Monika Sharma Wayne State University for the STAR Collaboration Measurements of Differential Transverse Momentum Correlation Function from the STAR Experiment Monika Sharma Wayne State University for the STAR Collaboration Outline: Motivation Measurement method Observable definition Results discussion Caveats & conclusions

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Motivation: determine medium viscosity Why study ? Shear viscosity relative to entropy density of the system indicates: how strongly a system is coupled? how perfect the liquid is? Transverse momentum correlation measurements used to extract information on kinematic viscosity: Sean Gavin, Phys. Rev Lett. 97 (2006) 162302 Tc: temperature s : entropy density : shear viscosity estimated based on broadening of correlation function vs. pseudorapidity as a function of collision centrality Hirano & Gyulassy arXiv:nucl-th/0506049 Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Motivation & measurement method Gavin estimated 0.08< <0.3 based on where: 0.08 pT correlations STAR, J. Phys. G32, L37, 2006 (AuAu 200 GeV) 0.3 Number density correlations STAR, PRC 73, 064907, 2006 (AuAu 130 GeV) s Gavin et al. However, correct estimation of requires: observable which has contributions from number density as well as pT correlations Gavin advocates: Where: Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Observable definition Two particle pT correlations studied vs. pseudorapidity and azimuth difference Gavin’s suggested Observable. We study it differentially Pairs Singles Differential observable contains much more information STAR studied this observable integrally J. Adams et. al., Phys. Rev. C 72 (2005) 044902 Similar to: STAR, J. Phys. G32, L37, 2006 We study both observables is what we need/want to compare with previous STAR results Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN What do we expect? How different are and Comparative study with PYTHIA of & p+p collisions at GeV GeV/c and have similar distributions but differ in magnitude Discussed in more detail: M. Sharma & C. A. Pruneau, Phys. Rev. C 79 (2009) 024905 Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN & are different to collectivity Example (radial flow): comparative study of & with radially boosted (v/c=0.3) p+p collisions at GeV. M. Sharma & C. A. Pruneau, Phys. Rev. C 79 (2009) 024905 Particles pushed in the same direction (kinematic focusing), Formation of the near side ridge-like structure: S. A. Voloshin, arXiv:nucl-th/0312065 Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN The STAR Experiment PMD Cuts applied: || < 1.0 0.2 < pT < 2.0 GeV/c Analysis done vs. collision centrality Centrality slices: 0-5%, 5-10%, 10-20%……. Analyzed data from TPC, has 2coverage Dataset: Run IV AuAu 200 GeV Events analyzed: 10 Million Minimum bias trigger Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Results I: Data Central Peripheral The dip at 0 is partially due to track merging Further checks under investigation Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Observable robustness Efficiency dependence .. study with PYTHIA, p+p collisions at GeV Linear efficiency dependence on particle transverse momentum Where:o=0.8, a =0.05 Statistical error = 0.001, difference = 0.0005 Efficiency = 100% Efficiency = 80% Difference Robust observable, pT dependent efficiency is under investigation Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Projections STAR Preliminary  projection with ||<1 rad Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Functional Fit in  Parameterization: fit based on projection with ||<1 rad Offset + Wide and Narrow Gaussians b : Offset an : amplitude of narrow Gaussian n : width of narrow Gaussian aw : amplitude of wide Gaussian w : width of wide Gaussian Used for the calculation of Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Projections + fit Observations: Pseudorapidity broadening Change in strength, not just dilution and are different Offset determination is based On ZYAM method in central collisions. As per Sean Gavin's paper: shear viscosity broadens the rapidity correlations of the momentum current This broadening can be observed by measuring the transverse momentum correlation function vs rapidity However, other effects contribute to the longitudinal shape of the correlation function such as resonances, thermal broadening jets etc. We assume in this analysis that the broadening is dominated by effects associated with shear viscosity. Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN 2/NDF minimization procedure Procedure: fix offset and get w,aw & ndf Adopt w for minimum ndf Similar procedure adopted for Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Comparison of w Statistical errors on Statistical errors on Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Calculation of Kinematic viscosity: Width in rapidity: central peripheral Freeze-out times: Central collisions, Peripheral collisions, Caveat: Value of may change if the estimated freeze-out times of peripheral and central collision change (0-5%) (70-80%) Tc= 170 MeV 7.0 0.08 +0.15 STAR, PRC 71(2005) 44906 Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Viscosity to Entropy Density Ratio Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Summary Measured two different transverse momentum correlation functions, and – Differences between them understood (partially). – used for the calculation of Preliminary estimation of viscosity to entropy density ratio Value larger than other estimates. Model caveats: – Initial distribution is Gaussian – Diffusion is the dominant process – Rely on Gavin's estimated freeze-out times of peripheral and central collisions • Experimental Caveats: – Relatively narrow rapidity coverage implies uncertainty in the offset – 3-component fit to data assumption – Systematic errors associated with track quality yet to be investigated Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN BACK-UP Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Source of error Baseline/offset is the primary source of uncertainty in the present analysis. Fit components w & aw vary with the change in the offset. Therefore, we adopt /ndf minimization procedure to calculate w for every centrality. Offset is varied until the fit converges, i.e we obtain a minimum value of c2/ndf. Statistical errors are calculated from the change in w for one unit of change in  Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Fit between 0.1<dEta<1.7 0-5% n=0.6 n=0.5 n=0.4 n=0.3 Offset Chi2/ndf Sigma w -0.006 11.77/10 2.108 12.41/10 2.243 14.42/10 2.369 19.38/10 2.484 -0.005 11.94/10 1.96 12.7/10 2.087 14.9/10 2.207 20.13/10 2.36 -0.004 12.19/10 1.799 13.12/10 1.919 15.59/10 2.032 21.18/10 2.135 -0.003 12.59/10 1.623 13.78/10 1.735 16.63/10 1.84 22.73/10 1.937 -0.002 13.34/10 1.425 14.92/10 1.529 18.37/10 1.627 25.26/10 1.716 Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Offset= -0.004 Sigma n =0.6 Sigma n =0.5 Sigma n =0.4 Sigma n =0.3 Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Other Physics effects: As per Sean Gavin's paper: the shear viscosity that broaden the rapidity correlations of the momentum current. This broadening can be observed by measuring the transverse momentum correlation function vs rapidity. This is exactly what we show in slide 9/12. However, there are other effects that contribute to the longitudinal shape of the correlation function such as resonances, thermal broadening, jets etc. We assume in this analysis that the broadening is dominated by effects associated with shear viscosity. Whether this assumption is fully justified is an open issue which goes beyond the scope of this analysis. Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN

Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN Fit components for Monika Sharma Quark Matter 2009, Mar 30 - Apr 4, Knoxville, TN