Yu Maezawa ( 前澤祐 ) Nuclear Physics group, YITP

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1 Yu Maezawa ( 前澤祐 ) Nuclear Physics group, YIP Phys. Rev. Lett. 111 (013) Phys. Lett. 737 (014) 10 A. azavov, 1 H.-. Ding, 1, P. Hegde, 3 O. Kaczmarek, 4 F. Karsch, 1,4 E. Laermann, 4 Y. Maezawa, 1 Swagato Mukherjee, 1 H. Ohno, 4 P. Petreczky, 1 C. Schmidt, 4 S. Sharma, 4 W. Soeldner, 5 and M. Wagner 4 1 Physics Department, rookhaven National Laboratory, Upton, New York 11973, USA Physics Department, Columbia University, New York, New York 1007, USA 3 Department of Physics R518, High Energy Physics Lab, National aiwan University, aipei 10617, aiwan 4 Fakultät für Physik, Universität ielefeld, D ielefeld, Germany 5 Institut für heoretische Physik, Universität Regensburg, D Regensburg, Germany Lunch YIP, June 4, 015

2 Hot QCD world ig ang Li.le ang ime Amazing plasma of quarks and gluons QCD thermodynamics

3 Quantum Chromo- Dynamics Quark: chiral symmetry Origin of mass Chiral condensate: qq Gluon: non- Abelian Color confinement Polyakov loop: L e ig H A 4 d Vanishing quark mass nd order P in N f and m 0 Real QCD world Phase transiron Color deconfinement 1st order P in m (pure Yang- Mills) m u 3 MeV, m d 5 MeV, m s 95 MeV, m c 175 MeV, various quark flavors

4 QCD Lace QCD simula>ons : Strong non- linearity and infinite- dimensional integral Field theory on layce in Euclidean space Monte- Carlo simularons based on importance sampling O 1 Z D qdqda O( q, q, A) e S QCD 1 N conf N conf {U i } O(U i ) ± O( 1 N conf ) {U i }: configurarons generated with the weight exp(- S QCD ) 1st principle and non- perturbarve calcularons in large- scale computaronal simularons

5 QCD Lace QCD simula>ons LaYce : Strong results: non- linearity (+1)- flavor and QCD infinite- dimensional simularons integral Phase transiron: Crossover Field Chiral: theory rapid on layce Monte- Carlo C 154 ± simularons 9 MeV Deconfinement: Euclidean space gradual based on importance sampling O 1 Z D qdqda O( q, q, A) e S QCD 1 N conf N conf {U i } O(U i ) ± O( 1 N conf ) Hot- QCD Coll. PRD 85 (011) {U i }: configurarons generated with the weight exp(- S QCD ) HISQ acron m l 0.05m s 1st principle and non- perturbarve N τ calcularons in large- scale computaronal simularons

6 Deconfinement of quarks QCD phase transiron at high temperature: Dominated by chiral transiron Color DoF gradually deconfined Polyakov loop: test color charge of a starc quark ( ) m How dynamical quarks deconfine? e.g. baryon number aryon (P/ 4 ) response to chemical potenral µ µ 0 Quark 1 (P/ 4 ) µ µ SuscepRbility: S mn m+n (P/ 4 ) ˆµ m ˆµn S µ 0 ˆµ µ/ n + m even µ S µ C

7 Deconfinement of quarks SuscepRbility (P/ 4 ) ˆµ µ 0 Hadron resonance gas azavov et al. in prepararon free Free quark gas continuum extrap. N PDG-HRG

8 P HRG 4 4 S 11 S 31 S S S 13 S4 Hadron resonance gas Non- interacrng Meson- aryon gas system i meson ±, RelaRon to susceprbilires (up to 4th order) g i 0,, K, K ±, K N,,N,,,, ( 1) 1 + ( ) + ( 3) 3 ( 1) 1 + ( ) + ( 3) 3 ( 1) M 1 + ( 1) 1 + ( ) + ( 3) 3 ( 1) 1 + ( ) + ( 3) 3 ( 1) ( ) 3 + ( 3) 3 3 ( 1) 4 M 1 + ( 1) ( ) 4 + ( 3) 4 3 K M 0 + M 1 cosh( ˆµ S ) cosh(s i ˆµ S )+ i baryon 4 0: constraint for u, d quarks g i K cosh( i ˆµ + S i ˆµ S ) + 0 cosh(ˆµ )+ 1 cosh(ˆµ ˆµ S )+ cosh(ˆµ ˆµ S )+ 3 cosh(ˆµ 3ˆµ S )

