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

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

1 Kenji Morita 24 June, 20141 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 with Fluctuations of Conserved Charges Kenji Morita (Frankfurt Institute for Advanced Studies)

2 Kenji Morita 24 June, 2014 2/19 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 QCD Fukushima-Hatsuda, Rep.Prog.Phys.74 ‘11 Towards understanding the origin of the matter Chiral transition Confinement Rich structure theoretically expected (from lattice QCD and models) For the statistical system specified by ( T, m ) Heavy Ion Collisions : Evidence for “Perfect Liquid” (QGP) Phase Transition ? 10 12 K

3 Kenji Morita 24 June, 2014 3/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Grand Canonical Ensemble Description Chemical freeze-out : Equilibrated hadron gas Particle number : OK T fo ～ phase boundary Expectation : measured fluctuations = those of GCE

4 Kenji Morita 24 June, 2014 4/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Fluctuations Indicate Phase Transition n -th order phase transition n -th order phase transition Singular behavior in Singular behavior in n=1 : Entropy, order parameter, charge density n=1 : Entropy, order parameter, charge density n=2 : specific heat n=2 : specific heat chiral susceptibility chiral susceptibility fluctuation of conserved charge fluctuation of conserved charge Observable through multiplicity distribution P(N) Higher order – more sensitive to criticality Not observable… (Stephanov ’09) of Conserved Charges

5 Kenji Morita 24 June, 2014 5/19 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 Collisions O (10 7 ) events@RHIC Counting # of particles within a given circumstance (centrality, acceptance etc) Averaging over events STAR, net-proton, PRL112 (’14)

6 Kenji Morita 24 June, 2014 6/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Quantifying Fluctuations Prob. Distribution ~ Canonical Partition Function Shape : Cumulants ∝ Volume Note: Need Cancellation ! Higher order c n contains → Need more information on the tail ! M : Mean, s 2 : Variance, S : Skewness, k : Kurtosis No statistically meaningful measurement of c 6 yet…

7 Kenji Morita 24 June, 2014 7/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” QCD ≒ Hadron Resonance Gas ？ Equation of state Baryon number fluctuations Wuppertal- Budapest BNL- Bielefeld T<155MeV : Good approx. Substantial deviation at Higher order

8 Kenji Morita 24 June, 2014 8/19 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 HRG =Skellam Distribution # of baryons （ Poisson) # of antibaryon (Poisson)   Statistical mechanics : Boltzmann distribution   2 parameters Expectation : c 1 and c 2 are well described by HRG Deviation from Skellam in higher order c n should reflect the phase transition Ratio cancels Volume dependence Karsch-Redlich ‘11

9 Kenji Morita 24 June, 2014 9/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Net-Proton Measurements at RHIC by STAR 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? =1 in HRG

10 Kenji Morita 24 June, 2014 10/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Th. Expectations for the Cumulants Chiral Limit T m TCP? mqmq 2 nd Order, 3d O(4) Phys. quark mass m phys Crossover – Feel O(4)? CP? BES@RHIC c 6 changes the sign across crossover General property from O(4) scaling function (Engels and Karsch ’11, Friman et al., ’11) c 2 divergence c 3,4 change the sign Hatta-Ikeda ’03, Asakawa et al.,’09, Skokov et al., ’11, Stephanov, ‘11 Pisarski-Wilczek ‘84

11 Kenji Morita 24 June, 2014 11/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Probability Distribution P(N) and Cumulants c n at nonzero m From QCD : Sign Problem ! (No MC simulation reliable) Use of chiral effective model (L s M, NJL, etc) Extract qualitative feature relevant to QCD Z(2) CP : Still uncertain Remnant of O(4) in Crossover : Our suggestion

12 Kenji Morita 24 June, 2014 12/19 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 (N f = 2 ) Effective dof : s, p, q (also below T c ) Effective dof : s, p, q (also below T c ) KM et al., PRC88 ’13 for detail Common fluctuation property with QCD near phase boundary Governed by 3d O(4) universality class in the chiral limit Solving the model : proper treatment of the critical fluctuations Use of Functional Renormalization Group (FRG) method to calculate the thermodynamic potential W

13 Kenji Morita 24 June, 2014 13/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” QM 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 < L qq Integrating from k = L to k = 0 gives a full quantum effective potential Put obtained W k =0 ( s min )into the integral formula for P(N) (Stokic-Friman-Redlich ’10 ) G L = S classical

14 Kenji Morita 24 June, 2014 14/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Phase Structure in Chiral Quark-Meson Model (N f = 2 ) Critical point @large m Sign change of c 6 Chiral Crossover c6/c2c6/c2

15 Kenji Morita 24 June, 2014 15/19 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) ratio Ratio < 1 at large |N| for c 6 / c 2 < 1 T Narrower tail as approaching T pc KM, Friman, Redlich, 1402.5982 P s (N) : Skellam w/ the same s 2 N 6 : # of bins to get c 6

