Measurement of net-particle multiplicity fluctuations at RHIC

Roli Esha Stony Brook University

Roli Esha AUM 2019

Introduction

Event-by-event fluctuation of conserved quantities (Charge, Q / Baryon number, B / Strangeness, S) to study phase transition

Cross-over at small µB

Critical point

First order at large µB

Experimental observables

Cumulants of event-by-event net-particle multiplicity distributions - Net charge / net-proton (proxy for net-baryon) / net-kaon (proxy for net-strangeness)

Correlation functions of particles

2

Roli Esha AUM 2019

Higher-order Fluctuations

3

Higher order cumulants are more sensitive to signatures of phase transition

Connection to the susceptibility of the system

Correlation functions have the same power law dependence as the cumulants

!" = (&')" ~*"; !, = (&'), ~*-./; !- = (&')- ~*0 &' = ' − '

M. A. Stephanov, Phys. Rev. Lett. 102, 032301 (2009). M. Asakawa, S. Ejiri and M. Kitazawa, Phys. Rev. Lett. 103, 262301 (2009). M. A. Stephanov, Phys. Rev. Lett. 107, 052301 (2011). Cheng et al, Phys. Rev. D 79, 074505 (2009). B. Ling, M. Stephanov, Phys. Rev. C 93, 034915 (2016); A. Bzdak, V. Koch, N. Strodthoff, arXiv:1607.07375; A. Bzdak, V. Koch, V. Skokov, arXiv:1612.05128

Theory Experiment

Roli Esha AUM 2019

Connections with Lattice QCD

4

LQCD predicts a “crossover” for µB = 0

No established approach to do QCD calculations at finite baryon chemical potential

By putting µQ = µS= 0 and using Taylor expansion, the equation of state for finite µB:

The sixth order cumulants of baryon number is expected to be negative at chiral transition temperature

P(T,µB)−P(T, 0)T 4

=12χ2B(T) µB

T⎛

⎝⎜

⎞

⎠⎟2

× 1+ 14χ4B(T)

χ2B(T)

µB

T⎛

⎝⎜

⎞

⎠⎟2

+1360

χ6B(T)

χ2B(T)

µB

T⎛

⎝⎜

⎞

⎠⎟4⎡

⎣⎢⎢

⎤

⎦⎥⎥+O(µB

8 )

B. Friman, F. Karsch, K. Redlich, V. Skokov Eur. Phys. J. C 71, 1694 (2011)

F. Karsch and K. Redlich, Phys. Lett. B 695, 136 (2011) STAR Collaboration, Phys.Rev.Lett. 112 (2014) 032302

Y. Aoki, Nature 443, 675(2006)

Roli Esha AUM 2019

Analysis methods

Centrality re-definition to exclude particle of interest to avoid auto-correlation

Centrality bin width correction to suppress volume fluctuation

5

X. Luo and N. Xu, arXiv:1701.02105 STAR Collaboration, Phys.Rev.Lett. 105 (2010) 022302. STAR Collaboration, Phys.Rev.Lett. 113 (2014) 092301 X. Luo, J. Xu, B. Mohanty, N. Xu, J. Phys. G 40, 105104 (2013)

Roli Esha AUM 2019

Analysis methods

Statistical error estimation using Bootstrap technique or Delta theorem

Detector efficiency correction.

The cumulants are expressed in terms of the factorial moments or factorial cumulants, which can easily be efficiency corrected by assuming binomial response function for efficiency.

6

X. Luo and N. Xu, arXiv:1701.02105 STAR Collaboration, Phys.Rev.Lett. 105 (2010) 022302. STAR Collaboration, Phys.Rev.Lett. 113 (2014) 092301 B. Efron et al. An Introduction to Bootstrap, Chapman & Hill (1993). Based on factorial cumulants: T. Nonaka, M. Kitazawa and S. Esumi, PRC.95 064912(2017) Based on factorial moments: A. Bzdak and V. Koch, PRC91, 027901 (2015). X. Luo, PRC91, 034907(2015).

