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Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Warsaw University of Technology Faculty of Physics Hot Quarks Conference La Londe-les-Maures June

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Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration

Warsaw University of Technology Faculty of Physics

Hot Quarks Conference La Londe-les-Maures June 2010

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 1/16

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SLIDE 2

Plan of presentation

Φφ measure

Motivation

Φφ definition

Model studies Toy models of elliptic flow and momentum conservation UrQMD – a full event generator NA49 experiment Detector Preliminary results Summary

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 2/16

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Φφ measure

Motivation

Motivation

Why was this study undertaken? ◮ search for plasma instabilities

Mrówczy´ nski, Phys.Lett.B314:118-121,1993

◮ critical point, onset of deconfinement ◮ flow fluctuations

Mrówczy´ nski, Shuryak, Acta Phys.Polon.B34:4241-4256,2003 Miller, Snellings, nucl-ex/0312008

Why the Φ measure is used

Φ measure of event-by-event fluctuations

Ga´ zdzicki, Mrówczy´ nski, Z. Phys. C54, 127 (1992)

◮ a strongly intensive measure of fluctuations ◮ successfully used to study other fluctuations (pT , q) Background effects involved ◮ resonance decays ◮ momentum conservation ◮ flow ◮ quantum statistics

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 3/16

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SLIDE 4

Φφ measure

Motivation

Motivation

Why was this study undertaken? ◮ search for plasma instabilities

Mrówczy´ nski, Phys.Lett.B314:118-121,1993

◮ critical point, onset of deconfinement ◮ flow fluctuations

Mrówczy´ nski, Shuryak, Acta Phys.Polon.B34:4241-4256,2003 Miller, Snellings, nucl-ex/0312008

Why the Φ measure is used

Φ measure of event-by-event fluctuations

Ga´ zdzicki, Mrówczy´ nski, Z. Phys. C54, 127 (1992)

◮ a strongly intensive measure of fluctuations ◮ successfully used to study other fluctuations (pT , q) Background effects involved ◮ resonance decays ◮ momentum conservation ◮ flow ◮ quantum statistics

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 3/16

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SLIDE 5

Φφ measure

Motivation

Motivation

Why was this study undertaken? ◮ search for plasma instabilities

Mrówczy´ nski, Phys.Lett.B314:118-121,1993

◮ critical point, onset of deconfinement ◮ flow fluctuations

Mrówczy´ nski, Shuryak, Acta Phys.Polon.B34:4241-4256,2003 Miller, Snellings, nucl-ex/0312008

Why the Φ measure is used

Φ measure of event-by-event fluctuations

Ga´ zdzicki, Mrówczy´ nski, Z. Phys. C54, 127 (1992)

◮ a strongly intensive measure of fluctuations ◮ successfully used to study other fluctuations (pT , q) Background effects involved ◮ resonance decays ◮ momentum conservation ◮ flow ◮ quantum statistics

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 3/16

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SLIDE 6

Φφ measure Φφ definition

Φφ definition

◮ Let φ be a single particle azimuthal angle. Using it we define a single-particle variable: zφ ≡ φ −φ where φ is an average over single-particle inclusive distribution ◮ Let us also define an event variable: Zφ ≡ ∑

N i=1(φi −φ)

where summation runs over particles in a given event

Φφ measure definition

Φφ ≡

  • Z2

φ

N −

  • z2

φ where ... is average over events

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 4/16

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Φφ measure Φφ definition

Φφ definition

◮ Let φ be a single particle azimuthal angle. Using it we define a single-particle variable: zφ ≡ φ −φ where φ is an average over single-particle inclusive distribution ◮ Let us also define an event variable: Zφ ≡ ∑

N i=1(φi −φ)

where summation runs over particles in a given event

Φφ measure definition

Φφ ≡

  • Z2

φ

N −

  • z2

φ where ... is average over events

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 4/16

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Φφ measure Φφ definition

Φφ definition

◮ Let φ be a single particle azimuthal angle. Using it we define a single-particle variable: zφ ≡ φ −φ where φ is an average over single-particle inclusive distribution ◮ Let us also define an event variable: Zφ ≡ ∑

N i=1(φi −φ)

where summation runs over particles in a given event

Φφ measure definition

Φφ ≡

  • Z2

φ

N −

  • z2

φ where ... is average over events

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 4/16

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SLIDE 9

Φφ measure Φφ definition

Properties of Φφ measure

◮ when particles are emitted by a number (Ns) of identical sources, which are independent of each other:

