christoph blume university of frankfurt winter workshop on nuclear dynamics, 2010, ochos rios,...

Christoph Blume

University of Frankfurt

Winter Workshop on Nuclear Dynamics,

2010, Ochos Rios, Jamaica

Particle Production at the SPS and the QCD Phase DiagramParticle Production at the SPS and the QCD Phase Diagram

Christoph BlumeUniversity of Frankfurt

26th Winter Workshopon Nuclear DynamicsOcho Rios, Jamaica

January 2010

Outline

Christoph Blume WWND 2010, Ocho Rios, Jamaica 2

How to probe different regions of the QCD phase diagram?

Variation of center-of-mass energyWay of scanning different freeze-out parameters T and μB

Variation of system sizeHow do T and μB depend on system size

Core corona approach

Critical point searchSystematic study of multiplicity fluctuationsOther observables

How to probe different regions of the QCD phase diagram?

Variation of center-of-mass energyWay of scanning different freeze-out parameters T and μB

Variation of system sizeHow do T and μB depend on system size

Core corona approach

Critical point searchSystematic study of multiplicity fluctuationsOther observables

QCD Phase Diagram


A. Andronic et al., arXiv: 0911.4806

L. McLarren and R.D. Pisarski,Nucl. Phys. A796,83 (2007).


QCD Phase DiagramExperimental Access

High energies (RHIC/LHC)B small

System reaches QGP phase

Low energies (AGS)B large

System stays in hadronic phase

In between (SPS/FAIR)Variation of B by changing sNN

Possible to localize critical point?

Other control parameters (e.g. system size)?


Significant change of shape at SPS energies

Peak dip structure

Rapid change of net-baryon density at y = 0

Strong variation of B

Significant change of shape at SPS energies

Peak dip structure

Rapid change of net-baryon density at y = 0

Strong variation of B

Energy DependenceNet-Baryon Distributions

BRAHMSPhys. Rev. Lett. 93 (2004), 102301

158A GeVPhys. Rev. Lett. 82 (1999), 2471

E802Phys. Rev. C 60 (1999), 064901

NA49 preliminary

Central Pb+Pb/Au+Au

6

Energy DependenceExample: /π- and /π-Ratios

NA49 dataPhys. Rev. C78, 034918 (2008)

Statistical models

Generally good description at allenergies

Fixes parameters T and μB

NA49 dataPhys. Rev. C78, 034918 (2008)

Statistical models

Generally good description at allenergies

Fixes parameters T and μB

|y| < 0.4

|y| < 0.5

SHM(B): A. Andronic et al. Nucl. Phys. A 772, 167 (2006).UrQMD: M. Bleicher et al., J. Phys. G 25, 1856 (1999) and private communicationHSD: E. Bratkovskaya et al., Phys. Rev. C69, 054907 (2004)

/

/−

-/ +/− = 1.5 (+ + -)

Christoph Blume WWND 2010, Ocho Rios, Jamaica


Results from differentbeam energiesAnalysis of particle yieldswith statistical models

Freeze-out points reach QGP phase boundary at top SPS energies

Caveat: Disagreement betweendifferent LQCD results on TC

Results from differentbeam energiesAnalysis of particle yieldswith statistical models

Freeze-out points reach QGP phase boundary at top SPS energies

Caveat: Disagreement betweendifferent LQCD results on TC

QCD Phase DiagramData Points

F. Becattini et al., Phys Rev. C69, 024905 (2004).

System Size DependenceFreeze-out Parameter


How do freeze-out parameters dependon system size ?

Statistical model fitsresult in different T

Central reactions

Way to move around in phase diagram?

How do freeze-out parameters dependon system size ?

Statistical model fitsresult in different T

Central reactions

Way to move around in phase diagram?