σ:widthofthedistributionn : Number of events

Roli Esha AUM 2019

Analysis details

7

Roli Esha AUM 2019

Raw Distributions

8

-50 0 50

-50 0 50

10

210

310

410

510

610

10

210

310

410

510

6100-5%

30-40%70-80%

| < 0.5η < 2 (GeV/c),| Tp0.2 <

= 14.5GeVNNSAu+Au

-50 0 50

-50 0 50

10

210

310

410

510

610

10

210

310

410

510

610 < 1.6 (GeV/c),|y| < 0.5Tp0.2 <

-50 0 50

-50 0 50

10

210

310

410

510

610

10

210

310

410

510

610 < 2 (GeV/c),|y| < 0.5Tp0.4 <

STAR Preliminary

)KN∆Net-Kaon ( )ChN∆Net-Charge ( )PN∆Net-proton (

Num

ber o

f Eve

nts

Uncorrected raw event-by-event net-particle multiplicity distribution for Au+Au collisions at √sNN = 14.5 GeV

Roli Esha AUM 2019

Corrected cumulant ratios from STAR

9J. Thaeder (for the STAR Collaboration), Quark Matter 2015

Net-Charge Net-Kaon Net-Proton

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Corrected cumulant ratios from PHENIX

10

A. Adare et al. (PHENIX Collaboration) Phys. Rev. C 93, 011901 P. Garg et al. Phys. Lett. B 726 (2013) 691-696

Within errors, the results of net-charge show flat energy dependence. More statistics are needed at low energies.

Roli Esha AUM 2019

Correlation function

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6 10 20 100 200

0

2

4

6

<N>4C

(a)

STAR Preliminary

(GeV)NNs6 10 20 30 100 200

0

2

4

6

<N>4κ(b)

Au+Au: 0-5%

<2 (GeV/c),|y|<0.5T

0.4<pProton

6 10 20 30 100 200

0

2

4

6

<N>4κ-4C

(c)

Cum

ulan

ts a

nd C

orr.

Func

.

Non-monotonic energy dependence is observed for 4th order net-proton and proton fluctuations in most central Au+Au collisions.

R. Esha (for the STAR Collaboration), Quark Matter 2017

⌢κ1 = C1⌢κ 2 = C2 −C1⌢κ 3 = C3 − 3C2 + 2C1⌢κ 4 = C4 − 6C3 +11C2 − 6C1

C1 =< N >C2 =< N > +κ̂ 2

C3 =< N > +3κ̂ 2 + κ̂ 3

C4 =< N > +7κ̂ 2 + 6κ̂ 3 + κ̂ 4

Roli Esha AUM 2019

Sixth-order cumulants

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R. Esha (for the STAR Collaboration), Quark Matter 2017 T. Nonaka (for the STAR Collaboration), Quark Matter 2018 T. Nonaka (for the STAR Collaboration), ATHIC 2018 A. Bazavov et al, arXiv:1701.04325.

Sixth-order cumulants of net-charge and net-baryon distributions are predicted to be negative if the chemical freeze-out is close enough to the phase transition.

C6/C2 for net-charge is consistent with zero with large statistical errors

Negative values are observed for C6/C2 of net-proton systematically from peripheral to central collisions for Au+Au collisions at 200 GeV.

Roli Esha AUM 2019

Net-Λ cumulants

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Net-Λ cumulants might provide additional constraints on freeze-out conditions

J. Norohna-Holster et al, arXiv:1805.00088

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Net-Λ cumulants

14T. Nonaka (for the STAR Collaboration), Quark Matter 2018

C2/C1 is closer to HRG results with kaon freeze out conditions

Statistical uncertainties are too large to provide any meaningful constraint

Unfolding and non-Binomial efficiencies

Roli Esha AUM 2019

Non-binomial efficiency

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Experimental effects — particle mis-identification, track splitting/merging etc.