Φφ(Ns) = const(Ns)

intensive measure

Φφ(P(Ns)) = const(P(Ns))

strongly intensive measure where P(Ns) is a distribution of the number of sources ◮ if particles are produced independently (no inter-particle correlations):

Φφ = 0

a clear reference value

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 5/16

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Model studies Toy models of elliptic flow and momentum conservation

Toy models

Simple models that allow us to test separately influence of various physical effects. Here we consider: ◮ elliptic flow and its fluctuations ◮ momentum conservation law Also studied (can be presented in discussion): ◮ pairs of correlated particles (e.g. from resonance decays) ◮ dijets

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 6/16

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Model studies Toy models of elliptic flow and momentum conservation

Elliptic flow –

Φφ vs. v2

The azimuthal angle of each particle was generated from the distribution:

ρ(φ) = 1+ 2v2cos(2(φ −φR))

◮

reaction plane angle φR was generated from flat distribution (2π)

◮

v2 was a simulation parameter (constant for each simulation series)

◮

multiplicity N of particles in an event was taken from Negative Binomial distribution with given N and dispersion DN ≈ 0.5·N

2

v 0.05 0.1 0.15 0.2 0.25 [radians]

φ

Φ

  • 1

1 2 3 4

<N>=50 <N>=400 <N>=700

0.02 0.04 0.1 0.2 0.3

Remarks:

Φφ > 0

correlation

Φφ ր

v2 ր

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 7/16

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Model studies Toy models of elliptic flow and momentum conservation

Elliptic flow with event-by-event v2 fluctuations

◮

simulation mostly as the previous one

◮

but v2 varies from event to event according to Gaussian distribution with σv2

Difference between Φφ values for constant and fluctuating v2

[%]

2

/v

2

v

σ 10 20 30 40 50 60 [radians]

=const.

2

, v φ

Φ

  • φ

Φ

  • 0.1

0.1 0.2

<N>=400 >=0.025

2

<v >=0.05

2

<v >=0.1

2

<v >=0.15

2

<v

Remarks:

Φφ ր σv2 ր

fluctuations

up to 20% increase for 50% v2 fluctuations

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 8/16

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Model studies Toy models of elliptic flow and momentum conservation

Effect of “global” momentum conservation on Φφ

◮

for every particle φ generated from flat distribution (2π) transverse momentum pT generated from P(pT) ∼ pT e

−pT

T

, where T = 200MeV

◮

for every particle px and py corrected: p

′ x = px − ∑

N i=1 pxi

N

,

p

′ y = py − ∑

N i=1 pyi

N

to obey momentum conservation law in the whole event

◮

and a new value of azimuthal angle is calculated <N> 10

2

10

3

10 [rad]

Φ

Φ

  • 0.4
  • 0.2

=0 in every event

T

p Σ

Remarks:

Φφ < 0

anti-correlation

|Φφ| ց

weakly N ր

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 9/16

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Model studies UrQMD – a full event generator

UrQMD 3.3: p+p interactions

◮ energy scan (SPS, RHIC, LHC) for p+p collisions ◮ default parameters (hard processes included, but no hydro)

[GeV]

NN

s 10

2

10

3

10

4

10 [mrad]

φ

Φ

  • 300
  • 200
  • 100

100

all charged negatively charged positively charged

Remarks:

Φφ < 0

anti-correlations

Φφ weakly depends on energy

  • Φφ(neg)−Φφ(pos)
  • ց

E ր

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 10/16

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NA49 experiment Detector

NA49 experiment

Succesor: NA61 (presentation by M. Ma´

ckowiak)

Data taking: 1994-2002 ◮ p+p, C+C, Si+Si and Pb+Pb interactions ◮ center of mass energy 6.3 - 17.3 GeV per N+N pair Key features: ◮ fixed target ◮ hadron spectrometer (4 TPCs, 2 of them with B field) ◮ centrality determination: Forward Calorimeter (energy of projectile spectators)

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 11/16

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NA49 experiment Detector

NA49 experiment

Succesor: NA61 (presentation by M. Ma´

ckowiak)

Data taking: 1994-2002 ◮ p+p, C+C, Si+Si and Pb+Pb interactions ◮ center of mass energy 6.3 - 17.3 GeV per N+N pair Key features: ◮ fixed target ◮ hadron spectrometer (4 TPCs, 2 of them with B field) ◮ centrality determination: Forward Calorimeter (energy of projectile spectators)

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 11/16

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NA49 experiment Detector

NA49 azimuthal acceptance

◮ limited (not 2π) ◮ opposite for opposite charges Detector is left-right symmetric Acceptance for positive and negative particles is the same, provided the azimuthal angle for one charge is reflected To allow quantitive comparison of Φφ for positive and negative particles we rotate by π particles of one charge.