F. Becattini et al.,Phys. Rev. C73, 044905 (2005)


System Size Dependence(Anti-)Proton y-Spectra

Preliminary data by NA49

Minimum bias Pb+Pb at 158A GeV

Preliminary data by NA49

Minimum bias Pb+Pb at 158A GeV

NA49 preliminary

NA49 preliminary

p p

H. Ströbele et al.arXiv:0908.2777


System Size DependenceNet-Protons

NA49 preliminary p - pCen.

Per.

No strong system sizedependence observed

No strong system sizedependence observed

Peripheral spectrum slightly more pronounced y-dependencethan central one

Beam rapidity not measured!

In measured rapdity range similar shape like p+p data

⇒ System size has no big influence on μB

p+p Data:M. Aguilar-Benitz et al.,Z. Phys. C 50 (1991), 405.

NA49 preliminary

central

per.

p+p

11

System Size DependenceEnhancement factors of , , and

Enhancement factor

p+p data: NA49

Early saturation

Nw > 60

Core Corona Model

f (NW) = fraction of nucleons that scatter more than once

F. Becattini and J. Manninen, J. Phys. G35, 104013 (2008)K. Werner, Phys. Rev. Lett. 98, 152301 (2007)J. Aichelin and K. Werner, arXiv:0810.4465

Enhancement factor

p+p data: NA49

Early saturation

Nw > 60

Core Corona Model

f (NW) = fraction of nucleons that scatter more than once

F. Becattini and J. Manninen, J. Phys. G35, 104013 (2008)K. Werner, Phys. Rev. Lett. 98, 152301 (2007)J. Aichelin and K. Werner, arXiv:0810.4465€

M NW( ) = NW f NW( ) MCore[

+ 1− f NW( )( )MCorona ]

C+C

00

211

yyw dyppdn

dyPbPbdn

NE

158A GeV

Si+SiPb+Pb


12

System Size DependenceAverage Transverse Mass: mt-m0

Similar dependence asfor multiplicities observed

Early saturation Nw > 60

Core Corona model

f(NW) = fraction of nucleons, that scatter more than once


NA49 data: Phys. Rev. C80 (2009), 034906.

Similar dependence asfor multiplicities observed

Early saturation Nw > 60

Core Corona model

f(NW) = fraction of nucleons, that scatter more than once


NA49 data: Phys. Rev. C80 (2009), 034906.

CoronatW

CoretWWWt

mNf

mNfNNm

1

|y| < 0.4 (0.5)


System Size DependenceCore-Corona: Central ↔ Peripheral


Core Corona model

f(Npart) = fraction of nucleons, that scatter more than once

Centrality dependenceStronger for smaller systems

Central reactionsStill clear change of fmax

with system size

Compare fmax(Pb+Pb) ≈ 0.9and fmax(C+C) ≈ 0.65

⇒ apparent change of T + μB

Not real, just different mixture of core and corona

Thanks to K. Reygers for providing the Glauber code

Core Corona model


Centrality dependenceStronger for smaller systems

Central reactionsStill clear change of fmax

with system size

Compare fmax(Pb+Pb) ≈ 0.9and fmax(C+C) ≈ 0.65

⇒ apparent change of T + μB

Not real, just different mixture of core and corona

Thanks to K. Reygers for providing the Glauber code

System size is not a good control parameterto move around inQCD phase diagram

System size is not a good control parameterto move around inQCD phase diagram

System Size DependenceCore-Corona: Asymmetric Systems


Core Corona model


Centrality dependence

Peculiar shape for small projectiles (e.g. C, O, Si, S)

Core Corona model


Centrality dependence

Peculiar shape for small projectiles (e.g. C, O, Si, S)

Limiting case: p + A

f(Npart) = 1 / Npart

Model applicable in p+A?First attempt in T. Šuša et al., Nucl. Phys. A698 (2002) 491c


Critical PointTheoretical Predictions

M. Stephanov,CPOD conference 09

Lattice QCD difficult for B > 0

Sign problem in Fermion-determinant

Progress in recent years(e.g. Fodor and Katz)