Multiplicity dependent efficiency

Au+Au@√sNN =200GeVSTARPreliminary

p Tin

tegr

ated

effi

cien

cy

(0.4 < pT (GeV/c) < 0.8)(0.4 < pT (GeV/c) < 0.8)

(0.8 < pT (GeV/c) < 2.0)

(0.8 < pT (GeV/c) < 2.0)

Nch – Np – NpA. Bzdak, R. Holzmann and V. Koch, Phys.Rev. C 94, 064907 (2016)

Roli Esha AUM 2019

Unfolding

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Correlation histogram

Contains the number correlation between measured protons and anti-protons

Response histogram

Contains the distribution of produced particles for every detected number of particles; these are obtained from embedding

Measured distribution

Detector responseProduced

distribution

Schemes

Unfolding with initial proton and anti-proton distributions assumed to be Poisson distributions

Unfolding with iterations

R. Esha, CPOD 2017 T. Nonaka (for the STAR Collaboration), Quark Matter 2018

Roli Esha AUM 2019

Unfolding - an example

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Poisson mean for proton = 10 Poisson mean for antiproton = 9

Efficiency for proton = 0.8 Efficiency for antiproton = 0.7

Poisson distribution for protons and antiprotons with Binomial efficiency

Cumulant for net-proton distribution

Skellam (Analytically) Efficiency corrected (this method)

Efficiency corrected (factorial moment method)

C1 1 0.9996 + 0.0004805 1.001 + 0.000649

C2 19 18.99 + 0.003335 18.99 + 0.004056

C3 1 1.035 + 0.02366 1.045 + 0.03139

C4 19 19.29 + 0.3905 18.696 + 0.2847

Roli Esha AUM 2019

Unfolding - an example

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AMPT model with multiplicity-dependent efficiency for 0-5% central Au+Au collisions at √sNN = 200 GeV

Efficiency for protons = 0.8 - 0.0003*(Ncharge - Nproton - Nantiproton) Efficiency for antiproton = 0.7 - 0.0003*(Ncharge - Nproton - Nantiproton)

2D response matrix : Protons and anti-protons are corrected simultaneously 1D response matrix : Protons and anti-protons are corrected separately Factorial moment method assumes binomial efficiency correction. CBWC is applied.

Even a seemingly small non-binomial effect could have a noticeable consequence on higher-order cumulants -- Pointed out by A. Bzdak et al.

A. Bzdak, R. Holzmann and V. Koch, Phys.Rev. C 94, 064907 (2016)

Local parton density fluctuations

Roli Esha AUM 2019

Local parton density fluctuations

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Phase transitions are known to lead to local density fluctuations

In the coalescence mechanism of particle production, the baryon formation probability can be influenced by local parton density fluctuations

These fluctuations in baryon formation could possibly lead to clustering and void in proton distributions in the phase space

Liquid-SolidProposedQCDphasetransition

ParamagnetictoFerromagneticusingKerrmicroscope

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Observable

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Np2 Np1

Np3 Np4Np1 + Np2 + Np3 + … + NpM

NpiRatio (R) =

where i = 1, 2 … M where M is the number of azimuthal divisions

X

The OBJECT of interest is :

The OBSERVABLE will be the various cumulants of the distribution of the ratio, R.

Roli Esha AUM 2019

The Monte-Carlo model

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Percentage-5 0 5 10 15 20 25 30

0.16

0.17

Mean

Percentage-5 0 5 10 15 20 25 30

0.06

0.07

0.08

0.09

0.10

Sigma

Percentage-5 0 5 10 15 20 25 30

0.0

0.2

0.4

0.6

0.8

Skewness

Percentage-5 0 5 10 15 20 25 30

0.0

0.1

0.2

0.3

0.4

0.5

Kurtosis

Monte Carlo model

Variation of moments of R with percentage of clustering for a Poisson distribution ofprotons with mean 20, probability of event clustering being 20% and azimuthal planedivided into 6 parts. The protons are distributed randomly in phi – plane.

