fluctuations of conserved charges and freeze-out...

Freeze-out parameters

Fluctuations of conserved charges

and freeze-out conditions in heavy ion collisions

Claudia RattiUniversita degli Studi di Torino, INFN, Sezione di Torino

and University of Houston, Texas

S. Borsanyi, Z. Fodor, S. Katz, S. Krieg, C. R., K. Szabo, arXiv:1403.4576

Claudia Ratti 1


Motivation

✦ Synergy between fundamental theory and experiment

✦ We can create the deconfined phase of QCD in the laboratory

✦ Lattice QCD simulations have reached unprecedented levels of accuracy

➟ physical quark masses

➟ several lattice spacings → continuum limit

✦ The joint information between theory and experiment can help us to shed light on QCD

Claudia Ratti 2


The observables: fluctuations of conserved charges

✦ They can be calculated on the lattice as combinations of quark number susceptibilities

✦ They can be directly compared to experimental measurements

✦ The chemical potentials are related:

µu =1

3µB +

2

3µQ;

µd =1

3µB −

1

3µQ;

µs =1

3µB −

1

3µQ − µS .

✦ susceptibilities are defined as follows:

χBSQlmn

=∂ l+m+np/T 4

∂(µB/T )l∂(µS/T )m∂(µQ/T )n.

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Relating lattice results to experimental measurement✦ the first four cumulants are:

χ1 = 〈(δx)〉 χ2 = 〈(δx)2〉

χ3 = 〈(δx)3〉 χ4 = 〈(δx)4〉 − 3〈(δx)4〉2

✦ we can relate them to higher moments of multiplicity distributions:

mean : M = χ1 variance : σ2 = χ2

skewness : S = χ3/χ3/22

kurtosis : κ = χ4/χ22

Sσ = χ3/χ2 κσ2 = χ4/χ2

M/σ2 = χ1/χ2 Sσ3/M = χ3/χ1

F. Karsch (2012)

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Caveats✦ Effects due to volume variation because of finite centrality bin width V. Skokov, B. Friman, K.

Redlich, PRC (2013)

➟ Experimentally corrected by centrality-bin-width correction method

✦ Finite reconstruction efficiency


✦ Spallation protons


✦ Canonical vs Gran Canonical ensemble


✦ Proton multiplicity distributions vs baryon number fluctuations

➟ Numerically very similar once protons are properly treated M. Asakawa and M. Kitazawa, PRC

(2012), M. Nahrgang et al., 1402.1238

✦ Final-state interactions in the hadronic phase J.Steinheimer et al., PRL (2013)


Claudia Ratti 5


Caveats✦ Effects due to volume variation because of finite centrality bin width V. Skokov, B. Friman, K.

Redlich, PRC (2013)


✦ Finite reconstruction efficiency

➟ Experimentally corrected based on binomial distribution A. Bzdak, V. Koch, PRC (2012)

✦ Spallation protons

➟ Experimentally removed with proper cuts in pT

✦ Canonical vs Gran Canonical ensemble

➟ Experimental cuts in the kinematics and acceptance V. Koch, S. Jeon, PRL (2000)

✦ Proton multiplicity distributions vs baryon number fluctuations

➟ Numerically very similar once protons are properly treated M. Asakawa and M. Kitazawa, PRC

(2012), M. Nahrgang et al., 1402.1238

✦ Final-state interactions in the hadronic phase J.Steinheimer et al., PRL (2013)

➟ Consistency between different charges = fundamental test

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Canonical vs Gran Canonical ensemble

V. Koch: 0810.2520

✦ ∆Ytotal: range for total charge multiplicity distribution

✦ ∆Yaccept: interval for the accepted charged particles

✦ ∆Ycorr : charge correlation length characteristic to the physics of interest

✦ ∆Ykick :rapidity shift that charges receive during and after hadronization

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Relations between chemical potentials

✦ µB , µS and µQ are NOT independent:

〈nS〉 = 0 〈nQ〉 =Z

A〈nB〉 ⇒

Z

A= 0.4

✦ By expanding nB , nS and nQ up to µ3B we get:

µQ(T, µB) = q1(T )µB + q3(T )µ3B + ...

µS(T, µB) = s1(T )µB + s3(T )µ3B + ...

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Taylor coefficients: results

-0.04

-0.035

-0.03

-0.025

-0.02

-0.015

-0.01

-0.005q1(T) Nt=8

Nt=10Nt=12Nt=16

extrapolationBNL-Bielefeld [1208.1220]

HRG

-0.05

0

0.05

0.1

0.15

140 160 180 200 220 240

T [MeV]

q3(T)/q1(T)

0.15

0.2

0.25

0.3

0.35 s1(T)

Nt=8Nt=10Nt=12Nt=16

extrapolationBNL-Bielefeld [1208.1220]

HRG

-0.05

0

0.05

0.1

0.15

140 160 180 200 220 240

T [MeV]

s3(T)/s1(T)

WB Collaboration: PRL (2013)

✦ µQ turns out to be very small

✦ Agreement between WB and BNL-Bielefeld collaborations

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Thermometer and Baryometer

✦ RB31: thermometer

RB31(T, µB) =

χB3(T, µB)

χB1(T, µB)

=χB4(T, 0) + χBQ

31(T, 0)q1(T ) + χBS

31(T, 0)s1(T )

χB2(T, 0) + χBQ

11(T, 0)q1(T ) + χBS

11(T, 0)s1(T )

