrality,

acceptance etc)

Averaging over events STAR, net-proton, PRL112 (’14)

24 June, 2014 4/19


Fluctuations Indicate Phase Fluctuations Indicate Phase TransitionTransition

Observable through Observable through multiplicity distribution multiplicity distribution

P(N)P(N)

Higher order – more sensitive to criticalityHigher order – more sensitive to criticality

Not observable…

(Stephanov ’09)

of Conserved Charges

24 June, 2014 5/19


Quantifying FluctuationsQuantifying FluctuationsProb. Distribution ~ Canonical Partition Function

Shape : Cumulants Volume∝Note: Need Cancellation !

Higher order n contains <(N)n>

→ Need more information on the tail !

M: Mean, 2: Variance, S: Skewness, : KurtosisNo statistically meaningful measurement of 6 yet…

24 June, 2014 6/19


Grand Canonical Ensemble Grand Canonical Ensemble DescriptionDescription

Chemical freeze-out : Equilibrated hadron gasChemical freeze-out : Equilibrated hadron gasParticle number (1st moment) : OK

Tfo ～ phase boundary

Expectation : measured fluctuations = those of GCEExpectation : measured fluctuations = those of GCE

24 June, 2014 7/19

Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”Net Baryon Number Fluctuation in Net Baryon Number Fluctuation in

HRGHRG=Skellam Distribution=Skellam Distribution

# of baryons （ Poisson) # of antibaryon (Poisson) Statistical mechanics : Boltzmann distribution 2 parameters

Expectation : 1 and 2 are well described by HRG

Deviation from Skellam in higher order n should reflect the phase transition

Ratio cancels Volume

dependence

Karsch-Redlich ‘11

24 June, 2014 8/19


QCD ≒QCD ≒HHadron adron RResonance esonance GGasas ？？

Wuppertal-Budapest

Wuppertal-Budapest

Wuppertal-Budapest BNL-

Bielefeld

T<155MeV : Good approx.

Substantial deviation at Higher order

24 June, 2014 9/19


Net-Proton Measurements by Net-Proton Measurements by STARSTAR

Correction by bin width and reconstruction efficiency

STAR, PRL114

Substantial Deviation from the HRG expectation

Caveat :

Net-proton≠Net-baryon

Q : Is this deviation consistent with phase transition?

Is there any other explanations?

What is the underlying probability distribution?

24 June, 2014 10/19


Th. Expectations for the Th. Expectations for the CumulantsCumulants

Chiral Limit

T

TCP?

mq

2nd Order, 3d O(4) Phys. quark mass

mphys

Crossover – Feel O(4)?

CP?

BES@RHIC

6 changes the sign

across crossoverGeneral property from O(4) scaling function

(Engels and Karsch ’11, Friman et al., ’11)

divergence

change the signHatta-Ikeda ’03, Asakawa et al.,’09, Skokov et al., ’11, Stephanov, ‘11

Pisarski-Wilczek ‘84

24 June, 2014 11 /19


Probability Distribution P(N) Probability Distribution P(N) and Cumulants and Cumulants nn at nonzero at nonzero

From QCD : Sign Problem ! (No MC simulation reliable)

Use of chiral effective model (LM, NJL, etc)

Extract qualitative feature relevant to QCD

Z(2) CP : Still uncertain

Remnant of O(4) in Crossover : Our suggestion

24 June, 2014 12/19


P(N) w/ Chiral Quark-Meson Model P(N) w/ Chiral Quark-Meson Model (N(Nff==22)) , , , q , q (also below T(also below Tcc))

Crossover at Crossover at =0 : T=0 : Tpcpc=214 MeV=214 MeV

Critical point @large

Common fluctuation property with QCD near phase boundary

Reminder : Criticality appears higher order cumulants

Solving the model : proper treatment of the critical flucuations

KM et al., PRC88 ’13 for detail

24 June, 2014 13/19


QM model w/ FRG approachQM model w/ FRG approach

Effective potential is obtained by solving the exact flow equation (Wetterich eq.) with approximations preserving correct critical exponents

Full propagators with k < q <

q q

Integrating from k= to k= gives a full quantum effective potential

Put obtained k=0(min)into the integral formula for P(N)

(Stokic-Friman-Redlich ’10)

S classical

24 June, 2014 14/19


Reference for the Critical Reference for the Critical BehaviorBehaviorHigher order cumulants need Higher order cumulants need tailtail of P(N) of P(N)

Skellam distribution w/ same Skellam distribution w/ same

Estimate # of data points to get correct Estimate # of data points to get correct 66 in Skellam, then rescale in Skellam, then rescale Removing different VTRemoving different VT33 effect in various P(N) data effect in various P(N) data

<N>

P(N)

N6

P(N) reproducing 6

24 June, 2014 15/19


Characterize Critical Behavior : P(N) Characterize Critical Behavior : P(N) ratioratio

Ratio < 1 at large |N| for 6/2 < 1

T

Narrower tail as approaching Tpc

6/2

At T=0.98Tc, 6 < 0 is consequence of the O(4) chiral transition

KM, Friman, Redlich, 1402.5982

24 June, 2014 16/19


P(N) Ratio at Small P(N) Ratio at Small Along phase boundaryAlong phase boundary

Dropping at small N/N6 for larger


24 June, 2014 17/19


How Exp. Data Look Like?How Exp. Data Look Like?