9 P HRG 4 Hadron resonance gas Non- interacrng Meson- aryon gas system i meson g i K cosh(s i ˆµ S )+ i baryon g i K cosh( i ˆµ + S i ˆµ S ) M 0 + M 1 cosh( ˆµ S ) + 0 cosh(ˆµ )+ 1 cosh(ˆµ ˆµ S )+ cosh(ˆµ ˆµ S )+ 3 cosh(ˆµ 3ˆµ S ) RelaRon to susceprbilires (up to 4th order) S 11 S 31 S S S 13 S M rank 4

10 P HRG 4 Hadron resonance gas Non- interacrng Meson- aryon gas system i meson g i K cosh(s i ˆµ S )+ i baryon g i K cosh( i ˆµ + S i ˆµ S ) M 0 + M 1 cosh( ˆµ S ) + 0 cosh(ˆµ )+ 1 cosh(ˆµ ˆµ S )+ cosh(ˆµ ˆµ S )+ 3 cosh(ˆµ 3ˆµ S ) RelaRon to susceprbilires (up to 4th order) v 1 S 31 v 1 3 ( S M 1 S S S 11 0 S 4 ) S 13 4 S S 31 0 constraints for s quark 1 1 S 4 S +5 S S S 4 S 4 S +4 S S S +3 S S

11 Deconfinement of u, d and s quarks PRL 111, (013) PHYSICAL REVIEW 4 0 v 1 0,v 0 u, d quarks constraints for s quark PRL 111 (013) non int. quarks uncorr. hadrons χ -χ4 v 1 v he constraints sarsfied below C : HRG system Deviate from 0 at ~ C : not only u,d but s quarks deconfined FIG. 1 Close (colorto online). free quark wo gas combinations high temperature v 1 and v [see Eqs. (7) and (8)] of strangeness fluctuations and baryon-strangeness cor-

12 Deconfinement of charm quarks Similar procedure for charm: µ S µ C PL 737 (014) 10 Charm quarks also deconfined at ~ C Similar to strange susceprbility

