高能重离子碰撞中逐事件守恒荷涨落的高阶矩测量以及 QCD 临界点的寻找 Xiaofeng Luo( 罗晓峰 ) 粒子物理研究所, 华中师范大学 April, 21, 2014 STAR Collaboration, Phys. Rev. Lett. 112, (2014) Xiaofe

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1 高能重离子碰撞中逐事件守恒荷涨落的高阶矩测量以及 QCD 临界点的寻找 Xiaofeng Luo( 罗晓峰 ) 粒子物理研究所, 华中师范大学 April, 21, 2014 STAR Collaboration, Phys. Rev. Lett. 112, (2014) 1 / 23

2 Outline Ø Introduction Ø Analysis Techniques Ø Results and Discussion Ø Summary 2 / 23

Exploring the Phase Diagram of QCD Matter 1 Temperature T/T C

5 2 T E RHIC, SPS, FAIR LHC SPS AGS SIS RHIC FAIR/NICA 1 2 3

3 Exploring the Phase Diagram of QCD Matter 1 Temperature T/T C T ini, T C LHC, RHIC T E RHIC, SPS, FAIR LHC SPS AGS SIS RHIC FAIR/NICA Chemical freeze-out* 3 Phase boundary RHIC, FAIR, CSR quark-gluon plasma (T C = 175 MeV) //models/kurtosis4science/figure/tmu_dl_15july2012.kumac// 0 hadronic phase Baryon Chemical Potential µ B /T C 3 / 23

4 STAR Detector Magnet MTD BEMC TPC TOF BBC EEMC HFT Ø Large Uniform Acceptance at Mid-rapidity. Ø Excellent Particle Identification. Ø Fast Data Acquisition. 4 / 23

RHIC Beam Energy Scan-Phase I In the first phase of the RHIC Beam Scan (BES), seven energies were surveyed in 2010 and 2011. s (GeV) µ B (MeV) 7.7 422 4 Events (Million) 11.5 316 12 19.

5 RHIC Beam Energy Scan-Phase I In the first phase of the RHIC Beam Scan (BES), seven energies were surveyed in 2010 and s (GeV) µ B (MeV) Events (Million) New Data: Year GeV. The main goals of BES program: Ø Turn-off of QGP signatures. Ø Search for QCD critical point. Ø Map the first order phase transition. 5 / 23

Search for the QCD Critical Point Theory Lattice QCD et al. Experiment HIC et al.

Ø Diverges of the thermodynamics quantities, such as correlation length (ξ), Susceptibilities (χ), heat

Finite size and time in HIC: Need Sensitive Observable!

6 Search for the QCD Critical Point Theory Lattice QCD et al. Experiment HIC et al.? At the Critical Point (CP): Ø 2nd order Phase Transition. Ø Diverges of the thermodynamics quantities, such as correlation length (ξ), Susceptibilities (χ), heat capacity (CV). Sign problem in Lattice QCD at large µb region. S. Gupta, 罗晓峰, B. Mohanty, H.G. Ritter, and 许怒, Science, 332, 1525 (2011). Finite size and time in HIC: Need Sensitive Observable! Experimental confirmation of QCD Critical Point is an excellent test of QCD theory in the nonperturbative region and is the milestone of exploring the QCD Phase Diagram. Xiaofeng Luo April 21, 2014 物理学会高能物理分会, Wuan, China 6 / 23

Higher Moments (I): Sensitive to the Correlation Length Skewness: C N N S = = ( C ) 3 3, N

= 2 4 ( C2, N ) σ κ > 0 3 S<0 S>0 κ < 0 κ = 0 Rodolfo Hermans Ø Ideal probe of non-gaussian

5 < (δn) 4 > - 3 < (δn) 2 > 2 ~ ξ 7 Search for CP in Heavy Ion Collisions (ξ~2-3 fm) M. A.

