measurement of net-particle multiplicity fluctuations at rhic · percentage of protons which...
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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
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Roli Esha AUM 2019
Raw Distributions
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-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
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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
Roli Esha AUM 2019
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
Roli Esha AUM 2019
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
Roli Esha AUM 2019
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 [email protected] GeV
Ratio0 0.2 0.4 0.6 0.8 1
Nor
mal
ized
cou
nts
-510
-410
-310
-210
-110 [email protected] GeV
Ratio0 0.2 0.4 0.6 0.8 1
Nor
mal
ized
cou
nts
-510
-410
-310
-210
-110 [email protected] 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 [email protected] 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
26
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!