13 Hadronic descrip>on he lines at low and high in temperatures strangeness indicate the two limiting FIG. 1 (color online). wo combinations v scenarios 1 and v when the [see Eqs. (7) DoF are described by uncorrelated hadron and (8)] of strangeness fluctuations and baryon-strangeness cor- gas and a noninteracting massless quark gas, respectively. he and the jsj ¼ 1,, 43 baryons sdof are their when respective one uses noninteracting, the actual uncorr. observable also vanishes identically when the baryon number massless q hadrons vacuum mass spectrum of the strange strangeness oltzmann approximation is well depending hadrons suited. It on reflects the in values an uncorrelated hadron gas. Specifically, num carrying degrees of freedom are described by an uncorrelated that the of c 1 and c baryon relevant degrees of freedom carry Strangeness Mðc gas of strange as well as nonstrange baryons. he shaded region integer 1 ;c Þ, strangeness in the 1 ðc quark 1 ;c Þ, gluon plasma. giving indicates the chiral crossover temperature jsj ðc ¼ 1 ;c 0, 1, c ¼ Þ,, 154ð9Þ and 3 and 3 MeV ðc integer 1 ;c [14]. Þ reproduce baryon whether the HRG number thejj sdof model ¼ in 0, the results 1. QGP can be desc for P In Fig. HRG jsj¼1;m, we, PHRG jsj¼1; study, the PHRG, partial interacting and PHRG jsj¼; pressures jsj¼3; quasiquarks, of, the respectively strangewe study corr S m hadrons [16]. Asusing can be theseen LQCD fromresults the strangeness insets for the of fluctuations four Fig., combinations description Mðc 1 ;cof Þ, the 1 ðc LQCD suchwith a fluctuations S mþ 1 ;c Þ, results ðc number 1 ;cbreaks Þ, anddown electric 3 ðc within 1 ;c charge. Þ [see the relations that vanish identically if the sdof are described by an Such observab LQCD results for the N ¼ 6 and 8 lattices are shown by the open uncorrelated gas of hadrons. Also shown is the difference of Eqs. c region (3) (6)], for each eachof for the three meson sets inand of Refs. baryon (c 1,[10,18] c ). sectors. One forof Above the second where order m, nc and filled symbols, respectively. quadratic and quartic baryon number fluctuations combinations c, all these corresponds quantities show toprl c a 1 extend ¼smooth c 111 ¼these 0approach and (013) correlations thustowards S represents theirthe respective basic projection noninteracting, onto a sdof given massless strangeness are quark weakly gas sector values, noninteracting scaled byqut carrying degrees of freedom are described + c his up to In thefig. four 3 observable also vanishes identically when the baryon number by an uncorrelated 1 v 1 + c depending von the values of c 1 strangeness and c. S ¼ 1 is associated with gas of strange as well as nonstrange oltzmann baryons. he approximation shaded regionis well suited. Strangeness It reflects in the that quark the gluon 1.0 baryon plasma. o number investigate ¼ 13 and electric cha indicates the chiral crossover temperature relevant c ¼degrees 154ð9Þ MeV of freedom [14]. whether carry integer the sdof strangeness in the QGP can 1 (0,0) giving be described by weakly jsj ¼ 0, 1,, 3 and integer baryon 0.5 number jj ¼ 0, 1. 1 (0,3/) he lines at low and high temperatures indicate the two limiting interacting quasiquarks, we 1 study 1 correlations of net (3,3/) scenarios when the DoF are describedinbyfig. an uncorrelated, we studyhadron the partial strangeness 0.0 pressures of fluctuations the strangewith0.50 fluctuations P HRG S 1, S mn of net hadrons using the LQCD results for the four combin- latticesmðc are shown 1 ;c Þ, by S ¼ ð 1Þn baryon QS mn gas and a noninteracting massless quark gas, respectively. he mþn 3 m and S ¼ ð number and electric charge. Such observables were studied LQCD results for the N mþn ¼ 6 and 8ations the ðc 1 ;c open Þ, ðc in 1 ;c Refs. Þ, and M(0,0) [10,18] 3 ðc 1 ;c for Þ the [seesecond order correlations. We -1.0 (0,0) and filled symbols, respectively Eqs. (3) (6)], each for three sets of M(0,-3) extend(cthese 1, c ). correlations One of the up where to the m, fourth n>0order. and mifþthe n ¼, 4. (0,-3/4) M(-6,-3) -1.5 (-3/,-3/4) combinations corresponds to c 1 sdof ¼ c HRG P HRG S 1,M ¼are0 and weakly thus or represents the basic projection onto a-.0 strangeness given strangeness S ¼ 1 sector isinassociated scaled by the proper powers noninteracting In Fig. quasiquarks, 3, we show then LQCD results P S, with the fractional of fraction oltzmann approximation is well suited. It reflects that the baryon number ¼ 13 and electric charge Q ¼ 13, relevant degrees of freedom carry integer strangeness 1.0 FIG giving (color online). Four combinations 0.5 [see Eqs. (3) (6)] of net strangenes jsj ¼ 0, 1,, 3 and integer baryon number jj ¼ 0, 1. 