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
Observables
Temperature
Strangeness
Resonances
Femtoscopy
Fluctuations
Flow
Jets +
Heavy Flavor
Photons
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Fluctuations
The Early Universe ...
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Fluctuations in Cosmology
WMAP
Only 1 Event
Fluctuations on the level of < 10-4
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 phase
Hadron gas reacts differently than QGP
Different number of degrees of freedom
Nature of the phase transition
Order of the transition (cross over ⇔ 1st order)
Existence of critical point
⇒ sudden increase of fluctuations
Quark number susceptibility
from lattice QCD (Bielefeld group)
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 events
Large and uniform detector acceptance is helpful
Need to separate simple statistical fluctuations from dynamical ones
Large effect in heavy ion physics: volume (impact parameter) fluctuations
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: 〈pT〉 Fluctuations
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)
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-wise
mean Mx (e.g. average pT):
Variance of Mx :
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: Multiplicity Fluctuations
NA49: PRC75,
064904 (2007)
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+p
M. Gazdzicki and S. Mrowczynski,
ZPC54, 127 (1992)
〈...〉 : averaging over events
Not a dimensionless quantity
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: 〈pT〉 Fluctuations
central Pb+Pb @ √sNN = 17.3 GeV
NA49: PLB459, 679 (1999)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: 〈pT〉 Fluctuations
NA49: PRC70, 034902 (2004)
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〉
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: 〈pT〉 Fluctuations
NA45: NPA727, 97 (2003)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Fluctuation Measures (VI): Particle Ratios A/B
Mixed events as reference
PRC79, 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
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: K/π Fluctuations
STAR: arXiv:0901.1795
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: K/π Fluctuations
Comparison of energy and system size dependence of νdyn
STAR: arXiv:0901.1795
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: K/p and p/π Fluctuations
S/B fluctuation as QGP signal
V. Koch, A. Majumder, and J. Randrup,
PRL95, 182301 (2005)
K/p
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)
p/π
Dominated by resonance decays
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Fluctuation Measures (VII): pT Correlations
Covariance of
transverse momenta
of different particles
STAR: PRC72, 044902 (2005)
with
Independent of detection
efficiencies
Influence of other effects
(e.g. Coulomb interaction
or Bose-Einstein corr.)
can more easily be studied
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: pT Correlations
STAR: PRC72, 044902 (2005)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: Net-Charge Fluctuations
Hadron Gas:
Quark Gluon Plasma:
Charge unit = 1
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)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Example: Net-Charge Fluctuations
Charge Conservation Limit
HIJING
QGP
Au+Au, √sNN = 130 GeV
Signal obscured by resonance decays
Strongly acceptance dependent
STAR: PRC68 044905 (2003)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Balance Function
⇒ Sensitive to hadronization time in an expanding system
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Balance Function
With, e.g.,
being the density of pairs inside a
given relative pseudo-rapidity range
Analysis done as a function of
S. Bass, P. Danielewicz, and S. Pratt, PRL85, 2689 (2000)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Balance Function
Shuffled: randomly shuffle
charges inside a given event
⇒ largest possible BF-width
Possible evidence
for delayed hadronization
STAR: PRC82, 024905 (2010)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Fluctuations
Fluctuations observed on the level of 1 - 10%
Many “trivial” effects
Volume 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
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
QCD Critical Point
The QCD Phase Diagram
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Analogy: Phase Diagram of Water
Cross over
Critical point
1st order
phase boundary
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
The QCD Phase Diagram
K. Rajagopal, CPOD Conference 09
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Critical Point Predictions
Lattice QCD calculation
at finite μB
Z. Fodor and S. Katz
JHEP 0404, 050 (2004)
But current predictions scatter quite a lot
M. Stephanov,
CPOD conference 09
The CP might even not exist at all ...
P. de Forcrand and O. Philipsen, JHEP01, 077 (2007)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Critical Point Predictions
Larger critical area possible
Focusing effect
Y. Hatta and T. Ikeda,
PRD67, 014028 (2003)
Proximity of critical point might
influence isentropic trajectories
M. Askawa et al.,
PRL101, 122302 (2008)
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
First Attempts
Multiplicity fluctuations as a function of B
NA49 data:
B from stat.
Phys. Rev. C79,
044904 (2009)
model fit:
Christoph Blume
F. Becattini et al.,
Phys. Rev. C73,
044905 (2006)
Position of
crit. point:
Amplitude of
Fluctuations:
Width of
crit. region:
Z. Fodor and S. Katz
JHEP 0404, 050 (2004)
M. Stephanov et al.
Phys. Rev. D60,
114028 (1999)
Y. Hatta and T. Ikeda,
Phys. Rev. D67,
014028 (2003)
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
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
The QCD Phase Diagram
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Critical Endpoint from Lattice QCD
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011
Order of the Phase Transition
Christoph Blume
Villa Gualino, Turino, 7-12 March 2011