ATHIC 2014Osaka Kenji Morita LeeYang Zero from Net

ATHIC 2014@Osaka Kenji Morita Lee-Yang Zero from Net Baryon Number Multiplicity Distributions Kenji Morita (YITP, Kyoto)* Collaborator : Atsushi Nakamura (Hiroshima) *from Aug. 1 2014 Aug. 07 1

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) Towards understanding the origin of the matter Chiral transition Confinement Heavy Ion Collisions : Evidence for “Perfect Liquid” (QGP) Phase Transition ? 2014 Aug. 07 ATHIC 2014@Osaka 2

Kenji Morita (YITP, Kyoto) Multiplicity Fluctuations in Heavy Ion Collisions Counting # of particles within a given circumstance (centrality, acceptance etc) O(107) events@RHIC Averaging over events 2014 Aug. 07 STAR, net-proton, PRL 112 (’ 14) ATHIC 2014@Osaka 3

Kenji Morita (YITP, Kyoto) Grand Canonical Ensemble Description Chemical freeze-out : Equilibrated hadron gas Particle number : OK Tfo ～phase boundary Expectation : measured fluctuations = those of GCE 2014 Aug. 07 ATHIC 2014@Osaka 4

Kenji Morita (YITP, Kyoto) Equilibrium Multiplicity Distribution Multiplicity dist. – Canonical Partition Function N dependence can be read off from exp. data Normalization Partition function is truncated; Losing Information stored in the tail 2014 Aug. 07 ATHIC 2014@Osaka 5

Kenji Morita (YITP, Kyoto) Relating Fluctuations To Phase Transition Shape of Multiplicity Distribution Characterized by Cumulants , Ratio to reference distributions Deviation from references (e. g. , Skellam dist =HRG) STAR, PRL 114 2014 Aug. 07 Theory KM, Friman, Redlich ‘ 14 ATHIC 2014@Osaka Data 6

Kenji Morita (YITP, Kyoto) Relating Fluctuations To Phase Transition Lee-Yang Zero [C. N. Yang and T. D. Lee, Phys. Rev. 87, 404 (‘ 52)] Distribution of Z(T, V, m)=0 in complex m plane Phase boundary in thermodynamic limit Application to Data: Nakamura-Nagata [ar. Xiv: 1305. 0760] Interesting behavior in data Phase Boundary or Truncation effect? This work : Use of a Solvable Model Characteristics of Phase Transition? 2014 Aug. 07 ATHIC 2014@Osaka 7

Kenji Morita (YITP, Kyoto) Chiral Random Matrix Model An effective model for lowest lying Dirac eigenmodes , w/ Phase transition, Analytic form in finite volume Partition Function (N s sites) Choice by Halasz et al. PRD 58 (’ 98) Temperature/Chemical Potential Scale parameters fitted to chiral condensate Phase diagram has expected features: T 3/Tc = 0. 78, m 3=0. 32 Nc/b Our choice : periodicity in imaginary m (=integer baryon number) No change in small m/T, problem in large m/T 2014 Aug. 07 ATHIC 2014@Osaka 8

Kenji Morita (YITP, Kyoto) Chiral Random Matrix Model An effective model for lowest lying Dirac eigenmodes , w/ Phase transition, Analytic form in finite volume Partition Function (N s sites) Analytic Form! Numerical evaluation requires > 50 -100 digits Hereafter results are for m=0 (Chiral limit) 2014 Aug. 07 ATHIC 2014@Osaka 9

Kenji Morita (YITP, Kyoto) LYZ : Truncated Partition Function Reconstructing Z Canonical Partition Function Z c Grand partition function as a finite series N=Ns recovers the original form LYZ : Ztr = 0 Antiparticle : Summation runs from N Reorganizing the series for Calculating roots for N=Ns, Ns-1, Ns-2, … 2014 Aug. 07 ATHIC 2014@Osaka 10

Kenji Morita (YITP, Kyoto) LYZ for different Ns T/Tc=0. 99 (2 nd order at m=180 Me. V) Stokes Boundary : defined by continuous REAL PART of pressure Distribution of zero approaches to Stokes boundary as Ns is increased 2014 Aug. 07 ATHIC 2014@Osaka 11

Kenji Morita (YITP, Kyoto) Effect of Truncation : LYZtr Cut here (first quadrant only) Split of zeros by cutting the tail Closest zeros to real axis remain unchanged down to Nmax=24 Original zero disappeared at Nmax=18 2014 Aug. 07 ATHIC 2014@Osaka 12

Kenji Morita (YITP, Kyoto) Similar Behavior in st 1 Order Transition LYZ closer to real axis than 2 nd order case Extrapolation may work better? 2014 Aug. 07 ATHIC 2014@Osaka 13

Kenji Morita (YITP, Kyoto) Truncated Skellam. Distribution Reference : Skellam w/ Same s Different systematics (→∞ as N→∞) Small Nmax behavior is similar to RM model 2014 Aug. 07 ATHIC 2014@Osaka 14

Kenji Morita (YITP, Kyoto) Summary and Outlook Lee-Yang zero from multiplicity distribution in Heavy Ion Collisions Locating phase boundary if sufficient statistics May suffer from lack of information on the tail Property of LYZ near Chiral Phase Transition Case study with Chiral Random Matrix Closest zero to real m is insensitive to cutting the tail Response to the cut is different in Skellam dist. More quantitative work (in progress) necessary for assessment of data 2014 Aug. 07 ATHIC 2014@Osaka 15

Kenji Morita (YITP, Kyoto) Backup 2014 Aug. 07 ATHIC 2014@Osaka 16

Kenji Morita (YITP, Kyoto) Analytic Expression 2014 Aug. 07 ATHIC 2014@Osaka 17