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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

Plan of presentation Φ φ measure Motivation Φ φ 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

Φ φ 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 Background effects involved Φ measure of event-by-event fluctuations ◮ resonance decays ◮ momentum conservation Ga´ zdzicki, Mrówczy´ nski, Z. Phys. C54 , 127 (1992) ◮ a strongly intensive measure of fluctuations ◮ flow ◮ successfully used to study other fluctuations ( p T , q ) ◮ 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

Φ φ 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 Background effects involved Φ measure of event-by-event fluctuations ◮ resonance decays ◮ momentum conservation Ga´ zdzicki, Mrówczy´ nski, Z. Phys. C54 , 127 (1992) ◮ a strongly intensive measure of fluctuations ◮ flow ◮ successfully used to study other fluctuations ( p T , q ) ◮ 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

Φ φ 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 Background effects involved Φ measure of event-by-event fluctuations ◮ resonance decays ◮ momentum conservation Ga´ zdzicki, Mrówczy´ nski, Z. Phys. C54 , 127 (1992) ◮ a strongly intensive measure of fluctuations ◮ flow ◮ successfully used to study other fluctuations ( p T , q ) ◮ 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

Φ φ measure Φ φ definition Φ φ definition ◮ Let φ be a single particle azimuthal angle. Using it we define a single-particle variable: z φ ≡ φ − φ where φ is an average over single-particle inclusive distribution ◮ Let us also define an event variable: Z φ ≡ ∑ N i = 1 ( φ i − φ ) where summation runs over particles in a given event Φ φ measure definition � � Z 2 φ � � Φ φ ≡ � N � − z 2 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

Φ φ measure Φ φ definition Φ φ definition ◮ Let φ be a single particle azimuthal angle. Using it we define a single-particle variable: z φ ≡ φ − φ where φ is an average over single-particle inclusive distribution ◮ Let us also define an event variable: Z φ ≡ ∑ N i = 1 ( φ i − φ ) where summation runs over particles in a given event Φ φ measure definition � � Z 2 φ � � Φ φ ≡ � N � − z 2 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

Φ φ measure Φ φ definition Φ φ definition ◮ Let φ be a single particle azimuthal angle. Using it we define a single-particle variable: z φ ≡ φ − φ where φ is an average over single-particle inclusive distribution ◮ Let us also define an event variable: Z φ ≡ ∑ N i = 1 ( φ i − φ ) where summation runs over particles in a given event Φ φ measure definition � � Z 2 φ � � Φ φ ≡ � N � − z 2 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

Φ φ measure Φ φ definition Properties of Φ φ measure ◮ when particles are emitted by a number ( N s ) of identical sources, which are independent of each other: Φ φ ( N s ) = const ( N s ) intensive measure Φ φ ( P ( N s )) = const ( P ( N s )) strongly intensive measure where P ( N s ) is a distribution of the number of sources ◮ if particles are produced independently (no inter-particle correlations): Φ φ = 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

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

Model studies Toy models of elliptic flow and momentum conservation Φ φ vs. v 2 Elliptic flow – The azimuthal angle of each particle was generated from the distribution: ρ ( φ ) = 1 + 2 v 2 cos ( 2 ( φ − φ R )) reaction plane angle φ R was generated from flat distribution (2 π ) ◮ ◮ v 2 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 D N ≈ 0 . 5 ·� N � 4 [radians] <N>=50 0.3 <N>=400 <N>=700 0.2 3 φ Φ 0.1 Remarks: 0 2 0 0.02 0.04 Φ φ > 0 correlation 1 Φ φ ր v 2 ր 0 -1 0 0.05 0.1 0.15 0.2 0.25 v 2 Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 7/16

Model studies Toy models of elliptic flow and momentum conservation Elliptic flow with event-by-event v 2 fluctuations ◮ simulation mostly as the previous one but v 2 varies from event to event according to Gaussian distribution with σ v 2 ◮ Difference between Φ φ values for constant and fluctuating v 2 [radians] <N>=400 0.2 <v >=0.025 2 <v >=0.05 2 <v >=0.1 2 <v >=0.15 =const. 2 Remarks: 2 , v 0.1 φ Φ Φ φ ր σ v 2 ր - fluctuations φ Φ up to 20% increase for 50% v 2 fluctuations 0 -0.1 0 10 20 30 40 50 60 σ /v [%] v 2 2 Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 8/16

Model studies Toy models of elliptic flow and momentum conservation Effect of “global” momentum conservation on Φ φ ◮ for every particle φ generated from flat distribution (2 π ) − pT transverse momentum p T generated from P ( p T ) ∼ p T e , where T = 200 MeV T ◮ for every particle p x and p y corrected: N N ′ x = p x − ∑ ′ y = p y − ∑ i = 1 p xi i = 1 p yi p , p to obey momentum conservation law in the whole event N N ◮ and a new value of azimuthal angle is calculated [rad] Σ p =0 in every event T Φ 0 Φ Remarks: Φ φ < 0 anti-correlation -0.2 | Φ φ | ց weakly � N � ր -0.4 2 3 10 10 10 <N> Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 9/16

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) 100 [mrad] all charged negatively charged φ Φ positively charged 0 Remarks: Φ φ < 0 anti-correlations -100 Φ φ weakly depends on energy -200 � � Φ φ ( neg ) − Φ φ ( pos ) ց E ր -300 2 3 4 10 10 10 10 s [GeV] NN Tomasz Cetner and Katarzyna Grebieszkow for the NA49 Collaboration Fluctuations of the azimuthal particle distribution in NA49 at the CERN SPS 10/16