7 Higher Moments (I): Sensitive to the Correlation Length Skewness: C N N S = = ( C ) 3 3, N < ( < > ) > 3/2 3 2, N σ C n : n th order cumulants κ Kurtosis: C N N 4 4, N < ( < > ) > = = 2 4 ( C2, N ) σ κ > 0 3 S<0 S>0 κ < 0 κ = 0 Rodolfo Hermans Ø Ideal probe of non-gaussian fluctuations. Ø Sensitive to the correlation length (ξ). < (δn) 2 > ~ ξ 2 < (δn) 3 > ~ ξ 4.5 < (δn) 4 > - 3 < (δn) 2 > 2 ~ ξ 7 Search for CP in Heavy Ion Collisions (ξ~2-3 fm) M. A. Stephanov, Phys. Rev. Lett. 102, (2009); Phys. Rev. Lett. 107, (2011); 7 / 23

8 Higher Moments (II): Related to the Susceptibility Pressure: Susceptibility: p T = 1 4 VT ln Z(V,T,µ,µ,µ ) 3 B Q S χ (n) q = n (p / T ^ 4), q = B,Q, S ( µ q ) n Lattice QCD (Conserved Charges) χ q (1) = 1 VT 3 δn q, χ q (2) = 1 VT 3 χ q (3) = 1 VT 3 χ q (4) = 1 VT 3 " $ # ( δn q ) 2 ( δn q ) 3 ( δn q ) 4 3 ( δn q ) 2 2 % ' & Ø Susceptibility ó Moments of Conserved Charges. κσ 2 ~ χ (4) (3) χ,sσ ~ (2) χ χ (2),σ 2 M ~ χ (2) χ (1) R.V. Gavai and S. Gupta, PLB 696, 459 (2011). S. Gupta, et al., Science, 332, 1525(2011). Y. Hatta, et al, PRL. 91, (2003). A. Bazavov et al.arxiv:: F. Karsch et al, PLB 695, 136 (2011). 8 / 23

9 Theoretical Prediction : Critical Point Induced Dip Baseline Frithjof Karsch,Talk at NFQCD 2013, Japan. A dip in the kurtosis*variance is likely to show up on the freeze-out line in the vicinity of a critical endpoint. see also: Misha Stephanov, Talk at EMMI Workshop 2013, LBNL, US M. A. Stephanov, Phys. Rev. Lett. 107, (2011); 9 / 23

First Measurement: Before BES STAR, Xiaofeng Luo et al, PRL105, 022302(2010). Expected by Central Limit Theorem.

10 First Measurement: Before BES STAR, Xiaofeng Luo et al, PRL105, (2010). Expected by Central Limit Theorem. (CLT) Ø First measurement of the higher moments of net-proton distributions at RHIC. Ø There has no evidence for the existence of QCD critical point at μ B <200 MeV. 10 / 23

Raw Event-by-Event Net-proton/Net-charge Distributions Net-proton STAR, PRL 112, 032302 (2014).

to net-baryon), net-charge, and net-kaon(approx. to net-strangeness.

11 Raw Event-by-Event Net-proton/Net-charge Distributions Net-proton STAR, PRL 112, (2014). Net-charge STAR,Acta Phys.Polon.Supp. 6 (2013) Event-by-event fluctuations of net-proton (approx.to net-baryon), net-charge, and net-kaon(approx. to net-strangeness.) The raw distributions are only for illustration purpose and should not be used to calculate the moments directly. Need corrections to extract the dynamical fluctuations. 11 / 23

Analysis Techniques Background/artifacts effects. Ø Auto-correlation effects. Ø Volume fluctuation effects. Initial volume fluctuation Techniques: 1.

Luo (STAR Collaboration), J. Phys. Conf. Ser. 316, 012003 (2011). (CBWC) X. Luo (STAR Collaboration), Nucl. Phys. A 904, 911c (2013). X. Luo (STAR Collaboration), Pos (CPOD 2013) 019 [arxiv: 1306.

