Christoph Blume University of Heidelberg
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Transcript of Christoph Blume University of Heidelberg
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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
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Observables
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FluctuationsFluctuations
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
The Early Universe ...
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Fluctuations in Cosmology
WMAP
Only 1 Event
Fluctuations on the level of < 10-4
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Example: 〈 pT 〉 Fluctuations
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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 :
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Example: Multiplicity Fluctuations
NA49: PRC75, 064904 (2007)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Example: 〈 pT 〉 Fluctuations
central Pb+Pb @ √sNN = 17.3 GeV
NA49: PLB459, 679 (1999)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Example: 〈 pT 〉 Fluctuations
NA49: PRC70, 034902 (2004)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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 〉
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Example: 〈 pT 〉 Fluctuations
NA45: NPA727, 97 (2003)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Example: K/π Fluctuations
STAR: arXiv:0901.1795
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Example: K/π Fluctuations
STAR: arXiv:0901.1795
Comparison of energy and system size dependence of νdyn
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Example: pT Correlations
STAR: PRC72, 044902 (2005)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Balance Function
⇒ Sensitive to hadronization time in an expanding system
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Balance Function
Possible evidence for delayed hadronization
STAR: PRC82, 024905 (2010)
Shuffled: randomly shufflecharges inside a given event
⇒ largest possible BF-width
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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
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QCD Critical PointQCD Critical Point
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
The QCD Phase Diagram
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Analogy: Phase Diagram of Water
Cross over
Critical point
1st order phase boundary
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
The QCD Phase Diagram
K. Rajagopal, CPOD Conference 09
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
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)
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Strategy: Energy Scan
STAR at RHIC
NA61 at the SPS
CBM at FAIR
Observables: Fluctuations
Flow
Spectra
Overview: arXiv:1007.2613
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
The QCD Phase Diagram
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Critical Endpoint from Lattice QCD
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Christoph Blume Villa Gualino, Turino, 7-12 March 2011
Order of the Phase Transition