Kenji Morita XXXth International Workshop on High Energy

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 with Fluctuations of Conserved Charges Kenji Morita (FIAS) 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” Search for Phase Transition in QCD Theoretical Expection Fukushima-Hatsuda, Rep. Prog. Phys. 74 ‘ 11 1012 K (from lattice QCD and models) For the statistical system specified by (T, m) Towards understanding the origin of the matter Chiral transition Confinement Heavy Ion Collisions : Evidence for high energy density matter (QGP) Phase Transition ? 24 June, 2014 2

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 Collisions Counting # of particles within a given circumstance (centrality, acceptance etc) O(107) events@RHIC Averaging over events 24 June, 2014 STAR, net-proton, PRL 112 (’ 14) 3

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 Transition of Conserved Charges n-th order phase transition Singular behavior in n=1 : Entropy, order parameter, charge density n=2 : specific heat chiral susceptibility Not observable… fluctuation of conserved charge Observable through multiplicity distribution P(N) Higher order – more sensitive to criticality (Stephanov ’ 09) 24 June, 2014 4

Kenji Morita 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 Note: Need Cancellation ! Shape : Cumulants ∝ Volume Higher order cn contains <(d. N)n> → Need more information on the tail ! No statistically meaningful measurement of c 6 yet… M: Mean, s 2: Variance, S: Skewness, k: Kurtosis 24 June, 2014 5

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 Description Chemical freeze-out : Equilibrated hadron gas Particle number (1 st moment) : OK Tfo ～phase boundary Expectation : measured fluctuations = those of GCE 24 June, 2014 6

XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Kenji Morita Net Baryon Number Fluctuation in HRG =Skellam. Distribution # of baryons （Poisson) # of antibaryon (Poisson) Ø Statistical mechanics : Boltzmann distribution Ø 2 parameters Ratio cancels Volume dependence Expectation : c 1 and c 2 are well described by HRG Karsch-Redlich ‘ 11 Deviation from Skellam in higher order cn should reflect the phase transition 24 June, 2014 7

XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Kenji Morita QCD ≒Hadron Resonance. Gas？ Equation of state T<155 Me. V : Good approx. Wuppertal. Budapest Baryon number fluctuations Substantial deviation at Higher order Wuppertal. Budapest 24 June, 2014 BNLBielefeld 8

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 STAR, PRL 114 Caveat : Net-proton≠Net-baryon Substantial Deviation from the HRG expectation Q : Is this deviation consistent with phase transition? Is there any other explanations? What is the underlying probability distribution? Correction by bin width and reconstruction efficiency 24 June, 2014 9

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

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) and Cumulants cn at nonzero From QCD : Sign Problem !m (No MC simulation reliable) Use of chiral effective model (Ls. M, NJL, etc) Extract qualitative feature relevant to QCD Z(2) CP : Still uncertain Remnant of O(4) in Crossover : Our suggestion 24 June, 2014 11

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 (Nf=2) s, p, q (also below T c) Common fluctuation property with Me. V QCD near phase boundary KM et al. , PRC 88 ’ 13 for detail Crossover at m=0 : Tpc=214 Reminder : Criticality appears higher order cumulants Solving the model : proper treatment of the critical flucuations Critical point @large m 24 June, 2014 12

XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Kenji Morita QM model w/ FRG approach Effective potential is obtained by solving the exact flow equation (Wetterich eq. ) with approximations preserving correct critical exponents (Stokic-Friman-Redlich ’ 10) q GL=Sclassical q - Full propagators with k < q < L Integrating from k=L to k=0 gives a full quantum effective potential 24 June, 2014 Put obtained Wk=0(smin)into the integral formula for P(N) 13

XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Kenji Morita Reference for the Critical Behavior Higher order cumulants need tail of P(N) Skellam distribution w/ same s 2 Estimate # of data points to get correct c 6 in Skellam , then rescale Removing different VT 3 effect in various P(N) data P(N) reproducing c 6 N 6 <N> 24 June, 2014 14

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) ratio KM, Friman, Redlich, 1402. 5982 Ratio < 1 at large |N| for c 6/c 2 < 1 c 6/c 2 T At T=0. 98 Tc, c 6 < 0 is consequence of the O(4) chiral transition Narrower tail as approaching T pc 24 June, 2014 15

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 Smallm Along phase boundary KM, Friman, Redlich, 1402. 5982 Dropping at small d. N/N 6 for larger m 24 June, 2014 16

XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Kenji Morita How Exp. Data Look Like? KM, Friman, Redlich, 1402. 5982 Very similar behavior to FRG/Skellam i. e. , remnant of O(4) Most central only : Avoid volume fluctuations Nev > 100 : Avoid effects from large error 24 June, 2014 17

Kenji Morita 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? Q: Does the dropping survive after correction? 24 June, 2014 Unambiguous interpretation needs c 6 – higher statistics 18

Kenji Morita 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 Interpretation is more difficult because of other non-critical effects Theoretical Challenges 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) Understanding possible other non-critical effects Connection to higher density regime (FAIR, NICA, etc…) 24 June, 2014 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 20

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 Smallm Fix m KM, Friman, Redlich, ar. Xiv: 1402. 5982 Asymmetric structure at nonzero m Dropping ratio turns into increasing at m<0 , but remains at m>0 24 June, 2014 21

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 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! Whether P(Nproton) is NBD/BD or not ? – Theoretically illdefined (Not a conserved number) NBD clearly cannot describe critical P(N) c 4 / c 2 , c 6 / c 2 > 1 24 June, 2014 22

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 Criticality? Fix parameters to reproduce model c 2 and c 4 BD: Possible for each cumulant ratio Impossible for simultaneous description! 24 June, 2014 23

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 exponenta Model based on Landau theory & Scaling func. Skellam dist. (Boltzman gas) Critical exponent for the specific heat a= 0. 11 : 3 d Z(2) 0 : Mean Field -0. 21 : 3 d Singular part : reproduce O(4) singular cumulants at Tc 24 June, 2014 24

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 exponenta Model based on Landau theory & Scaling func. Ratio to Skellam reveals differences Long tail – divergence 24 June, 2014 25

Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Experimental Results 24 June, 2014 26

XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Kenji Morita Step 3 : Scaling Property Scattered 24 June, 2014 27

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 sets Check same underlying physics : scaling property w/ s – close to HRG Too small # of events (< 100) Insufficient Statistics Centrality > 40% : Deviation from Scaling Apparent deviation by chemical potential 24 June, 2014 28

Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Nmax dependence of cn V dep – N/V 1/2 c 2 : Exact c 4, c 6 : Approxmate 24 June, 2014 29

Kenji Morita XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Fermi gas Cumulants Narrow Critical < Fermi < Skellam Broad But deviation from Skellam in the tail is as large as critical case 24 June, 2014 30

XXX-th International Workshop on High Energy Physics “Particle and Astroparticle Physics, Gravitation and Cosmology: Predictions, Observations and New Projects” Kenji Morita Why P(N)? - Tail of P(N) is important in c 6 Higher order cumulants need P(N) at large N Cut here Nmax 24 June, 2014 P(Nmax)~ 10 -10 to get correct c 6 31