1 (0,0) 3 (0,0) Mðc 1 ;c 1 (0,3/) Þ, 1 ðc 1 ;c Þ, ðc 1 ;c Þ, and 3 ðc 1 ;c Þ (from left to right), each for 3 (0,1/6) three In Fig., we study the partial pressures of the strange temperature 1 (3,3/) c S mn 154ð9Þ MeV [14] (shown by the shaded regions), independe 3 (1/3,1/6) HRG P pressures of jsj 1 mesons (P HRG S 1, ) and jsj ¼ 1,, 3 baryons (PHRG jsj¼1;m jsj¼1;, HRG hadrons using the LQCD results for the four combinations Mðc 1 ;c Þ, 1 ðc 1 ;c Þ, ðc P S ¼ ð 1Þn PHRG S 3, mþn 3 m and QS mn S ¼ ð 1Þmþn mþn 3 m ; (9) 0.05 jsj¼; ;c Þ, and 3 ðc 1 ;c Þ [see masses equal to their vacuum masses, i.e., in the HRG model (indicated by the so Eqs. (3) (6)], each for three sets of M(0,0) (c 1, c ). One of the -1.0 such where a hadronic m, n>0 description and m þbreaks n ¼, down 4. (shown (0,0) in the insets) and all the combin -0.5 M(0,-3) combinations corresponds to c (c 1, c )-dependent, high temperature limits (0,-3/4) 1 ¼ c ¼ 0 and thus represents the basic projection onto a given In Fig. 3, we show the LQCD results (indicated for these byratios the solid horizontal M(-6,-3) -1.5 (-3/,-3/4) HRG P strangeness HRG S 1,M sector in interacting scaled bymassless the proper strange powers quarks. of hefractional dotted P horizontal lines at high temperatur S, baryonic and -.0 all -0.50these observables obtained using -0.50one-loop resummed HL calculations [19] shown by the open and filled symbols, respectively. M 1 (c 1,c ) S M(0,0) 1.0 M(0,-3) FIG. 1 (0,0) (color online). Four combinations [see Eqs. (3) (6)] of net strangeness 3 (0,0) 0.10 fluctuations and baryon-strange (0,3/) 3 (0,1/6) Mðc M(-6,-3) 1 ;c 1 (3,3/) Þ, 1 ðc 1 ;c Þ, ðc 1 ;c Þ, and 3 ðc 1 ;c Þ (from left to right), each for 3 (1/3,1/6) three different sets of (c 1, c ). Up to th temperature c HRG P S 1, ¼ 154ð9Þ MeV [14] (shown by the shaded regions), 3 HRG P independent S 3, of (c 1, c ), these combination HRG pressures of jsj ¼ 1 mesons (P HRG ) and jsj ¼ 1,, 3 baryons (PHRG jsj¼1;m jsj¼1; P, PHRG jsj¼;, PHRG ) in an uncorrelated gas jsj¼3; M(0,0) S 1,M masses equal to their vacuum masses, i.e., -1.0 (0,0) in the HRG model (indicated by the solid lines at low temperatures). Ab -0.5 M(0,-3) such a hadronic description breaks down (0,-3/4) (shown in the insets) and all the combinations smoothly approach toward M(-6,-3) -1.5 (-3/,-3/4) HRG P HRG S 1,M (c 1, c )-dependent, high temperature limits P (indicated by the solid horizontal lines at high temperatures) descr S, interacting massless strange quarks he dotted horizontal lines at high -0.05temperatures depict the perturbative estimate all these observables obtained using one-loop resummed HL calculations [19]. he LQCD results for the N ¼ 6 Four combinations shown by the [seeopen Eqs. and (3) (6)] filled symbols, of net strangeness respectively. fluctuations and baryon-strangeness correlations Mðc 1 ;c Þ, 1 ðc 1 ;c Þ, ðc 1 ;c Þ, and 3 ðc 1 ;c Þ (from left to right), each for three different sets of (c 1, c ). Up to the chiral crossover temperature c ¼ 154ð9Þ MeV [14] (shown by the shaded regions), independent of (c 1, c ), these combinations give the partial ) in an uncorrelated gas of hadrons having masses equal to their vacuum masses, i.e., in the HRG model (indicated by the solid lines at low temperatures). Above the c region, such a hadronic description breaks down (shown in the insets) and all the combinations smoothly approach towards their respective, (c 1, c )-dependent, high temperature limits (indicated by the solid horizontal lines at high temperatures) described by the noninteracting massless strange quarks. he dotted horizontal lines at high temperatures depict the perturbative estimates (see the text) for all these observables obtained using one-loop resummedandersen HL calculations et [19]. al. he (013) LQCD results for the N ¼ 6 and 8 lattices are shown by the open and filled symbols, respectively. 140 FIG. 180 (color online) Hadronic descripron pressures of jsj ¼ 1breaks mesons (P down at ~ HRG jsj¼1;m ) and jsj ¼ 1,, 3 baryons (PHRG jsj¼1;, C PHRG jsj¼;, PHRG jsj¼3; Hard thermal loop perturbaron theory (doeed lines) at > C

14 Summary: Hot QCD world Deconfinement of u, d, s and c quarks: ~ C Strongly correlated quark- gluon plasma Crossover chiral transiron C 154 ± 9 MeV Hadron Resonance Gas HL perturbaron ( > C ) Free quark- gluon gas