The ELEMENTS of the model are :

Distribution of the number of protons Probability of clustering in an event Percentage of protons which cluster Number of divisions in azimuthal plane

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Distribution of ratio for BES data

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(for 0-5% central collisions and N = 6)

Ratio0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

cou

nts

-510

-410

-310

-210

-110 Au+Au@7.7 GeV

Ratio0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

cou

nts

-510

-410

-310

-210

-110 Au+Au@11.5 GeV

Ratio0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

cou

nts

-510

-410

-310

-210

-110 Au+Au@19.6 GeV

Ratio0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

cou

nts

-510

-410

-310

-210

-110 Au+Au@27 GeV

Ratio0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

cou

nts

-510

-410

-310

-210

-110 Au+Au@39 GeV

Ratio0 0.2 0.4 0.6 0.8 1

Nor

mal

ized

cou

nts

-510

-410

-310

-210

-110 Au+Au@62.4 GeV

data

mixed

STAR Preliminary STAR Preliminary STAR Preliminary

STAR Preliminary STAR Preliminary STAR Preliminary

Roli Esha AUM 2019

Cumulants from data

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(for N = 6)

centrality0 10 20 30 40 50

0.0

0.1

0.2

0.37.7 GeV11.5 GeV19.6 GeV27 GeV39 GeV62.4 GeV

Mean

centrality0 10 20 30 40 50

0.0

0.1

0.2

0.3

Sigma

centrality0 10 20 30 40 50

0.6

0.8

1.0

1.2

1.4

Skewness

centrality0 10 20 30 40 50

0.6

0.8

1.0

1.2

1.4

Kurtosis

(GeV)NNs100.0

0.1

0.2

0.3 0- 5 %

10-15 %

20-25 %

Mean

(GeV)NNs100.0

0.1

0.2

0.3

Sigma

(GeV)NNs10

0.6

0.8

1.0

1.2

1.4

Skewness

(GeV)NNs10

0.6

0.8

1.0

1.2

1.4

Kurtosis

Variation with energy Variation with centrality

STAR Preliminary STAR Preliminary

Roli Esha AUM 2019

Comparison with mixed events

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centrality0 10 20 30 40 50

data

/mix

ed

0.8

1

1.2

7.7 GeV11.5 GeV19.6 GeV27 GeV39 GeV62.4 GeV

Mean

centrality0 10 20 30 40 50

data

/mix

ed

0.6

0.8

1

1.2

1.4

Sigma

centrality0 10 20 30 40 50

data

/mix

ed

0.6

0.8

1

1.2

1.4

Skewness

centrality0 10 20 30 40 50

data

/mix

ed

0.6

0.8

1

1.2

1.4

Kurtosis

(GeV)NNs10

data

/mix

ed

0.9

1

1.1

0- 5 %

10-15 %

20-25 %

Mean

(GeV)NNs10

data

/mix

ed

0.8

0.9

1

1.1

1.2

Sigma

(GeV)NNs10

data

/mix

ed

0.8

0.9

1

1.1

1.2

Skewness

(GeV)NNs10

data

/mix

ed

0.8

0.9

1

1.1

1.2

Kurtosis

(for N = 6)

Variation with centrality Variation with energy

STAR Preliminary STAR Preliminary

Roli Esha AUM 2019

BES-II at RHIC

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0

2

4

6

8

10

12

14

0 0.5 1 1.5 2Proton Rapidity Width 6yp

Net

-pro

ton

k*m

2

TPC iTPC

BES-II Error

f = 1 - p0*x + p1*x3

STAR Data: 0-5% Au+Au Collisions at 7.7 GeV

0.4 < pT < 0.8 GeV/c0.4 < pT < 2 GeV/c

AMPT-SM

More Data RHIC Luminosity Upgrade for Low Energies iTPC upgrade extends the rapidity coverage to Δy = 1.6

STAR Collaboration, https://drupal.star.bnl.gov/STAR/starnotes/public/sn0619

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Summary

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Non-monotonic energy dependences of net-proton and proton C4/C2 are observed for 0-5% central Au+Au collisions.

Four-particle correlations contribute dominantly to the observed non-monotonicity.

C6/C2 is negative for net-protons for central collisions with large statistical uncertainties.

The result of C2/C1 from the cumulants of net-Λ is closer to those of HRG with kaon freeze-out condition rather than light flavor hadrons.

Efficiency correction is an important ingredient in order to reliably calculate the higher-order cumulants. We need to develop an approach to explore these issues adequately, which we have not done previously in our data analyses.

We studied the cumulants of a self-normalized distribution of baryons as a probe into the local parton density fluctuations near critical point. A dynamic model including critical phenomenon is needed to test the applicability of the observable.

More data is being collected in the ongoing BES-II at STAR

Thank you!