12 Analysis Techniques Background/artifacts effects. Ø Auto-correlation effects. Ø Volume fluctuation effects. Initial volume fluctuation Techniques: 1. Define the centrality without p and pbar 2. Define the centrality with large η window. Ø Detector efficiency effects. 3. Centrality Bin Width Correction (CBWC). X. Luo (STAR Collaboration), J. Phys. Conf. Ser. 316, (2011). (CBWC) X. Luo (STAR Collaboration), Nucl. Phys. A 904, 911c (2013). X. Luo (STAR Collaboration), Pos (CPOD 2013) 019 [arxiv: ]. (Initial volume fluctuation) X. Luo, J. Phys. G 39, (2012). (Statistical Error) X. Luo, J. Xu, B. Mohanty, N. Xu, J. Phys. G 40, (2013). (Volume flu. and auto-correlation) 4. Efficiency Correction 12 / 23

13 Centrality Definition Refmult3 (Charged Pion+Kaon) To avoid auto-correlation. η <1, Current TPC Acceptance Limit. STAR Preliminary 13 / 23

14 C 2 ( X Y ) = Detector Efficiency Correction: Binomial Efficiency This correction is done for refmult3 by refmult3 and corrected for bin width after efficiency correction. 5% uncertainty on the efficiency number is considered. C 2 (x y)+(ε 1)(<x>+<y>) ε 2 C 3 ( X Y )= C 3 (x y)+3(ε 1)(C 2 (x) C 2 (y))+(ε 1)(ε 2)(<x> <y>) ε 3 X: Input Proton, Y: Input Anti-proton, ε = ε + ε p p x: measured proton 2 y: measured anti-proton C 2, C 3, C 4 : 2 nd, 3 rd 4 th order cumulants. C 4 ( X Y ) = C 4 (x y) 2(ε 1)C 3 (x+y)+8(ε 1)(C 3 (x)+c 3 (y))+(5 ε )(ε 1)C 2 (x+y)+8(ε 2)(ε 1)(C 2 (x)+c 2 (y))+(ε 2 6ε+6)(ε 1)(<x>+<y>) ε 4 Average Efficiency within transverse momentum range (a,b): Embedding efficiency weighted by p T spectra. ε(p or p ) = b a ε ' (p T ) f (p T )p T dp T b a f (p T )p T dp T ε ' (p T ) : embedding p T dependent efficiency for proton or anti-proton. 7.7 GeV proton 14 / 23

15 Error Estimation Method Delta theorem and Bootstrap method give reasonable error estimation While the sub-group method overestimate the statistical errors. 15 / 23

16 Mean net-proton, proton and anti-proton Ø Net-proton, proton and anti-proton number increase with N part. Ø Net-proton increase when energy decrease and dominated by proton at low energies. (Interplay between baryon stopping and pair production) 16 / 23

17 Centrality Dependence of Net-proton Cumulants Ø Linear increase with N part. Ø C1~C3 and C2~C4 for all energies. 17 / 23

18 Baseline (I) : Poisson and Binomial Ø For Poisson case, the order of cumulant increases the deviations of the data from the Poisson expectation for net-proton and proton increase. Largest deviation is found for C4 at 19.6 and 27 GeV. Ø For Binomial case, the agreement persist up to 3 rd order. But fails to describe the data for C4 at 19.6 and 27 GeV. 18 / 23

19 Baseline (II) : UrQMD Ø The anti-proton distributions follow reasonably well the UrQMD expectations. Ø The UrQMD model results for higher order cumulants can not explain the measured values at 19.6 and 27 GeV. 19 / 23

20 Moments of Net-proton Distribution at RHIC S 2 (S )/Skellam Au+Au Collisions at RHIC Net-proton 0.4<p <0.8 (GeV/c), y <0.5 T Skellam Distribution 70-80% 0-5% p+p data Au+Au 70-80% Au+Au 0-5% Au+Au 0-5% (UrQMD) Colliding Energy s NN (GeV) 1) All data show deviations below Poisson beyond statistical and systematic errors in the 0-5% most central collisions for κσ 2 and Sσ at all energies. Larger deviation at s NN ~ 20GeV 2) UrQMD model show monotonic behavior in the moment products 3) Higher statistics needed for collisions at s NN < 20 GeV. BES-II is needed. 4) Compare with QCD based dynamical model. STAR: Xiaofeng Luo et al. Phys. Rev. Lett. 112, (2014) [arxiv: ] 20 / 23

