K fluctuations and the balance function
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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/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

  • 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/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/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 π Identification in STAR


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 σdyn

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


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

  • 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 σdyn and νdyn,Kπ Different?

200 GeV Au+Au

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


νdyn,Kπ for Au+Au at 62 and 200 GeV

Au+Au

  • 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 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 dN/dηin Central Collisions

B. Back et al. (PHOBOS Collaboration)

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


νdyn,Kπ Plotted versus dN/dη

Au+Au

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


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

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

200 GeV Au+Au


HIJING Predictions - Separated Charges

200 GeV Au+Au


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 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/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

    Au+Au

    T = 170 MeV


    Full

    Acceptance

    Dependence on Acceptance

    Au+Au 200 GeV


    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 Function

    200 GeV Au+Au

    Data

    Shuffled

    Mixed


    Balance Function Widths - All Charged Particles

    200 GeV


    Balance Function Widths - Pions and Kaons

    200 GeV


    B(qinv) for Pions

    200 GeV Au+Au

    Data

    Shuffled


    B(qinv) for Pions

    Charged pion pairs

    0.2 < pt < 0.6 GeV/c


    B(qinv) for Kaons

    Charged kaon pairs

    0.2 < pt < 0.6 GeV/c


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

    Kaons

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

      • The 0 peak is shifted down as previously observed

    • B(qinv) for kaons shows 

    Pions


    Balance Function Widths from B(qinv)

    Pions

    Kaons


    Balance Function - Excitation Function

    NA49

    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

    NA49

    Phys. Rev. C 76, 024914 2007

    NA49

    Large W means narrow balance function

    UrQMD predicts wide balance function with no centrality dependence


    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/

    • 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

    • 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


    Extra Slides


    Balance Function with Identified Pions - Excitation Function

    Charged pion pairs

    0.2 < pt < 0.6 GeV/c


    B(qinv) Widths using Identified Pions - Excitation Function

    Charged pion pairs

    0.2 < pt < 0.6 GeV/c


    Kinetic Temperatures as a Reference


    The QCD Phase Diagram


    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(qinv)

    • Expanded scale in qinv

    • Compare correlation function to B(qinv)


    RHIC Energy Scan

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

    T. Satogota, RHIC


    NA 49/61 Future Program

    M. Gazdzicki


    Proposed Energy and Mass Scans


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