Results strongly divergent

Typically B > 200 MeV

Perhaps no critical point at allfor B < 500 MeV (de Forcrand and Philipsen)

Lattice QCD difficult for B > 0

Sign problem in Fermion-determinant

Progress in recent years(e.g. Fodor and Katz)

Results strongly divergent

Typically B > 200 MeV

Perhaps no critical point at allfor B < 500 MeV (de Forcrand and Philipsen)

Critical PointObservables


Elliptic flow v2

R. A. Lacey et al., arXiv:0708.3512: η/s versus T and μB.

E. Shuryak, arXiv:hep-ph/0504048: Decrease (increase) of baryon (meson) flow.Higher experimental precision required.

mt-Spectra of baryons and anti-baryonsAsakawa et al., Phys. Rev. Lett. 101 (2008) 122302.Higher experimental precision required.

Di-pion (sigma) intermittency studyT. Anticic et al., arXiv 0912.4198.No unambiguous signal seen yet

Fluctuations: multiplicity and/or 〈 pt 〉Stephanov, Rajagopal, Shuryak, Phys. Rev. D60 (1999), 114028.

Elliptic flow v2

R. A. Lacey et al., arXiv:0708.3512: η/s versus T and μB.

E. Shuryak, arXiv:hep-ph/0504048: Decrease (increase) of baryon (meson) flow.Higher experimental precision required.

mt-Spectra of baryons and anti-baryonsAsakawa et al., Phys. Rev. Lett. 101 (2008) 122302.Higher experimental precision required.

Di-pion (sigma) intermittency studyT. Anticic et al., arXiv 0912.4198.No unambiguous signal seen yet

Fluctuations: multiplicity and/or 〈 pt 〉Stephanov, Rajagopal, Shuryak, Phys. Rev. D60 (1999), 114028.


Critical PointMultiplicity Fluctuations

Pb+Pb, 158A GeV1 < y < ybeam

Charged multiplicity n

Extensive quantity tight centrality selection (1%) to reduce volume fluctuations

Scaled variance

Energy dependence of

Data narrower than Poisson ( < 1)

Trend reproduced by UrQMD

Charged multiplicity n

Extensive quantity tight centrality selection (1%) to reduce volume fluctuations

Scaled variance

Energy dependence of

Data narrower than Poisson ( < 1)



Critical PointMultiplicity Fluctuations

n-Fluctuations as a function of B n-Fluctuations as a function of B

NA49 data:Phys. Rev. C79,044904 (2009)

B from stat. model fit:F. Becattini et al.,Phys. Rev. C73,044905 (2006)

Amplitude ofFluctuations:M. Stephanov et al.Phys. Rev. D60, 114028 (1999)

Width of crit. region:Y. Hatta and T. Ikeda, Phys. Rev. D67, 014028 (2003)

Position ofcrit. point:Z. Fodor and S. KatzJHEP 0404, 050 (2004)

Critical PointElliptic Flow v2


Energy dependenceof v2 of protons and pions

Large systematic effects

Especially for proton v2!

Clearly needs improvements onthe experimental side

Energy dependenceof v2 of protons and pions

Large systematic effects

Especially for proton v2!

Clearly needs improvements onthe experimental side


Critical region

Larger area in T - B plane

Focusing effect

Proximity of critical point might influence isentropictrajectories (nB/s = const.)

Critical region

Larger area in T - B plane

Focusing effect

Proximity of critical point might influence isentropictrajectories (nB/s = const.)

Critical PointTheoretical Predictions

Y. Hatta and T. Ikeda, Phys. Rev. D67, 014028 (2003)

Askawa et al., Phys. Rev. Lett. 101, 122302 (2008)

Critical Pointmt-Spectra of Baryons and Antibaryons


Expectation: B/B ratio should fall with mt

Askawa et al., PRL. 101, 122302 (2008)

Expectation: B/B ratio should fall with mt

Askawa et al., PRL. 101, 122302 (2008)

No significant energydependence of slope aobservedK. Grebieszkov et al., Nucl. Phys. A830 (2009), 547c

Summary


How to probe different regions of the QCD phase diagram ?

