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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
P(N) Ratio at Small P(N) Ratio at Small Along phase boundaryAlong phase boundary
Dropping at small N/N6 for larger
KM, Friman, Redlich, 1402.5982
24 June, 2014 17/19
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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)
KM, Friman, Redlich, 1402.5982
24 June, 2014 18/19
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
Backup
24 June, 2014 21/19
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
Can NBD/BD Reproduce Can NBD/BD Reproduce Criticality?Criticality?
24 June, 2014 23/19
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
Experimental ResultsExperimental Results
24 June, 2014 27/19
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
Step 3 : Scaling PropertyStep 3 : Scaling Property
Scattered
24 June, 2014 28/19
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
NNmax max dependence of cdependence of cnn
V dep – N/V1/2
c2 : Exact
c4,c6 : Approxmate
24 June, 2014 30/19
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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
Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”
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