21 Moments of Net-charge Distribution at RHIC STAR, arxiv: , Submitted to PRL. Ø Within the present uncertainty, no non-monotonic behavior is observed as a function of beam energy. Ø More statistics is needed at low energies. Net-kaon Analysis is ongoing. and will be presented on QM / 23

22 Location of CP:Recent Theory Prediction Dyson-Schwinger approach (Nf=2+1) Lattice QCD (Nf=2+1): Taylor Expansion (Quark Chemical Potential) C. S. Fischer,Talk at NFQCD 2013, Japan S. Gupta, Talk at Lattice 2013, France. μ E B /TE ~ 5 s NN ~5 GeV μ E B /TE ~1.7 s NN ~20 GeV Different Theory/Method gives very different CP location. 22 / 23

23 Summary Measurements: Ø We present the moments of net-proton cumulants in Au+Au collisions at RHIC BES-Phase I energies (7.7, 11.5, 19.6, 27, 39, 62.4 and 200 GeV). Comparisons with Various Baselines and Transport Model: Ø Deviations below various baselines are observed in Au+Au collision below 39 GeV. Most significant deviation are found around 19.6 and 27 GeV. Ø Not conclusive yet on searching for the QCD critical point, higher statistics are needed below 27 GeV to get more precise measurement: BES-II (from 2018). Ø For net-charge, we see no non-monotonic behavior.net-kaon analysis is ongoing. Future Physics Opportunities: Ø Find the QCD Critical Point:Need efforts from experimentalist and theorist. Ø Precision measurement of the QGP Properties by comparing the data with the theoretical calculations, such as Lattice QCD. 23 / 23

24 Thank you! 24 / 23

25 Back Up Slides 25 / 23

26 QCD Critical Point Search: Strategy Ø Need sensitive observable. Ø Search for the non-monotonic dependence on energy. Ø Understand the non-cp physics effect. Ø Comparing with the QCD based dynamical model. Characteristic Signature of Critical Point: Non-monotonic dependence on colliding energy. 26 / 23

27 Net-baryon Study by Hadron Resonance Gas Model P. Garg, et al, PLB 726, 691 (2013) Net-charge Ø Net-proton is a good approximation of Net-baryon. Ø Net-baryon has less decay effect than in net-charge and net-strangeness. Net-strangeness Ø Particle carrying 2 charge play important role in net-charge. Ø Net-kaon is not good approximation of net-strangeness 27 / 23

28 Centrality Bin Width Effect and Correction STAR Preliminary CBWC: N (1) : C 2 = ω r C 2,r r=1 N (2) : C 3 = ω r C 3,r r=1 N (3) : C 4 = ω r C 4,r r=1 ω r = n r n r r: r th multiplicity. n r : # of events in r. 1. The trend are different with different bin width. 2. Low energy has larger effects. 3. Volume fluctuations within one centrality bin will enlarge the cumulants / 23

29 Centrality Resolution Effect Ø Large difference are observed in mid-central /peripheral and low energies for different Refmult3 definition (different centrality resolutions). 29 / 23

30 C 2 ( X Y ) = Detector Efficiency Correction: Binomial Efficiency This correction is done for refmult3 by refmult3 and corrected for bin width after efficiency correction. 5% uncertainty on the efficiency number is considered. C 2 (x y)+(ε 1)(<x>+<y>) ε 2 C 3 ( X Y )= C 3 (x y)+3(ε 1)(C 2 (x) C 2 (y))+(ε 1)(ε 2)(<x> <y>) ε 3 X: Input Proton, Y: Input Anti-proton, ε = ε + ε p p x: measured proton 2 y: measured anti-proton C 2, C 3, C 4 : 2 nd, 3 rd 4 th order cumulants. C 4 ( X Y ) = C 4 (x y) 2(ε 1)C 3 (x+y)+8(ε 1)(C 3 (x)+c 3 (y))+(5 ε )(ε 1)C 2 (x+y)+8(ε 2)(ε 1)(C 2 (x)+c 2 (y))+(ε 2 6ε+6)(ε 1)(<x>+<y>) ε 4 Average Efficiency within transverse momentum range (a,b): Embedding efficiency weighted by p T spectra. ε(p or p ) = b a ε ' (p T ) f (p T )p T dp T b a f (p T )p T dp T ε ' (p T ) : embedding p T dependent efficiency for proton or anti-proton. 7.7 GeV proton 30 / 23

