Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 11

Event By Event FluctuationEvent By Event Fluctuation in in K/K/ ratio ratio

at at RHICRHIC

Supriya Das §

VECC, Kolkata(for STAR Collaboration)

§ Present address: GSI, Darmstadt

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 22

Statistical fluctuations:Statistical fluctuations: Arise due to the measurement process itself Arise due to the measurement process itself

such as finite number statisticssuch as finite number statistics

Dynamical fluctuationsDynamical fluctuations::

Reflect the dynamics and responses of the system Reflect the dynamics and responses of the system (density fluctuations etc.)(density fluctuations etc.)

MotivationMotivation

Why K/ ?

• K/ ratio shows interestingbehavior as function of collision energy.• It would be interesting tosee what happens to the fluctuation of the ratio.

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 33

Search for QCD Phase TransitionSearch for QCD Phase TransitionSearch for QCD Phase TransitionSearch for QCD Phase Transition

The production of The production of strangeness may be strangeness may be

related to the onset of related to the onset of deconfinementdeconfinement

Excitation function of Excitation function of <K<K++>/<>/<++> shows > shows

structure around sstructure around sNNNN1/21/2

= 7 GeV= 7 GeV

The excitation function of The excitation function of <K<K-->/<>/<--> is smooth> is smooth C. Blume (NA49), hep-ph/0505137

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 44

Fluctuations in <K>/<Fluctuations in <K>/<> > Fluctuations in <K>/<Fluctuations in <K>/<> >

Event-by-event fluctuations in <K>/<Event-by-event fluctuations in <K>/<> > may give insight into the production may give insight into the production

mechanism of K’smechanism of K’s

NA49 measured dynamical fluctuation in NA49 measured dynamical fluctuation in K/K/ ratio by comparing the width of ratio by comparing the width of

distributions from data and mixed eventsdistributions from data and mixed events

σ dyn = σ data2 − σ mixed

2

Pb+Pb at 158 A GeV (top 5% central)

S. V. Afanasiev et al. for NA 49 Collaboration PRL 86 (2001)σmixed width of K / distribution for mixed events

σdata width of K / distribution for data

K number of K K

per event

number of per event

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 55

Fluctuations in <K>/<Fluctuations in <K>/<> > Fluctuations in <K>/<Fluctuations in <K>/<> >

NA49 has also measured theNA49 has also measured thefluctuation of <K>/<fluctuation of <K>/<>>as a function of incidentas a function of incidentenergy for central Pb+Pbenergy for central Pb+Pbcollisions from 6 to 17collisions from 6 to 17GeV using the observable GeV using the observable σσdyndyn

C. Roland QM 2004

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 66

RHIC BRAHMSPHOBOS

PHENIXSTAR

AGS

TANDEMS

1 km

v = 0.99995c = 186,000 miles/sec

RRelativisticelativistic HHeavyeavy IIonon CColliderollider

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 77

Tracking Detectors:TPC, FTPC, SVT

Calorimeters:BEMC, EEMC, ZDC

Trigger Detectors:CTB, BBC, MWPC

Photon Detector:PMD Others: TOF, FPD

Goal : to track all the hadrons (and photons) in each collision

SSolenoidalolenoidal TTrackerracker AAtt RRHICHIC SSolenoidalolenoidal TTrackerracker AAtt RRHICHIC

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 88

Large acceptance detector ( 2 units of with full symmetry)

Good K to separation (for a wide momentum range) from Time Projection Chamber

M. Anderson et al. for STAR Collaboration, NIMA499 (2003)

Potential at STARPotential at STARPotential at STARPotential at STAR

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 99

Analysis MethodAnalysis Method IIσdyn

Kaons and Pions are counted event by event and the ratio is plotted for a large number of events. Same ratio is calculated from mixed events and distribution of that is obtained. Width of the distribution (σ) is the measure of fluctuation Dynamical fluctuation, σdyn is calculated as

σdyn = (σdata2 –σmixed

2)

Statistical fluctuation

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1010

Phase space distributions of identified K and Phase space distributions of identified K and

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1111

Analysis Method I (contd…)Analysis Method I (contd…)

Mixed Event :

To get the measure of the statistical fluctuation from

Finite number statistics Experimental resolution Correlations if any

Mixed track pool constructed by randomly picking up one track from each event. Same cuts applied on the mixed tracks before applying the particle identification.

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1212

σσdyndyn KK for different center of for different center of

momentum energiesmomentum energies

[ Data not corrected for efficiency]

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1313

ExcitationExcitation Function for Function for σσdyndynExcitationExcitation Function for Function for σσdyndyn

We extracted We extracted σσdyndyn for Au+Au, 0 - 5% most central, for 20, 62, for Au+Au, 0 - 5% most central, for 20, 62,

130, and 200 GeV and compared the results with the NA49-130, and 200 GeV and compared the results with the NA49-SPS results SPS results

PossibilitiesPossibilities

Related to KRelated to K++//++ horn horn Increase of resonances Increase of resonances

decaying intodecaying intoK + K + with increasing with increasing incident energyincident energy

Dilution of correlations as Dilution of correlations as multiplicity increases with multiplicity increases with

energyenergyStatistical errors only

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1414

Better MeasureBetter MeasureBetter MeasureBetter MeasureThe use of The use of σσdyndyn is problematic because it involves event-by- is problematic because it involves event-by-

event fluctuations of a ratioevent fluctuations of a ratio

A better measure is A better measure is dyn,Kdyn,K

Insensitive to efficiencyInsensitive to efficiency Properly deals with small multiplicitiesProperly deals with small multiplicities Centrality studiesCentrality studies

We will use We will use dyn,Kdyn,K for our systematic studies of K/ for our systematic studies of K/ fluctuations fluctuations

dyn,Kπ =NK NK −1( )

NK

2 +Nπ Nπ −1( )

Nπ

2 − 2NK Nπ

NK Nπ

First proposed by First proposed by Pruneau, Gavin and VoloshinPruneau, Gavin and Voloshin PRC 66 (2002) PRC 66 (2002)Used in Used in STAR Net Charge fluctuation paperSTAR Net Charge fluctuation paper – PRC 68 (2003) – PRC 68 (2003)

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1515

Based on multiplicity of charged particles in the STAR TPC (||<0.5)

Determination of collision centralityDetermination of collision centrality

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1616

Centrality dependence of dynamical Centrality dependence of dynamical fluctuation for different collision energiesfluctuation for different collision energies

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1717

ConclusionsConclusionsConclusionsConclusions

Excitation function of Excitation function of σσdyndyn remains flat at RHIC remains flat at RHIC

energies.energies.

Study of the excitation function and centrality Study of the excitation function and centrality dependence of K/dependence of K/ fluctuations requires a robust fluctuations requires a robust variable like variable like dyn,Kdyn,K . .

dyn,Kdyn,K is positive and it decreases with increasing is positive and it decreases with increasing

centrality of collisions for 62 and 200 GeV centre centrality of collisions for 62 and 200 GeV centre of mass energies.of mass energies.

Supriya DasSupriya Das SQM 2006 , 26th March 2006, UCLASQM 2006 , 26th March 2006, UCLA 1818

STAR ~500 Collaborators

STAR CollaborationSTAR CollaborationSTAR CollaborationSTAR Collaboration