Terence J Tarnowsky (for the STAR Collaboration) Michigan State University

Searching for the QCD Critical Point Using Particle Ratio Fluctuations and

Higher Moments of Multiplicity Distributions

Terence J Tarnowsky (for the STAR Collaboration)

Michigan State UniversityQuark Matter 2011, Annecy, France

May 23, 2011

Terence Tarnowsky Quark Matter 2011May 23, 2011

2

Outline

• Introduction

• STAR Detector

• Higher moments of Conserved Quantities.

• Particle Ratio Fluctuations

• Summary


3

Motivation Behind Correlations and Fluctuations

• Have been many theoretical predictions that the behavior of correlations and fluctuations in a deconfined phase are different than that in hadron gas.

• Experimental justification from studies of the thermodynamics of phase transitions.

• Even w/o such guidance, can search for discontinuities in fluctuations and correlations as functions of incident energy and centrality (not an inclusive list):– Particle ratio fluctuations (K/, p/, K/p).– Forward-Backward multiplicity correlations.– Balance Functions– Higher moments of conserved quantities.– Etc.

See Posters:Lizhu Chen, Poster #146, Xiaofeng Luo, Poster #141, Nihar Sahoo, Poster #191, Amal Sarkar, Poster #93,Michael Skoby, Poster #89,Prithwish Tribedy, Poster #86,Hui Wang, Poster #95


4

Search for the QCD Critical Point

• In a phase transition near a critical point, an increase in non-statistical fluctuations is expected.

• Finite system-size effects may influence fluctuation measurements.

• Finite-size scaling of fluctuations may indicate existence of critical point.

• E.g. Change in behavior of quark susceptibilities.

Aoki, Endrodi, Fodor, Katz, and Szabó Nature 443, 675-678 (2006)

• These may manifest in final-state measurements.

X2χ

X4χ

B = 0

B = 0


5

RHIC “Energy Scan”

• Using RHIC to run an “energy scan” to search for predicted QCD critical point.

• For 2010, we had Au+Au collisions at √sNN = 200, 62.4, 39, 11.5, and 7.7 GeV.– 2011 added Au+Au collisions at √sNN = 19.6 GeV.

– 2012 should bring Au+Au collisions √sNN = 27 GeV.

• Can examine our fluctuation observables to look for non-monotonic behavior as a function of collision energy.


6

STAR Detector• STAR is a large acceptance

detector.– Good and coverage for

measuring fluctuations.

• TPC: || < 1.0, TOF: || < 0.9

• TOF upgrade has enhanced STAR’s PID capabilities.

Particle Ratio Fluctuations

p/(p+ + p-)/(

K/

K/ppp


8

Fluctuation Observables, dyn

• NA49 uses the variable dyn

dyn sign data2 mixed

2 data2 mixed

2

is relative width of K / distribution is the reduced width of K/ distribution


9

Fluctuation Observables, dyn

• STAR uses a different fluctuation observable, dyn.

• Introduced to study net-charge fluctuations.

• Measures deviation from Poisson behavior.

• It has been demonstrated that,

dyn,K NK NK 1 NK

2 N N 1 N

2 2NKN

NK N

dyndyn 2


10

Excitation Function for dyn,K/

STAR central Au+Au (0-5%) collisions with SPS central Pb+Pb collisions (0-3.5%).

• Large decrease in fluctuations as function of energy from NA49.

• Fluctuations measured by STAR approximately constant as function of energy from 19.6-200 GeV.

• || < 1.0

• , K: 0.2 < pT < 0.6 GeV/c.

Phys.Rev.Lett.103:092301,2009


11

Excitation Function for dyn,p/

• NA49 dyn,p/ converted to dyn,p/.

• TPC+TOF (GeV/c):• : 0.2 < pT < 1.4• p : 0.4 < pT < 1.8

• TPC+TOF includes statistical and systematic errors from electron contamination.

• Agreement with measurements from NA49 at low energies.

(NA49 data from: C. Alt et al. [NA49 Collab.], Phys. Rev. C 79, 044910 (2009)

• UrQMD and HSD predictions both change sign at high energies.


12

Excitation Function for dyn,K/p

• NA49 dyn,K/p converted to dyn,K/p using 2dyn = dyn. • TPC+TOF (GeV/c):

• K : 0.2 < pT < 1.4• p : 0.4 < pT < 1.8

• TPC+TOF includes statistical and systematic errors from electron contamination

• Large deviation between STAR and NA49 result at √sNN = 7.7 GeV.