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 12/16

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SLIDE 18

NA49 experiment Detector

NA49 azimuthal acceptance

◮ limited (not 2π) ◮ opposite for opposite charges Detector is left-right symmetric Acceptance for positive and negative particles is the same, provided the azimuthal angle for one charge is reflected To allow quantitive comparison of Φφ for positive and negative particles we rotate by π particles of one charge.

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 12/16

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SLIDE 19

NA49 experiment Detector

NA49 azimuthal acceptance

◮ limited (not 2π) ◮ opposite for opposite charges Detector is left-right symmetric Acceptance for positive and negative particles is the same, provided the azimuthal angle for one charge is reflected To allow quantitive comparison of Φφ for positive and negative particles we rotate by π particles of one charge.

Example of such an angle transformation

B E F O R E

[rad] φ

  • 3
  • 2
  • 1

1 2 3 2000 4000 6000 8000 10000 12000

negative

  • riginal

[rad] φ

  • 3
  • 2
  • 1

1 2 3 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000

positive

  • riginal

A F T E R

[rad] φ

  • 3
  • 2
  • 1

1 2 3 2000 4000 6000 8000 10000 12000

negative rotated

[rad] φ

  • 3
  • 2
  • 1

1 2 3 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000

positive

  • riginal

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 12/16

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NA49 experiment Preliminary results

Energy dependence NA49 preliminary

Energy dependence of Φφ for 7.2% most central Pb+Pb collisions. Comparison with UrQMD 1.3 Remarks:

Φφ(neg) > 0 Φφ(pos) ≈ 0 Φφ weakly depends on energy

neg: different than UrQMD

Detailed cuts description: PRC 79, 044904 (2009)

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 13/16

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NA49 experiment Preliminary results

UrQMD 1.3: Pb+Pb – acceptance cuts

◮ energy scan (SPS) for Pb+Pb collisions ◮ default process selection (UrQMD 1.3) ◮ real NA49 (energy scan) cuts succesively applied (pT → y → φ )

[GeV]

NN

s 4 6 8 10 12 14 16 18 20 [mradians]

φ

Φ

  • 200
  • 100

100

NA49 acceptance φ NA49 acceptance but full cut

T

  • nly p

positive

[GeV]

NN

s 4 6 8 10 12 14 16 18 20 [mradians]

φ

Φ

  • 150
  • 100
  • 50

50 100

NA49 acceptance φ NA49 acceptance but full cut

T

  • nly p

negative Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 14/16

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SLIDE 22

NA49 experiment Preliminary results

System size dependence NA49 preliminary

System size dependence of Φφ as a function of number of wounded nucleons NW . p+p, C+C, Si+Si and 6 centrality bins of Pb+Pb collisions at 158A GeV. Remarks:

Φφ > 0

significant maximum for peripheral Pb+Pb

qualitatively similar effect was observed for multiplicity N and transverse momentum pT fluctuation analysis J.Phys.G30:S701-S708,2004 Effect still not understood

Detailed cuts description and Pb+Pb centrality binning: PRC 70, 034902 (2004)

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 15/16

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SLIDE 23

Summary

Summary

Event-by-event azimuthal fluctuations have been analyzed using Φφ measure for NA49 data. ◮ First the properties of Φφ were studied using toy models and UrQMD.

◮ flow increases Φφ values ◮ Φφ is sensitive to flow fluctuations ◮ momentum conservation produces negative Φφ values ◮ UrQMD showed negative Φφ values and a week energy dependence

◮ Energy scan for central Pb+Pb collisions in NA49 showed week energy dependence and non-zero Φφ values for negative particles ◮ Significant effect is visible for system size dependence in NA49. Results are qualitatively similar to results of multiplicity N and transverse momentum pT fluctuation analysis in NA49.