+O(µ2B)

✦ Expand numerator and denominator around µB = 0: ratio is independent of µB

✦ RB12: baryometer

RB12(T, µB) =

χB1(T, µB)

χB2(T, µB)

=χB2(T, 0) + χBQ

11(T, 0)q1(T ) + χBS

11(T, 0)s1(T )

χB2(T, 0)

µB

T+O(µ3

B)

✦ Expand numerator and denominator around µB = 0: ratio is proportional to µB

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Experimental measurement I

Star Collaboration: arXiv 1212.3892

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Experimental measurement II

Star Collaboration: arXiv 1402.1558

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Thermometer from electric charge

WB Collaboration: PRL (2013)

✦ Would be ideal observable: less ambiguous than baryon number vs proton

✦ Present uncertainty in the experimental data does not allow to extract Tch

Claudia Ratti 13


Extracting freeze-out parameters from baryon number

0

0.2

0.4

0.6

0.8

1

1.2

1.4

140 160 180 200 220 240

T [MeV]

STARNt=6Nt=8

Nt=10Nt=12

WB continuum limit

RB31=SB σB

3 / MB

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100 120 140 160 180 200

µB [MeV]

RB12=MB/σB

2

STAR, 27 GeV

STAR, 39 GeV

STAR, 62.4 GeV

STAR, 200 GeV

T=140 MeVT=145 MeVT=150 MeV

WB Collaboration: arXiv 1403.4576; STAR data from 1309.5681

✦ Upper limit: Tf ≤ 148± 4 MeV √s[GeV ] µf

B [MeV]

200 25.6±2.4

62.4 69±5.7

39 104±10

27 -

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Baryon number vs protons.

0.7

0.8

0.9

1

1.1

120 125 130 135 140 145 150 155 160

χ 3/χ

1

T (MeV)

net-baryon

net-proton+feed

net-proton+feed+i.r.

M. Nahrgang, M. Bluhm, P. Alba, R. Bellwied, C. R., arXiv:1402.1238

✦ Study in the HRG model

✦ Take into account feed-down from resonance decay

✦ Take into account resonance regeneration −> Isospin randomization

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Extracting freeze-out µB from electric charge

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 20 40 60 80 100 120 140 160 180 200

µB [MeV]

RQ12=MQ/σQ

2

STAR, 27 GeV

STAR, 39 GeV

STAR, 62.4 GeV

STAR, 200 GeV


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100 120 140 160 180 200

µB [MeV]

RB12=MB/σB

2

STAR, 27 GeV

STAR, 39 GeV

STAR, 62.4 GeV

STAR, 200 GeV


WB Collaboration: arXiv 1403.4576; STAR data from 1309.5681 and 1402.1558

✦ It is of fundamental importance to test the consistency between the freeze-out parameters

obtained with different conserved charges

✦ This consistency check validates the method and shows equilibration of the medium

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Consistency is found!√s[GeV ] µf

B [MeV] (from B) µfB [MeV] (from Q)

200 25.6±2.4 22.6±2.4

62.4 69±5.7 65.9±7.2

39 104±10 100±9

27 - 134.5±12.5

0

20

40

60

80

100

120

140

160

0 50 100 150 200

√s [GeV]

µB [MeV]from Bfrom Q

SHM model

Lattice: WB Collaboration: arXiv 1403.4576; SHM: Andronic et al., NPA (2006)Claudia Ratti 17


Ratio of ratios

0

0.05

0.1

0.15

0.2

120 140 160 180 200 220 240

T [MeV]

STAR, 39 GeVSTAR, 62.4 GeVSTAR, 200 GeV

µB= 100 MeVµB= 65 MeVµB= 25 MeV

µB= 0

[MQ/σQ2] / [MB/σB

2]

RQ12/R

B12 = [χQ

1 /χQ2 ]/[χ

B1 /χ

B2 ] = [MQ/σ

2Q]/[MB/σ

2B ]

Claudia Ratti 18


Freeze-out temperature from experiment

✦ Fit to yields of identified particles: Statistical Hadronization Model (SHM)

✦ Model-dependent. Parameters: freeze-out temperature and chemical potential

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Strange vs light thermometer

0

0.2

0.4

0.6

0.8

1

150 200 250 300 350 400

T [MeV]

χ2u cont.

χ2s cont.

S. Borsanyi et al.: JHEP (2012); R. Bellwied et al.: PRL (2013)

✦ Flavor-specific fluctuations show separation between light and strange quarks

✦ Does it mean that light and strange quarks have different freeze-out temperatures?

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Conclusions

✦ It is possible to extract freeze-out parameters from first principles

✦ Higher order fluctuations of baryon number:

➟ RB31(T, µB) =

χB3(T,µB)

χB1(T,µB)

: Thermometer

➟ RB12(T, µB) =

χB1(T,µB)

χB2(T,µB)

: Baryometer

✦ Higher order fluctuations of electric charge:

➟ independent measurement

➟ RQ12(T, µB) =

χQ

1(T,µB)

χQ

2(T,µB)

: Baryometer

✦ The freeze-out parameter sets obtained from B and Q are consistent with each other

✦ Looking forward to strangeness fluctuation data!

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HRG model and particle ratios

✦ Freeze-out conditions in agreement with HRG model analysis

P. Alba et al., arXiv:1403.4903.

✦ Yields of strange particles would need a higher Tch

Claudia Ratti 22

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