(NA49 data from: T. Anticic, et al [NA49 Collab.] arXiv:1101.3250v1 [nucl-ex])

• Models predominantly independent of experimental acceptance.


13

• TPC+TOF (GeV/c):• : 0.2 < pT < 1.4• K : 0.2 < pT < 1.4

• TPC+TOF includes statistical and systematic errors from electron contamination.

• Pion contamination of kaons < 3% using TPC and TOF.

• Difference between STAR and NA49 result below √sNN = 11.5 GeV.(NA49 data from C. Alt et al. [NA49 Collab.], Phys. Rev. C 79, 044910 (2009)

• Both models show little acceptance effects.

• UrQMD predicts little energy dependence.• HSD predicts an energy dependence.

Excitation Function for dyn,K/

• NA49 dyn,K/ converted to dyn,K/ using 2dyn = dyn.

Higher Moments of Conserved Quantities

(Skewness and kurtosis of net-protons and net-charge)


15

Higher Moments of Net-Proton Distributions

• 1st moment: mean = M

• 2nd moment: variance = 2

• 3rd standardized moment: skewness = S

• 4th standardized moment: kurtosis =

• Calculate moments from the event-by-event net proton distribution.

– Have similar plots for net-charge and net-kaon distributions.

STAR Preliminary

See Posters:Xiaofeng Luo, Poster #141, Nihar Sahoo, Poster #191, Amal Sarkar, Poster #93


16

Connection to Physical Quantities• Higher moments of net-proton distribution can be related to

thermodynamic susceptibilities.– (S)B = B

3B2

– (2)B = B4B

2

– (M.Cheng et al, Phys. Rev. D 79, 074505 (2009), F. Karsch and K. Redlich, Phys. Lett. B 695, 136 (2011))

• Predictions that critical fluctuations contribute to higher moments and are strongly dependent on correlation length ( of the system:– 4th order moments go as 7. (M. A. Stephanov, Phys. Rev. Lett. 102,

032301 (2009))

• For net-charge, change index from B to Q. For net-kaons, change B to S.


17

Products of the Moments

• Products of the moments cancel volume effects.

• Deviation from Hadron Resonance Gas (HRG) prediction below 62.4 GeV. – For HRG:

• S = tanh(B/T)• = 1

See Xiaofeng Luo, Poster #141


18

Products of the Moments

• Products of the moments cancel volume effects.

See Nihar Sahoo, Poster #141


19

Summary• New results for dynamical particle ratio fluctuations from data

collected during first part of the RHIC energy scan to search for QCD critical point.– For p/ fluctuations:

• From √sNN = 7.7-200 GeV, all measured fluctuations are negative.– For K/p fluctuations:

• Similar to p/, fluctuations measured from √sNN = 7.7-200 GeV are negative.– For K/ fluctuations

• STAR does not observe any strong energy dependence of K/ fluctuations in central Au+Au collisions.

– Additional systematics under study.– An additional data point below √sNN = 7.7 GeV (e.g. √sNN = 5 GeV) could

provide additional support to the observed trends.

• Higher moments of the distributions of conserved quantities (e.g. net-proton, net-charge) are expected to be sensitive to critical fluctuations.– For net-proton, S and are consistent with the HRG prediction above

√sNN = 39 GeV, but slightly below the prediction at lower energies.


20

BACKUP


21

STAR Fluctuation and Correlation Posters

• Mix-Ratios of Higher Order Moments of Protons and Kaons for QCD Critical Point search at RHIC. (Lizhu Chen, Poster #146)

• Higher Moments of Event-by-Event Net-proton Multiplicity Distributions at RHIC. (Xiaofeng Luo, Poster #141)

• Search for the QCD Critical Point by the Higher Moments of the Net-charge Multiplicity Distribution. (Nihar Sahoo, Poster #191)

• Net Kaon Fluctuations in the STAR Beam Energy Scan Program. (Amal Sarkar, Poster #93)

• Forward-Backward Multiplicity Correlations for Identified Particles at STAR. (Michael Skoby, Poster #89)

• Local Parity Violation or Local Charge Conservation/Flow? A Reaction-Plane-Dependent Balance Function Study. (Hui Wang, Poster #95)

• Charge-to-Neutral Fluctuations in AuAu Collisions at Forward Rapidity at RHIC. (Prithwish Tribedy, Poster #86)


22

7.7 GeV

04/24/2322Hui Wang

Hui Wang

Documents

Terence J Tarnowsky (for the STAR Collaboration) Michigan State University