Most central only :

Avoid volume fluctuations

Nev > 100 :

Avoid effects from large error

Very similar behavior to FRG/Skellam

i.e., remnant of O(4)


24 June, 2014 18/19


Concluding RemarksConcluding RemarksFluctuation measurements in Heavy Ion CollisionsFluctuation measurements in Heavy Ion Collisions

Deviation from a reference distribution may signal critical Deviation from a reference distribution may signal critical phenomena in QCDphenomena in QCDParticle yield and lower cumulants validate thermal Particle yield and lower cumulants validate thermal equilibrium pictureequilibrium picture

Property of P(NProperty of P(NBB) near Chiral Phase Transition) near Chiral Phase TransitionNarrowing (relative to Skellam) in the tail near TNarrowing (relative to Skellam) in the tail near Tpcpc

P(N) Ratio supplements cumulant analyses

Most central data of net-proton show perfect coincidence Consistent w/ O(4) expectation Non-critical effects on P(N) ratio?

Q: Does the dropping survive after correction?

Unambiguous interpretation needs 6 – higher statistics

24 June, 2014 19/19


OutlookOutlookOther conserved chargesOther conserved charges

Electric charge and net strangeness (net-kaon) measurement Electric charge and net strangeness (net-kaon) measurement done by STARdone by STAR Interpretation is more difficult because of other non-critical Interpretation is more difficult because of other non-critical effectseffects

Theoretical ChallengesTheoretical Challenges More elaborated effective models or solving the sign More elaborated effective models or solving the sign problem in QCD to locate the phase boundaryproblem in QCD to locate the phase boundary More complete information from Lee-Yang zero More complete information from Lee-Yang zero (work in progress)(work in progress)

Understanding possible other non-critical effectsUnderstanding possible other non-critical effects Connection to higher density regime (FAIR, NICA, etc…)Connection to higher density regime (FAIR, NICA, etc…)

24 June, 2014 20/19


Backup

24 June, 2014 21/19


P(N) Ratio at Small P(N) Ratio at Small Fix Fix

Asymmetric structure at nonzero

Dropping ratio turns into increasing at <0 , but remains at >0

KM, Friman, Redlich, arXiv: 1402.5982

24 June, 2014 22/19


Can NBD/BD Reproduce Can NBD/BD Reproduce Criticality?Criticality?

24 June, 2014 23/19


Can NBD/BD Reproduce Can NBD/BD Reproduce Criticality?Criticality?

Fix parameters to reproduce model Fix parameters to reproduce model 22 and and 44 BD:

Possible for each cumulant ratio

Impossible for simultaneous description!

24 June, 2014 24/19


P(N) vs Critical exponent P(N) vs Critical exponent

Model based on Landau theory & Scaling func.Model based on Landau theory & Scaling func.

Skellam dist. (Boltzman gas)Critical exponent for the specific heat

: 3d Z(2)

: Mean Field

: 3d O(4)

Singular part : reproduce singular cumulants at Tc

24 June, 2014 25/19


P(N) vs Critical exponent P(N) vs Critical exponent

Model based on Landau theory & Scaling func.Model based on Landau theory & Scaling func.

Ratio to Skellam reveals differences

Long tail – divergence

24 June, 2014 26/19


Experimental ResultsExperimental Results

24 June, 2014 27/19


Step 3 : Scaling PropertyStep 3 : Scaling Property

Scattered

24 June, 2014 28/19


Selection of Data setsSelection of Data sets

Centrality > 40% : Deviation from Scaling

Apparent deviation by chemical potential

Insufficient Statistics

Check same underlying physics : scaling property w/ Check same underlying physics : scaling property w/ – close to HRG – close to HRG

Too small # of events (< 100)

24 June, 2014 29/19


NNmax max dependence of cdependence of cnn

V dep – N/V1/2

c2 : Exact

c4,c6 : Approxmate

24 June, 2014 30/19


Fermi gas CumulantsFermi gas Cumulants

NarrowNarrow Critical < Fermi < Skellam BroadBroadBut deviation from Skellam in the tail is as large as critical caseBut deviation from Skellam in the tail is as large as critical case

24 June, 2014 31/19


Why P(N)? - Tail of P(N) is Why P(N)? - Tail of P(N) is important in cimportant in c66

Higher order cumulants need P(N) at large NHigher order cumulants need P(N) at large N

Cut here

Cut here

Nmax P(Nmax)~ 10-10 to get correct c6

Documents

Kenji Morita 24 June, 20141 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions,