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K / π Fluctuations and the Balance Function. Gary Westfall Michigan State University For the STAR Collaboration INT Workshop on the QCD Critical Point August 12, 2008. Fluctuations in the K / π Ratio. Event-by-event fluctuations in K / π may give insight into the QCD critical point

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K / π Fluctuations and the Balance Function

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K fluctuations and the balance function

K/π Fluctuations and the Balance Function

  • Gary Westfall

  • Michigan State University

  • For the STAR Collaboration

  • INT Workshop on the QCD Critical Point

  • August 12, 2008

Fluctuations in the k ratio

Fluctuations in the K/π Ratio

  • Event-by-event fluctuations in K/π may give insight into the QCD critical point

  • NA49 measured the fluctuations of K/π as a function of incident energy for central Pb+Pb collisions fromsNN1/2 = 6 to 17 GeV using the observable σdyn

    • measure the K/π ratio event-by-event

      • K = K+ + K-

      • π = π+ + π-

    • produce histogram of the K/π ratio

    • extract the width of K/π histogram to get σdata

    • do the same for mixed event to get σmixed

K fluctuations at the sps

K/π Fluctuations at the SPS

  • Define the dynamical fluctuations in terms of σdyn

  • Divide by the mean and multiplity by 100 to get %

C. Blume (NA49), hep-ph/0505137

K fluctuations in star

K/π Fluctuations in STAR

  • Study Au+Au collisions at sNN1/2 = 20, 62, 130 and 200 GeV

  • Extract the number of K+ + K- and π+ + π- event-by-event using energy loss and curvature in the STAR TPC

  • Take kaons and pions with 0.2 < pt < 0.6 GeV/c and |η| < 1.0

    • kaons: Nσ,K < 2, Nσ,π > 2

    • pions: Nσ,π < 2, Nσ,K > 2

    • electrons are suppressed with Nσ,e > 1

K and identification in star

K and π Identification in STAR

K histograms for au au collisions

K/π Histograms for Au+Au Collisions

  • Mixed events are created by taking one track from different events to produce new events that have no correlations

  • Mixed events are produced using 10 bins in centrality and 5 bins in vertex position

  • The K/ distributions are wider for real events than for mixed events

Excitation function for dyn

Excitation Function for σdyn

  • Compare STAR results for central Au+Au collisions with SPS results for central Pb+Pb collisions

Excitation function for dyn 2

Excitation Function for σdyn (2)

  • STAR results for σdyn are similar to those at the top SPS energies

  • The statistical hadronization model (SH) of Torrieri [nucl-th/0702062 (2007)] for the light quark phase space density γq = 1 (equilibrium) under-predicts σdyn at all energies

  • The statistical hadronization model for a fitted γq (non-equilibrium) explains the STAR results but under-predicts the SPS measurements

Different fluctuations measure

Different Fluctuations Measure

  • The use of σdyn is problematic for low multiplicities

  • A better measure is νdyn,Kπ

  • dyn was introduced to study net charge fluctuations (PRC 68, 044905 [2003])

  • dyn,K is insensitive to efficiency

  • dyn,K deals well with low multiplicities and does not require mixed events

Are dyn and dyn k different

Are σdyn and νdyn,Kπ Different?

200 GeV Au+Au

Sergei Voloshin, J. Phys. Conf. 50, 111 (2006)

Dyn k for au au at 62 and 200 gev

νdyn,Kπ for Au+Au at 62 and 200 GeV


  • Centrality dependence of K/π fluctuations

    • Inverse multiplicity dependence

    • Relatively poor fit versus 1/Npart

  • NA49 results are all central Pb+Pb collisions

    • Similar Npart

Compare with na49 using d n d

Compare with NA49 using dN/d

  • We can compare the results for the centrality dependence of νdyn,Kπ to the incident energy dependence of σdyn in central collisions using the following method

    • Use PHOBOS systematics fordN/dη versus sNN1/2

    • Use the identity σdyn2 = νdyn,Kπ

Phobos systematics for d n d in central collisions

PHOBOS Systematics for dN/dηin Central Collisions

B. Back et al. (PHOBOS Collaboration)

Phys. Rev. C 74, 021902(R) (2006)

Dyn k plotted versus d n d

νdyn,Kπ Plotted versus dN/dη


Better fit with 1/(dN/dη)than with 1/Npart

Excitation function for dyn1

Excitation Function for σdyn

  • Scale centrality dependence of νdyn,Kπ to compare with excitation function of σdyn in central collisions

Addition of tof to star

Addition of TOF to STAR

P. Sorensen

Charged pions and kaons

0.2 < pt < 0.6 GeV/c

STAR will add TOF for Run 10

The TOF will provide excellent particle identification for π, K, and p for a large fraction of the measured particles event-by-event

Improved K/π fluctuation measurements

Improved balance functions with identified π, K, and p

Look at charges separately

Look at Charges Separately

200 GeV Au+Au

Hijing predictions separated charges

HIJING Predictions - Separated Charges

200 GeV Au+Au

Scale with d n d and compare with hijing

Scale with dN/dη andCompare with HIJING

  • Average νdyn,K+/π+ and νdyn,K-/π- to get Same

  • Average νdyn,K+/π- and νdyn,K-/π+ to get Opposite

Scale with d n d and compare with ampt

Scale with dN/dη andCompare with AMPT

  • AMPT (version 1.21, hard scattering) for summed charges is better than HIJING, but centrality dependence is not correct

  • No difference between same and opposite

Relation of k fluctuations to resonance re interaction

Relation of K/π Fluctuations to Resonance Re-interaction

  • Model of Torrieri, Jeon and Rafelski

  • Predict K/π fluctuations and resonance production using statistical hadronization model

    • www.gsi.de/documents/DOC-2007-Jul-101-1.pdf

    • Jeon and Koch, PRL 83, 5435 (1999) (π+/π-)

  • Relate νdyn,K+/π- and νdyn,K-/π- to K*(892)/K ratio

    • (3/4)<Nπ>(νdyn,K+/π- - νdyn,K-/π-) ∼K*/K

  • Resonance reinteraction compared with thermal model of torrieri

    Resonance Reinteraction Compared with Thermal Model of Torrieri


    T = 170 MeV

    Dependence on acceptance



    Dependence on Acceptance

    Au+Au 200 GeV

    Balance function

    Balance Function

    • Balance function represents charge balance of charge/anti-charge pairs

    • Balance functions can be expressed in terms of , y, qinv, qout, qside, qlong, and 

    Bass, Danielewicz, Pratt PRL 85 2689 (2000)

    Balance function1

    Balance Function

    200 GeV Au+Au




    Balance function widths all charged particles

    Balance Function Widths - All Charged Particles

    200 GeV

    Balance function widths pions and kaons

    Balance Function Widths - Pions and Kaons

    200 GeV

    B q inv for pions

    B(qinv) for Pions

    200 GeV Au+Au



    B q inv for pions1

    B(qinv) for Pions

    Charged pion pairs

    0.2 < pt < 0.6 GeV/c

    B q inv for kaons

    B(qinv) for Kaons

    Charged kaon pairs

    0.2 < pt < 0.6 GeV/c

    B q inv for pions and kaons from p p at 200 gev

    B(qinv) for Pions and Kaonsfrom p+p at 200 GeV


    • B(qinv) for pions shows K0 and 0

      • The 0 peak is shifted down as previously observed

    • B(qinv) for kaons shows 


    Balance function widths from b q inv

    Balance Function Widths from B(qinv)



    Balance function excitation function

    Balance Function - Excitation Function


    Phys. Rev. C 76, 024914 2007

    Balance functions for

    Pb+Pb at sNN½ =

    6.3 to 17.3 GeV

    STAR, QM 02, QM 04

    Balance functions for

    Au+Au at sNN½ =

    20 to 200 GeV

    Balance function widths excitation function

    Balance Function Widths -Excitation Function


    Phys. Rev. C 76, 024914 2007


    Large W means narrow balance function

    UrQMD predicts wide balance function with no centrality dependence

    Rhic low energy scan

    RHIC Low Energy Scan

    • For central Au+Au and Pb+Pb collisions, dyn for K/ fluctuations may show a deviation from the fluctuations predicted by a statistical hadronization model as a function of incident energy

    • The width of the balance function in central Au+Au and Pb+Pb collisions decreases as the energy is increased until around 20 GeV, where it seems to stay constant

    • These two observations hint at some kind of phase transition occurring between 7 and 20 GeV

    • A comprehensive energy scan from 7 to 60 GeV with STAR and the new TOF will answer many questions

    Conclusions k

    Conclusions - K/

    • Dynamical fluctuations in the K/π ratio in central Au+Au collisions represented by σdyn show little incident energy dependence at RHIC energies within errors and compare reasonably with SPS results at the top energies

    • νdyn,Kπ seems to scale with dN/dη

    • (dN/dη)νdyn,Kπ increases slightly with centrality

    • νdyn,Kπ for same sign particles is close to zero

    • νdyn,Kπ for opposite sign particles is negative

    • HIJING overpredicts (dN/dη)νdyn,Kπ while AMPT seems to get the correct magnitude but not the centrality dependence

    • Fluctuations of same and opposite sign particles may give us information about the re-interaction of kaons and pions

    Conclusions balance function

    Conclusions - Balance Function

    • Balance function B() for all charged particles narrows in central Au+Au collisions

      • HIJING shows no centrality dependence

      • AMPT narrows in central collisions, but not as much as the data

    • Balance function B(y) widths for pions and kaons are different

    • Balance function B(qinv) widths for pions and kaons are the same

    • Central Au+Au widths scaled with shuffled events (W) are the same at 20, 62, 130, and 200 GeV

    • Balance function B(qinv) for pions shows the K0, but not the 0

    • Widths extracted from B(qinv) for pions scale with dN/d

    The end

    The End

    Extra slides

    Extra Slides

    Balance function with identified pions excitation function

    Balance Function with Identified Pions - Excitation Function

    Charged pion pairs

    0.2 < pt < 0.6 GeV/c

    B q inv widths using identified pions excitation function

    B(qinv) Widths using Identified Pions - Excitation Function

    Charged pion pairs

    0.2 < pt < 0.6 GeV/c

    Kinetic temperatures as a reference

    Kinetic Temperatures as a Reference

    The qcd phase diagram

    The QCD Phase Diagram

    The search for the qcd phase transition

    The Search for the QCD Phase Transition

    • The production of strangeness may be related to the onset of deconfinement

    • Excitation function of<K+>/<π+> shows “horn” aroundsNN1/2 = 7 GeV

    • The excitation function of <K->/<π-> is smooth

    C. Blume (NA49), hep-ph/0505137

    Hbt coulomb effects for b q inv

    HBT-Coulomb Effects for B(qinv)

    • Expanded scale in qinv

    • Compare correlation function to B(qinv)

    K fluctuations and the balance function

    RHIC Energy Scan

    • Energies as low as sNN1/2 = 4.5 GeV (10 AGeV fixed target)

    T. Satogota, RHIC

    Na 49 61 future program

    NA 49/61 Future Program

    M. Gazdzicki

    Proposed energy and mass scans

    Proposed Energy and Mass Scans

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