16 Kenji Morita 24 June, 2014 16/19 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 m Along phase boundary Dropping at small d N/N 6 for larger m KM, Friman, Redlich, 1402.5982

17 Kenji Morita 24 June, 2014 17/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” STAR Data Shows Similar Behavior Most central only : Avoid volume fluctuations N ev > 100 : Avoid effects from large error Very similar behavior to FRG/Skellam i.e., remnant of O(4) KM, Friman, Redlich, 1402.5982

18 Kenji Morita 24 June, 2014 18/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Concluding Remarks Fluctuation measurements in Heavy Ion Collisions Deviation from a reference distribution may signal critical phenomena in QCD Particle yield and lower cumulants validate thermal equilibrium picture Property of P(N B ) near Chiral Phase Transition Narrowing (relative to Skellam) in the tail near T pc 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? Unambiguous interpretation needs c 6 – higher statistics

19 Kenji Morita 24 June, 2014 19/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects”Outlook Other conserved charges Electric charge and net strangeness (net-kaon) measurement done by STAR Electric charge and net strangeness (net-kaon) measurement done by STAR Interpretation is more difficult because of other non-critical effects (work in progress) Interpretation is more difficult because of other non-critical effects (work in progress) Theoretical Challenges Theoretical Challenges More elaborated effective models or solving the sign problem in QCD to locate the phase boundary More elaborated effective models or solving the sign problem in QCD to locate the phase boundary More complete information from Lee-Yang zero (work in progress) More complete information from Lee-Yang zero (work in progress) Understanding possible other non-critical effects Understanding possible other non-critical effects Connection to higher density regime (FAIR, NICA, etc…) Connection to higher density regime (FAIR, NICA, etc…)

20 Kenji Morita 24 June, 2014 20/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Backup

21 Kenji Morita 24 June, 2014 21/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Reference for the Critical Behavior Higher order cumulants need tail of P(N) Skellam distribution w/ same s 2 Skellam distribution w/ same s 2 Estimate # of data points to get correct c 6 in Skellam, then rescale Estimate # of data points to get correct c 6 in Skellam, then rescale Removing different VT 3 effect in various P(N) data Removing different VT 3 effect in various P(N) data P(N) N6N6 P(N) reproducing c 6

22 Kenji Morita 24 June, 2014 22/19 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 m Fix m Asymmetric structure at nonzero m Dropping ratio turns into increasing at m 0 KM, Friman, Redlich, arXiv: 1402.5982

23 Kenji Morita 24 June, 2014 23/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Can NBD/BD Reproduce Criticality? Take NBD/BD for baryon and antibaryon 4 parameters (r,p) for B and (r’,p’) for B At m =0, r=r’ and p=p’ (2 parameters) At m >0, one can fit the first four cumulants c 1 - c 4 ! At m >0, one can fit the first four cumulants c 1 - c 4 ! Whether P(N proton ) is NBD/BD or not ? – Theoretically ill- defined (Not a conserved number) Whether P(N proton ) is NBD/BD or not ? – Theoretically ill- defined (Not a conserved number) NBD clearly cannot describe critical P(N) c 4 / c 2, c 6 / c 2 > 1 c 4 / c 2, c 6 / c 2 > 1

24 Kenji Morita 24 June, 2014 24/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Can NBD/BD Reproduce Criticality? Fix parameters to reproduce model c 2 and c 4 BD: Possible for each cumulant ratio Impossible for simultaneous description!

25 Kenji Morita 24 June, 2014 25/19 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 a Model based on Landau theory & Scaling func. Skellam dist. (Boltzman gas) Critical exponent for the specific heat a= 0.11 : 3d Z(2) 0 : Mean Field -0.21 : 3d O(4) Singular part : reproduce singular cumulants at T c

26 Kenji Morita 24 June, 2014 26/19 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 a Model based on Landau theory & Scaling func. Ratio to Skellam reveals differences Long tail – divergence

27 Kenji Morita 24 June, 2014 27/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Experimental Results

28 Kenji Morita 24 June, 2014 28/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Step 3 : Scaling Property Scattered

29 Kenji Morita 24 June, 2014 29/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Selection of Data sets Centrality > 40% : Deviation from Scaling Apparent deviation by chemical potential Insufficient Statistics Check same underlying physics : scaling property w/ s – close to HRG Too small # of events (< 100)

30 Kenji Morita 24 June, 2014 30/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” N max dependence of c n V dep – N/V 1/2 c 2 : Exact c 4,c 6 : Approxmate

31 Kenji Morita 24 June, 2014 31/19 XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Fermi gas Cumulants Narrow Broad Narrow Critical < Fermi < Skellam Broad But deviation from Skellam in the tail is as large as critical case

32 Kenji Morita 24 June, 2014 32/19 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 important in c 6 Higher order cumulants need P(N) at large N Cut here N max P(N max )~ 10 -10 to get correct c 6

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