31 Error Estimation Method Delta theorem and Bootstrap method give reasonable error estimation While the sub-group method overestimate the statistical errors. 31 / 23

coverage beneficial to many crucial measurements e-cooling itpc Upgrade China : USTC, SDU,

32 The STAR Upgrades and BES Phase II Ø Fine energy scan at s NN <~ 20 GeV Ø Electron cooling will provide increased luminosity ~ 3-10 times Ø STAR itpc upgrade extend mid-rapidity coverage beneficial to many crucial measurements e-cooling itpc Upgrade China : USTC, SDU, SINAP For moment analysis, itpc upgrade will provide better efficiency and centrality resolution. 32 / 23

33 Proposed Statistics for BES-II in BES White Paper BES Phase II is planned for two 22 cryo-week runs in 2018 and / 23

Critical Point T. Andrews. Phil. Trans. Royal Soc., 159:575, 1869. At the Critical Point (CP): Ø 2nd order Phase Transition.

34 Critical Point T. Andrews. Phil. Trans. Royal Soc., 159:575, At the Critical Point (CP): Ø 2nd order Phase Transition. Ø Diverges of the thermodynamics quantities, such as correlation length (ξ), Susceptibilities (χ), heat capacity (C V ). Ø light wavelength comparable with the correlation length: Critical Opalescence. Critical Opalescence as observed in CO2 liquid-gas transition. Ø Universality Class: QCD critical point has the same critical exponents as liquid-gas critical point (Z 2 Class). Ø Critical slowing down, finite size effects et al. 34 / 23

Event and Track Selection Energy (GeV) 7.7 11.5 19.6 27 39 62.

6 ~15 ~30 ~87 ~47 ~238 Year 2010 2010 2011 2011 2010 2010 2010 Ø Events QA: Some

(bad Run/Events Removed) Ø PID : Energy loss (de/dx) in STAR TPC is used to

35 Event and Track Selection Energy (GeV) Statistics (Million), 0-80% ~3 ~6.6 ~15 ~30 ~87 ~47 ~238 Year Ø Events QA: Some quality cuts have been applied.(bad Run/Events Removed) Ø PID : Energy loss (de/dx) in STAR TPC is used to identify protons with high purity within 0.4<p T <0.8 (GeV/c) and at mid-rapidity y <0.5. Z p = ln((de / dx) exp. / (de / dx) theory ) σ TPC STAR TPC de/dx PID Proton Phase Space Z p < 2 35 / 23

36 Baselines Ø If proton and anti-proton are independent,then Net-proton: C n (p p) = C n (p) + ( 1) n C n (p), n = 1,2, Poisson Baseline: Assuming that the proton and antiproton are independent distributed as Poisson distribution. Then Cn (X) =< X >, X = p, p 2. Binomial Baseline: Assuming that the proton and anti-proton are independent distributed as Binomial distribution. Mean: µ=<x> Variance to mean ratio: ε=σ 2 /µ C 2 (X) = σ 2 = εµ C 3 (X) = Sσ 3 = εµ(2ε 1) C 4 (X) = κσ 4 = εµ(6ε 2 6ε +1) X = p, p 3. Models: HRG, UrQMD, AMPT, Hijing etc. 36 / 23

Medium induced modified Fragmentation Function for Multiple Parton Scattering

Medium induced modified Fragmentation Function for Multiple Parton Scattering Medium-Modified Fragmentation Function due to Multiple Parton Scattering Wei-ian Deng Sandong Universit Xin-Nian Wang LBNL & Sandong Universit Outline Introduction Modified fragmentation function in Brick