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 16/16

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SLIDE 24

Backup

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 17/16

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SLIDE 25

Backup pairs of correlated particles

Pairs of particles with a specified difference in azimuthal angle ∆φ between them. ◮ φ generated from flat distribution (2π) ◮ ∆φ is the main simulation parameter, modified between simulation series ◮

Events consist only of such “pairs”

◮

Multiplicity (N) of particles in an event differs between simulation series X Y

 

[rad] Φ ∆ 0.5 1 1.5 2 2.5 3 3.5 [rad]

Φ

Φ

  • 0.5

0.5 1

N=10 N=100 N=1000

[rad] Φ ∆ 0.5 1 1.5 2 2.5 3 3.5 [rad]

Φ

Φ

  • 0.5

0.5 1

N=Poisson(8) N=Gaus(100,10) Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 18/16

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Backup pairs of correlated particles

Simulations differed also by the fraction (f) of particles that originated from ’pairs’: ◮

f · N – number of paired particles

◮ (1− f)· N – number of uncorrelated particles

[rad] Φ ∆ 0.5 1 1.5 2 2.5 3 3.5 [rad]

Φ

Φ

  • 0.5

0.5 1

f=0.3 f=0.5 f=0.7 f=1.0

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 19/16

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SLIDE 27

Backup dijets

Dijet is a pair of groups (sprays) of particles heading into opposite directions: ◮ φ generated from flat distribution (2π) ◮

width σφ of such a spray is one of the simulation parameters

◮

number of particles that form a spray is another parameter

◮

in every event there is exactly one dijet X Y

 

3+3

[rad] Φ σ

  • 0.1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 [rad]

Φ

Φ

  • 1

1 2 3

2+2 czastki 5+5 czastek 10+10 czastek Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 20/16

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SLIDE 28

Backup momentum conservation

Acceptance cuts were applied to momentum conservation data for multiplicity of N = 50 ◮

Random cut: exclusion of some fraction of particles randomly

◮

Angle cut: exclusion of particles that have azimuthal angle in a given, “realistic” range

◮

results plotted as a function of fraction of particles remaining after cuts [%]

left

f 10 20 30 40 50 60 70 80 90 100 [rad]

Φ

Φ

  • 0.4
  • 0.2

0.2

random cut angle cut 100% <N>=50 from NegBin

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 21/16

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SLIDE 29

Backup Pythia

Simulations in Pythia

included p+p collisions at various energies Accelerator Energies √ sNN SPS 6.27 7.62 8.73 12.3 17.3 [GeV] RHIC 19.6 62.4 130 200 [GeV] LHC 5.5 14 [TeV]

Table: Energies used in simulations

Minimum bias setting was used additionally decays of following particles and their antiparticles were forbidden:

µ−, π+, K 0, K+, K 0

L, K 0 S, Λ, Σ+, Σ−, Ξ0, Ξ−, Ω−

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 22/16

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Backup Pythia

Energy dependence for Pythia minimum bias: ◮

no cuts

[GeV]

NN

s 10

2

10

3

10

4

10 [rad]

φ

Φ

  • 0.3
  • 0.2
  • 0.1

0.1

all charged negatively charged positively charged

  • corr. pythia

all charged

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 23/16

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SLIDE 31

Backup Pythia

Energy dependence for Pythia minimum bias: ◮

protons removed from the data

[GeV]

NN

s 10

2

10

3

10

4

10 [rad]

φ

Φ

  • 0.3
  • 0.2
  • 0.1

0.1

no protons all part all charged negatively charged positively charged

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 24/16

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SLIDE 32

Backup Pythia

Energy dependence for Pythia minimum bias: ◮

pT < 1.5GeV transverse momentum cut

[GeV]

NN

s 10

2

10

3

10

4

10 [rad]

φ

Φ

  • 0.3
  • 0.2
  • 0.1

0.1

<1.5GeV all part

T

p all charged negatively charged positively charged

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 25/16

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SLIDE 33

Backup Pythia

Energy dependence for Pythia minimum bias: ◮

SPS 1.1 < y⋆

π < 2.6

(forward rapidity) 0.005 < pT < 1.5 [GeV/c] RHIC

−1 < η < 1

(mid-rapidity) 0.15 < pT < 1.5 [GeV/c]

[GeV]

NN

s 10

2

10 [rad]

φ

Φ

  • 0.1

0.1

all charged negatively charged positively charged

  • accept. SPS

acceptance RHIC

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 26/16

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SLIDE 34

Backup Hijing

Hijing

represents the superposition model of ion collisions. p+p (1+1), C+C (12+12), Si+Si (28+28) and Pb+Pb (208+208) at √ SNN = 17.3GeV system

p+p C+C Si+Si Pb+Pb [rad]

φ

Φ

  • 0.3
  • 0.2
  • 0.1

0.1

all charged negatively charged positively charged

Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 27/16

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SLIDE 35

Energy scan acceptance; here for 2.0 < y*

p < 2.2

System size dependence acceptance

slide-36
SLIDE 36

Energy scan acceptance; here for 1.2 < y*

p < 1.4