Kenji MoritaYITP Kyoto Reimei Workshop at JPARC Fluctuations

Kenji. Morita(YITP, Kyoto) Reimei Workshop at J-PARC Fluctuations of Conserved Charges in Heavy Ion Collisions Kenji Morita (YITP, Kyoto) Collaborators : B. Friman, F. Karsch, K. Redlich, V. Skokov T. Ichihara, A. Ohnishi A. Nakamura Jan 20, 2016 1

Kenji Morita (YITP, Kyoto) Outline 1. Fluctuations of conserved charges and Phase Transitions in QCD • Lessons from small m. B 2. Reference distributions • Lessons from electric-charge fluctuations 3. Implications for lower colliding energies 4. Concluding remarks Jan 20, 2016 Reimei Workshop at J-PARC 2

Kenji Morita (YITP, Kyoto) Search for Phase Transition in QCD Fukushima-Hatsuda, Rep. Prog. Phys. 74 ‘ 11 1012 K Rich structure theoretically expected (from lattice QCD and models) For the statistical system specified by ( T, m. B) Towards understanding the origin of the matter Chiral transition Confinement Heavy Ion Collisions : Evidence for “Perfect Liquid” (QGP) Phase Transition ? Jan 20, 2016 Reimei Workshop at J-PARC 3

Kenji Morita (YITP, Kyoto) Fluctuation Studies in Heavy Ion Collisions STAR, net-proton, PRL 112 (’ 14) Hadronic observables - information at freeze-out : Determination of T and m of a subsystem of the hot matter from particle yields / fluctuations Borsanyi, QM 15 Extracted ( T, m. B) coincides with the Crossover transition region in QCD Up to m. B ~ 400 Me. V (Remnant) critical property of QCD from fluctuation observables! Jan 20, 2016 Reimei Workshop at J-PARC 4

Kenji Morita (YITP, Kyoto) Characterizing Fluctuations Cumulants (=7. 61) (=9. 16) (=7. 23) (=7. 36) Skellam (Data) Gauss Ratios characterize the shape of P(N) Jan 20, 2016 Reimei Workshop at J-PARC 5

Kenji Morita (YITP, Kyoto) QCD Phase Transition / NB Fluctuations Chiral Limit Phys. quark mass T Pisarski-Wilczek ‘ 84 2 nd Order, 3 d O(4) TCP? Crossover – Feel O(4)? BES@R HIC CP? c 2 diverges c 3, 4 change the sign mphys mq Jan 20, 2016 m Hatta-Ikeda ’ 03, Asakawa et al. , ’ 09, Skokov et al. , ’ 11, Stephanov, ‘ 11 c 6 (m=0), c 3, 4(m>>0) changes General property from O(4) scaling function the sign across (Engels and Karsch ’ 11, Friman et al. , ’ 11) crossover Reimei Workshop at J-PARC 6

Kenji Morita (YITP, Kyoto) Origin of Critical Behavior incn 2 nd order transition in Landau Theory: a= Universality Class Divergence (m=0) (m > 0) n=2 0. 11 : 3 d n = 4 Z(2) Discontinuity 0 : Mean n=6 n=3 Field -0. 21 : 3 d O(4) Nonzero a : fluctuation of soft modes • Importance of fluctuations beyond MF KM et al. , Eur. Phys. J. C 74, 2706 (’ 14) Jan 20, 2016 Divergence is smeared by explicit symmetry breaking (finite mq or V ) Reimei Workshop at J-PARC 7

Kenji Morita (YITP, Kyoto) Sign Change of Cumulants Across CP (A) (B) Higher order cumulants : more sensitive to criticality Jan 20, 2016 Reimei Workshop at J-PARC 8

Kenji Morita (YITP, Kyoto) Sign Change of Cumulants Near CP (or Finite V) Higher order cumulants : more sensitive to criticality Divergence replaced by sign changes Jan 20, 2016 Reimei Workshop at J-PARC 9

Kenji Morita (YITP, Kyoto) Sign Change of Cumulants Near TCP, Chiral Limit, Finite V (Lattice QCD in Strong Coupling Limit, Ichihara-KM-Ohnishi, ‘ 15) Higher order cumulants : more sensitive to criticality Divergence replaced by sign changes Jan 20, 2016 Reimei Workshop at J-PARC 10

Kenji Morita (YITP, Kyoto) Sign Change of Cumulants Crossover near O(4) (PQM+FRG) Skokov, Friman, Redlich, PRC’ 11 Weaker “Critical behavior” No peak in c 2, no negative c 3 Smeared by fluctuations via FRG Jan 20, 2016 Reimei Workshop at J-PARC 11

