Higher moments of net-charge multiplicity distributions at RHIC energies in STAR Nihar R. Sahoo, VECC, India (for the STAR collaboration) 1 Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012 STAR

Overview Motivation QCD Phase Diagram and Critical Point Connection between theory and experiment Extraction of the freeze-out parameter Experiment RHIC Beam Energy Scan Program STAR detector system Analysis details Results Summary 2 Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

3 QCD Phase Diagram and Critical Point  At large baryon chemical potential (μ B ): a 1 st order phase transition is expected. S.Ejiri et al., Phys.Rev.D78, (2008 )  At μ B = 0  crossover.. Aoki et al., Nature 443, (2006)  The end point of the 1 st order phase transition: QCD Critical Point (CP). Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012 Quark Gulon plasma Hadron Gas Crossover Critical Point

4 Theoretical prediction for critical point Freezout point from Experiment Model Prediction Lattice Prediction Magnitude of slope d 2 T/dμ 2 obtained by lattice Taylor expansion Various theoretical models, predict various location of Critical Point (CP). STAR Experiment has undertaken beam energy scan program. Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

5 Search for the signature of CP locating QCD phase boundary Varying beam energy, one can tune Temperature and Chemical Potential. QCD phase diagram can be mapped between μ B values 20 to 450 MeV. RHIC Beam Energy Scan (BES) program arXiv: μ Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012 √s NN (GeV) Year BES J. Cleymans, et. all, PRC 73, (2006)

Introduction to Various moments Mean (M) = C 1 = Standard Deviation (σ) = C 2 = ) 2 > 1/2 Skewness (S) =, Kurtosis (κ) = Where, C n is the nth order cumulant X f f X  Degree of the asymmetry of the distribution.  Tail-ness of the distribution.  Degree of the peakedness of the distribution. 6 Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

Connection between theory and experiment 7 Divergence of the correlation Divergence of the thermodynamic susceptibility  Signature of Critical Point (QCD based calculation)  Bridge between Theory and Experiment Thermodynamic  Moments of the conserved susceptibility charge distribution  To cancel the volume term, product of higher moments are taken. (σ) (S) (κ) μ B = 0  Non-monotonic behavior of the product of higher moments as a function of the beam energy could be signature of the CP. M. Cheng et al., arXiv: M.A. Stephanov, PRL. 102, (2009) (Lattice QCD results) Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

8 Extraction of the freeze-out parameter For T f = 160 MeV QM12: S. Mukherjee arXiv: Lattice QCD  Add another dimension to this field.  Direct connection with experiment (product of net-charge higher moment) to extract freeze-out parameter. Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012 (at given T) Experiment and Lattice QCD Freeze-out parameter (at given √s NN )

9 Baseline for net-charge higher moments  Hadron Resonance Gas (HRG) Non-Critical Point model  Poisson baseline Assume: positive and negative charged particles distributions as independent Poisson distributions. Difference of the two Poisson distribution is a Skellam Distribution. Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012 F. Karsch et al., PLB 695 (2011) σ 2 /M κσ 2 Sσ  Baseline for Critical Point Search μ 1 and μ 2 mean of positive and negative charge particles distributions respectively.,

 Uniform pT and rapidity acceptance.  Full 2π coverage  Very good particle identification capabilities (TOF and TPC) Important tools for any fluctuation analysis AuAu 200 GeV 7.7 GeV Rapidity Transverse momentum Proton Pion Kaon Uniform Acceptance STAR Detectors 10 Experimental details Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

Analysis Details 11 Charged particles selection Centrality selection dN ch /dη By STAR Time Projection Chamber. Transverse momentum range to 2.0 GeV/c. Background protons have been removed transverse momentum below 400 MeV. Pseudo-rapidity range - |η| < 0.5 To remove auto-correlation effect, centrality selection done outside analysis rapidity region (|η| < 0.5). Uncorrected charged particles multiplicity within 0.5 < |η| < 1.0. Rapidity Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

Analysis Details 12 Centrality bin width correction (To reduce the finite bin width effect) Statistical error estimation Delta theorem is used. Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012 X. Luo, arXiv:

 The raw net-charge multiplicity distribution shows that with decreasing colliding energy, the distribution shifts towards positive side. 13 Net-charge distribution Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

14 Various moments STAR Preliminary Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012  The number of participant nucleons (proxy of volume (V)) dependence of the moments follows the trends as expected by CLT. Central Limit Theorem (CLT)

 Sσ are found to have values that have increasing deviations from Poisson expectations with decreasing in beam energy. 15 Centrality dependence of product of higher moments Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

 κσ 2 shows consistence within all centralities for all beam energies.  At all energies κσ 2 shows larger value than unity (Poisson expectation). 16 Centrality dependence of product of higher moments Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

 σ 2 /M increases with increase in colliding energy.  Sσ increases with decreasing colliding energies. Below 27 GeV, Sσ starts to deviate from Poisson expectation. HRG model over-predicts the data.  κσ 2 shows no energy dependence and all the values are above unity, except in top central events at 7.7 GeV with large error bar. The shaded band corresponding to Poisson expectation reflects the range covering 0-5% to 60-70% centrality. 17 Beam energy dependence Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012 HRG: F. Karsch et al., PLB 695 (2011 )

Summary 18  Higher moments of the net-charge multiplicity distributions have been measured in Au+Au collisions at √s NN = 7.7 to 200 GeV.  The centrality dependence of the moments follows the expectation from the CLT.  σ 2 /M increases with increase in colliding energy.  Sσ deviates from Poisson expectations below 27 GeV.  Within statistical uncertainty, Κσ 2 is seen to be independent of collision energy and no significant enhancement is observed. Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

19 Back Up Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

20 Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

21 Lattice and Experiment QM12: S. Mukherjee arXiv: = M/σ 2 Nihar R. Sahoo, WPCF2012, Frankfurt am Main, Germany, Sept , 2012

22 Net-Proton