Christoph Blume University of Heidelberg

International School on:

Quark-Gluon Plasma and Heavy Ion Collisions:Past, Present, Future

Villa Gualino, Turino, Italy

Soft Probes III

Christoph Blume

University of Heidelberg

Christoph Blume Villa Gualino, Turino, 7-12 March 2011

Observables

FluctuationsFluctuations


The Early Universe ...


Fluctuations in Cosmology

WMAP

Only 1 Event

Fluctuations on the level of < 10-4


Fluctuations in Heavy Ion Physics

Probe the medium response (susceptibilities)

Study hadronization properties

Might be sensitive to QGP phaseHadron gas reacts differently than QGP

Different number of degrees of freedom

Nature of the phase transitionOrder of the transition (cross over ⇔ 1st order)

Existence of critical point ⇒ sudden increase of fluctuations

Quark number susceptibilityfrom lattice QCD (Bielefeld group)


Fluctuations Measures (I): Basics

Basic event-by-event observables: Multiplicities

Average transverse momenta 〈 pT 〉

Particle ratios (e.g. K/π)

Conserved quantities (charge Q, strangeness S, baryon number B )

Fluctuations usually characterized by second moments variance⇒Higher moments (kurtosis) recently investigated

Two averages: inside a given event and over all eventsLarge and uniform detector acceptance is helpful

Need to separate simple statistical fluctuations from dynamical onesLarge effect in heavy ion physics: volume (impact parameter) fluctuations


Example: 〈 pT 〉 Fluctuations


Fluctuation Measures (II): Means and Variances

Observable x (e.g. pT ) for a single particle i ⇒ mean in a given event of multiplicity Nj :

Mean over all events of a quantity Xj, which characterizes each event :

The weighting factor is wj = 1 for quantities such as the event-wise multiplicity (i.e. ).In the case (e.g. average pT) we have

The variance of Xj is :

see also: NPA727, 97 (2003)


Fluctuation Measures (III): Means and Variances

Mean over all particles i and events j of the single particle observable xi :

Corresponding variance :

Mean over all events j of the event-wisemean Mx (e.g. average pT):

Variance of Mx :


Example: Multiplicity Fluctuations

NA49: PRC75, 064904 (2007)


Fluctuation Measures (IV): Φx

Properties:

Φx = 0 for independent particle emission(no interparticle correlations)

Φx(A+A) = Φx(p+p) if A+A was a simple superposition of p+pM. Gazdzicki and S. Mrowczynski, ZPC54, 127 (1992)

Not a dimensionless quantity

〈 ... 〉 : averaging over events



central Pb+Pb @ √sNN = 17.3 GeV

NA49: PLB459, 679 (1999)



NA49: PRC70, 034902 (2004)


Fluctuation Measures (V): σdyn

Definition :S. Voloshin, V. Koch, H.G. Ritter, PRC60, 024901 (1999)

If only statistical fluctuations are present ⇒

Normalized dynamical fluctuation:NA45: NPA727, 97 (2003)

Normalization removes energy dependencies, e.g. due to increase of 〈 pT 〉



NA45: NPA727, 97 (2003)


Fluctuation Measures (VI): Particle Ratios A/B

Mixed events as referencePRC79, 044910 (2009)

Poisson statistics as reference:C. Pruneau, S. Gavin, and S. Voloshin, PRC66, 044904 (2002)

Negative values imply dominating correlations between A and B


Example: K/π Fluctuations

STAR: arXiv:0901.1795


Example: K/π Fluctuations

STAR: arXiv:0901.1795

Comparison of energy and system size dependence of νdyn


Example: K/p and p/π Fluctuations

S/B fluctuation as QGP signalV. Koch, A. Majumder, and J. Randrup, PRL95, 182301 (2005)

T < Tc: S and B can be unrelated (Kaons: S = -1, B = 0)

T > Tc: S and B are correlated(s-Quark: S = -1, B = 1/3)

Dominated by resonance decays

K/p

p/π


Fluctuation Measures (VII): pT Correlations

Covariance of transverse momentaof different particlesSTAR: PRC72, 044902 (2005)

Independent of detectionefficiencies

Influence of other effects(e.g. Coulomb interactionor Bose-Einstein corr.) can more easily be studied


Example: pT Correlations

STAR: PRC72, 044902 (2005)


Example: Net-Charge Fluctuations

Hadron Gas:

Charge unit = 1

Quark Gluon Plasma:

Charge unit = 1/3

⇒ Charge fluctuations should be reduced in QGP relative to hadron gas S. Jeon and V. Koch, PRL85, 2076 (2000) M. Asakawa, U. Heinz and B. Müller, PRL85, 2072 (2000)


Example: Net-Charge Fluctuations

Charge Conservation Limit

QGP

HIJING

Signal obscured by resonance decaysStrongly acceptance dependent

STAR: PRC68 044905 (2003)

Au+Au, √sNN = 130 GeV


Balance Function

⇒ Sensitive to hadronization time in an expanding system


Balance Function

S. Bass, P. Danielewicz, and S. Pratt, PRL85, 2689 (2000)

With, e.g., being the density of pairs inside a given relative pseudo-rapidity range

Analysis done as a function of


Balance Function

Possible evidence for delayed hadronization

STAR: PRC82, 024905 (2010)

Shuffled: randomly shufflecharges inside a given event

⇒ largest possible BF-width


Fluctuations

Fluctuations observed on the level of 1 - 10%

Many “trivial” effectsVolume fluctuations

Resonance decays

Acceptance effects

Short range correlations (Bose-Einstein)

Conservation laws

(Mini-)jets

Elliptic flow

...

But clear evidence for dynamical fluctuations with non-trivial energy or system size dependencies

QCD Critical PointQCD Critical Point


The QCD Phase Diagram


Analogy: Phase Diagram of Water

Cross over

Critical point

1st order phase boundary



K. Rajagopal, CPOD Conference 09


Critical Point Predictions

Lattice QCD calculationat finite μB

Z. Fodor and S. KatzJHEP 0404, 050 (2004)

M. Stephanov,CPOD conference 09

But current predictions scatter quite a lot

The CP might even not exist at all ...P. de Forcrand and O. Philipsen, JHEP01, 077 (2007)


Critical Point Predictions

Larger critical area possibleY. Hatta and T. Ikeda, PRD67, 014028 (2003)

Focusing effect

Proximity of critical point mightinfluence isentropic trajectories

M. Askawa et al., PRL101, 122302 (2008)


First Attempts

Multiplicity 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)


Strategy: Energy Scan

STAR at RHIC

NA61 at the SPS

CBM at FAIR

Observables: Fluctuations

Flow

Spectra

Overview: arXiv:1007.2613




Critical Endpoint from Lattice QCD


Order of the Phase Transition

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Christoph Blume University of Heidelberg

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