Variation of center-of-mass energyGood control parameter to move around in phase diagram

Variation of system sizeChanges only relative contribution of core and pp-like corona (if core-corona ansatz holds)

Change in T only apparent, μB = const.

Search for critical pointFirst results from multiplicity fluctuations negativeNeed for better observables

Multi-dimensional (scale and pt-dependent) fluctuation studies

How to probe different regions of the QCD phase diagram ?

Variation of center-of-mass energyGood control parameter to move around in phase diagram

Variation of system sizeChanges only relative contribution of core and pp-like corona (if core-corona ansatz holds)

Change in T only apparent, μB = const.

Search for critical pointFirst results from multiplicity fluctuations negativeNeed for better observables

Multi-dimensional (scale and pt-dependent) fluctuation studies

23

Backup

System Size Dependencep+A Collisions


No clear evidence fordecrease with Npart

Significant decrease visible only for anti-lambda

Data not fully consistent

NA57: F. Antinori et al.,J. Phys. G32 (2006) 427

NA49: T. Šuša et al., Nucl. Phys. A698 (2002) 491c

No clear evidence fordecrease with Npart

Significant decrease visible only for anti-lambda

Data not fully consistent

NA57: F. Antinori et al.,J. Phys. G32 (2006) 427

NA49: T. Šuša et al., Nucl. Phys. A698 (2002) 491c

Critical PointDi-Pion (Sigma) Intermittency


π+π- Pairs above di-pion threshold

Factorial moments F2(M)M: Number of bins in transversemomentum space

Subtract mixed event background ⇒ ΔF2(M)

Search for power law behaviorΔF2(M) (∼ M2) Φ2

Φ2 : critical exponent

Φ2 > 0 for Si+SiCoulomb effects becomean issue for larger systems

π+π- Pairs above di-pion threshold

Factorial moments F2(M)M: Number of bins in transversemomentum space

Subtract mixed event background ⇒ ΔF2(M)

Search for power law behaviorΔF2(M) (∼ M2) Φ2

Φ2 : critical exponent

Φ2 > 0 for Si+SiCoulomb effects becomean issue for larger systems

p+p, C+C, Si+Si at 158A GeV

T. Anticic et al. arXiv 0912.4198

N.G. Antoniou, F.K. Diakonos,and G. Mavromanolakis


Critical Pointpt-Fluctuations

Measure of pt-fluctuations

Energy dependence of pt

No significant variation with sNN for central collisions


Measure of pt-fluctuations

Energy dependence of pt

No significant variation with sNN for central collisions



Critical Pointpt-Fluctuations

pt-Fluctuations as a function of B pt-Fluctuations as a function of B

NA49 data:Phys. Rev. C79,044904 (2009)

B from stat. model fit:F. Becattini et al.,Phys. Rev. C73,044905 (2006)

Amplitude offluctuations:M. Stephanov et al.Phys. Rev. D60, 114028 (1999)

Width of crit. region:Y. Hatta and T. Ikeda, Phys. Rev. D67, 014028 (2003)

Position ofcrit. point:Z. Fodor and S. KatzJHEP 0404, 050 (2004)


Stronger n-Fluctuations seen in smaller systems

Hypothetic critical point (CP2)at T = 178 MeV and B = 250 MeV

Stronger n-Fluctuations seen in smaller systems

Hypothetic critical point (CP2)at T = 178 MeV and B = 250 MeV

Critical PointSystem Size Dependence of n-Fluctuations

F. Becattini et al.,Phys. Rev. C73,044905 (2006)

29

System Size DependencedN/dy at Mid-rapidity for Λ, Ξ, and Ω

Transport models

OK for

Slightly below

Too low for

UrQMD: H. Petersen et al. arXiv: 0903.0396

HSD: W. Cassing and E. Bratkovskaya,Phys. Rep. 308, 65 (1999)and private communication