Kenji Morita (YITP, Kyoto) Importance of Reference Hadron Gas Divergent contribution in c limit or CP Finite, cause sign changes in crossover Suppression factor (mq/T)n Obscured when cn, regular > cn, singular Remnant of the divergence may only appear as deviation from the regular part contribution Ø Net-Baryon : N, D, Hyperon, etc… • m >> T, m – Boltzmann Gas －Skellam Distribution Ø Net-electric charge : p, K, r, N, …. • p and D++ cause substantial deviation from Skellam Ø Net-strangeness : K, K*, Hyperon, …. • Heavy enough, but multi-charged (up to 3!) Jan 20, 2016 Reimei Workshop at J-PARC 12

Kenji Morita (YITP, Kyoto) Baryon Gas : Skellam Distribution # of baryons （Poisson) # of antibaryon (Poisson) Ø Statistical mechanics : Boltzmann distribution Ø 2 parameters Independent of momentum integration range Expectation (confirmed by lattice): c 1 and c 2 are well described by HRG Deviation from Skellam in higher order cn can reflect the phase transition Jan 20, 2016 Reimei Workshop at J-PARC 13

Kenji Morita (YITP, Kyoto) Electric Charge Fluctuations Pion mp~T : Bose statistics = Multicomponent Boltzmann gas pressure with mass km, charge k, and degeneracy kn-4 Ø Leading order : Skellam Ø all k >1 terms : positive P. Braun-Munzinger et al. , NPA’ 12 Jan 20, 2016 Reimei Workshop at J-PARC 14

Kenji Morita (YITP, Kyoto) M/s 2 in HRG : STAR vs PHENIX A : pt cut for p only B : Same pt cut for all hadrons C : ptmin = 0. 4 Ge. V for protons (STAR) 0. 2 < pt < 2. 0, |h| < 0. 5 0. 3 < pt < 2. 0, |h| < 0. 35 10% larger M/s 2 in PHENIX acceptance Data : PHENIX/STAR ~ 1. 35 After rescaling, data become closer F. Karsch, KM, K. Redlich, 1508. 02614 Jan 20, 2016 Reimei Workshop at J-PARC 15

Kenji Morita (YITP, Kyoto) Implications for lower energies Use of Z(N) : extrapolation to larger m Nakamura-Nagata, ‘ 13 KM-Nakamura, ‘ 15 Remedy far freeze-out from the boundary Equilibrium reference at low s NN? Smeared signal : deviation from reference What is the baseline physics? Dynamics may be different at lower energies Wider rapidity : effect of global conservation Sign problem in LQCD : we need model-independent prediction, but non-universal regular part is also important Jan 20, 2016 Reimei Workshop at J-PARC 16

Kenji Morita (YITP, Kyoto) Concluding Remarks Smeared critical fluc. from QCD transition Remnant at freeze-out Higher order cumulants (or tail of P(N)) Choice of an appropriate reference – deviation may signal critical behavior High energy : subsystem in GC ensemble at ( T, m) Lattice QCD, Hadron Resonance Gas Freeze-out near T c, weaker O(4) criticality Low energy : need further check Theoretical baseline is not so clear; more dynamical – subsystem? stat. ensemble? Jan 20, 2016 Reimei Workshop at J-PARC 17

Kenji Morita (YITP, Kyoto) Backup Jan 20, 2016 Reimei Workshop at J-PARC 18

Kenji Morita (YITP, Kyoto) Fluctuations near CP Skokov et al. , PRC 83 ‘ 11 Along C. L. Any other direction (MF) Hyperscaling relation Jan 20, 2016 Reimei Workshop at J-PARC 19

Kenji Morita (YITP, Kyoto) M/s 2 in HRG M = (p, r, etc) + (strange mesons) + (baryons) + (hyperons) < 0 (m. Q < 0) > 0 (m. S > 0) > 0 (m. B > 0) Negative meson contribution is reduced by pt cut Jan 20, 2016 Reimei Workshop at J-PARC > 0 (m. B-(1~3)m. S > 0) Total M can be nonmonotonic in ptmin s 2 simply decreases 20

Kenji Morita (YITP, Kyoto) (Negative) Binomial Distribution? NB (ks 2 >1), BD(ks 2<1) can fit the critical c 2 and c 4, but cannot reproduce c 6 Higher (n>4) cumulants necessary to identify the critical fluctuations KM, Friman, Redlich, PLB ’ 15 Jan 20, 2016 Reimei Workshop at J-PARC 21

Kenji Morita (YITP, Kyoto) Charge Fluctuations in Equilibrium fixed m ≠ fixed N - Probability distribution in a GC subsystem T ✖ N Jan 20, 2016 Reimei Workshop at J-PARC 22