Core Corona model

OK for and

F. Becattini and J. Manninen, Phys. Lett. B673, 19 (2009)

J. Aichelin and K. Werner, arXiv:0810.4465

Transport models

OK for

Slightly below

Too low for

UrQMD: H. Petersen et al. arXiv: 0903.0396

HSD: W. Cassing and E. Bratkovskaya,Phys. Rep. 308, 65 (1999)and private communication

Core Corona model

OK for and

F. Becattini and J. Manninen, Phys. Lett. B673, 19 (2009)

J. Aichelin and K. Werner, arXiv:0810.4465

−



Energy DependenceTotal Multiplicities

AGS NA49 RHICCentral A+A collisions

Only total multiplicities (4) shown

Chemical freeze-out

Experimental points in T-B plane

Analysis with statistical modelsBaryons (stopping) B

Strange particles T (+ B)

Phase boundary reached ?

Central A+A collisions

Only total multiplicities (4) shown

Chemical freeze-out

Experimental points in T-B plane

Analysis with statistical modelsBaryons (stopping) B

Strange particles T (+ B)

Phase boundary reached ?


Lattice QCD

General consensus: cross over for B = 0

Critical Temperature Tc

Depends on order parameter

e.g. chiral condensate:

or s-quark susceptibility s

Significant differences between collaborations(Budapest-Wuppertal, Riken-Bielefeld-Columbia “hotQCD”)

Lattice QCD

General consensus: cross over for B = 0

Critical Temperature Tc

Depends on order parameter

e.g. chiral condensate:

or s-quark susceptibility s

Significant differences between collaborations(Budapest-Wuppertal, Riken-Bielefeld-Columbia “hotQCD”)

QCD Phase DiagramPhase Boundary for B = 0

Figs. and table: Budapest-Wuppertal-Group,Y. Aoki et al., arXiv:0903.4155.

ssm

m

s

dusl

,,

2


QCD Phase Diagram

K. Rajagopal, MITCPOD conference 09


Strangeness in Heavy Ion ReactionsStatistical Models

F. Becattini et al., Phys. Rev. C69,024905 (2004)

A. Andronic, P. Braun-Munzinger,and J. Stachel, arXiv: 0812.1186

Assumption:

Multiplicities are determined by statistical weights (chemical equilibrium)

Grand-canonical partition function:

Parameters:

V, T, B, (s)

Allows in general excellent fits to measured multiplicities

Limits of applicability ?

Rare particles and low energies

Assumption:

Multiplicities are determined by statistical weights (chemical equilibrium)

Grand-canonical partition function:

Parameters:

V, T, B, (s)

Allows in general excellent fits to measured multiplicities

Limits of applicability ?

Rare particles and low energies

34

Energy DependenceK+/π+ and /π--Ratios

Extended statistical model

Higher mass resonances included(up to 3 GeV)

Improved description of pions and thus of the K+/+-ratio

Limiting temperature reachedin SPS energy region

Equilibration due toproximity of phase boundary?

Extended statistical model

Higher mass resonances included(up to 3 GeV)

Improved description of pions and thus of the K+/+-ratio

Limiting temperature reachedin SPS energy region

Equilibration due toproximity of phase boundary?

A. Andronic, P. Braun-Munzinger and J. Stachel, arXiv:0812.1186.


Energy DependenceK+/π+-Ratio: Comparison to STAR Data


STAR measurements at lower energies

√sNN = 9.2 + 19.6 GeV

Good agreement with NA49 data

STAR measurements at lower energies

√sNN = 9.2 + 19.6 GeV

Good agreement with NA49 data

STAR: L. Kumar et al., SQM2008 arXiv:0812.4099

christoph blume university of frankfurt winter workshop on nuclear dynamics, 2010, ochos rios,...

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