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NEW Fluctuation and Low-p T Correlation Results from PHENIX

Workshop on Correlations and Fluctuations in Relativistic Nuclear Collisions – 7/8/06 Jeffery T. Mitchell (Brookhaven National Laboratory). NEW Fluctuation and Low-p T Correlation Results from PHENIX. Outline Multiplicity Fluctuations Correlation Lengths

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NEW Fluctuation and Low-p T Correlation Results from PHENIX

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  1. Workshop on Correlations and Fluctuations in Relativistic Nuclear Collisions – 7/8/06 Jeffery T. Mitchell (Brookhaven National Laboratory) NEW Fluctuation and Low-pT Correlation Results from PHENIX • Outline • Multiplicity Fluctuations • Correlation Lengths • (using multiplicity fluctuations) • Low-pT Correlations Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  2. The PHENIX Detector Acceptance: |h| ~ 0.35, |Df|~ p Two “central arm” spectrometers anchored by drift chambers and pad chambers for 3-D track reconstruction within a focusing magnetic field. Although the PHENIX acceptance is traditionally considered small for event-by-event measurements, the acceptance is large enough to provide a competitive sensitivity to most observables. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  3. Measuring Multiplicity Fluctuations with Negative Binomial Distributions Multiplicity distributions in hadronic and nuclear collisions can be described by the Negative Binomial Distribution. The magnitude of the parameter k describes the deviation from a Poisson distribution  higher k means more Poissonian. UA5 UA5: sqrt(s)=546 GeV p-pbar, Phys. Rep. 154 (1987) 247. E802: 14.6A GeV/c O+Cu, Phys. Rev. C52 (1995) 2663. E802 PHENIX Preliminary, 62 GeV Au+Au 5-10% Central 25-30% Central Central 62 GeV Au+Au Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  4. Impact Parameter Fluctuations: Data A major source of non-dynamical fluctuations are contributions due to geometry (Npart) fluctuations due to the finite width of the centrality bin. This can be demonstrated directly with data… PHENIX Preliminary Geometry fluctuations drive s2/m down and N.B.D. k up. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  5. Impact Parameter Fluctuations:Estimation Using HIJING 1.37 Corrections for geometry fluctuations are estimated using HIJING 1.37 run a) with a fixed impact parameter, and b) with an impact parameter covering the range of the 5% centrality bin. Estimations match the 1% centrality data. Estimated systematic errors are 12-15% (included in all further data points. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  6. A Survey of Scaled Variance, s2/m PHENIX Preliminary • Inclusive charged hadron fluctuations. • 0.2 < pT < pT,max GeV/c • These values are corrected to remove the contribution due to impact parameter (geometrical) fluctuations and projected to 2p in azimuth for direct comparisons to NA49 and other experiments. • The Poissonian (random) limit is 1.0. • Large non-random fluctuations are observed that increase with pT and decrease with centrality, although the pT-dependence is relatively weak, unlike <pT> fluctuations. PHENIX Preliminary Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  7. Fluctuations over the entire pT range 0.2 < pT < 3.0 GeV/c 0.2 < pT < 3.0 GeV/c PHENIX Preliminary PHENIX Preliminary Inclusive charged hadron fluctuations. All points are projected to 2p azimuthal acceptance, corrected for detector occupancy and efficiency. All points are corrected for non-dynamical geometry fluctuations due to the finite width of the centrality bins. Errors include time-dependent systematic errors, azimuthal extrapolation systematic errors, and impact parameter correction systematic errors. p+p fluctuations are consistent with projections of UA5 results to sqrt(s)=200 GeV. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  8. Thermodynamically Motivated Observables: Relating distributions to compressibility • In the Grand Canonical Ensemble, the variance in particle number N (with m=<N>) is related to the compressibility, kT, via • The N.B.D. k parameter is related to the scaled variance via • N.B.D. k and the scaled variance can then be related to compressibility: Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  9. Multiplicity Fluctuations: Universal Scaling All species scaled to the 200 GeV dataset. The data appear to follow a universal curve. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  10. Multiplicity Fluctuations: Universal Scaling NA49 data corrected for geometry fluctuations (10% centrality bins) also lie on the universal curve. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  11. Multiplicity Fluctuations: Universal Scaling The universal curve can be described by a power law function of Npart. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  12. Multiplicity Fluctuations: Extracting a Correlation Length • The correlation length, x , is expected to diverge at the critical point. • To extract x, the N.B.D. k parameter is extracted by fitting the multiplicity distribution in successive ranges of dh or df. • NBD k can be related to a correlation length as follows (see E802, Phys. Rev. C52 (1995) 2663 and K. Homma’s presentation): Here, a is fixed to 0.5 (based on PHENIX preliminary correlation function measurements). b and x are free parameters. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  13. Example: N.B.D. k vs. dh PHENIX Preliminary Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  14. Correlation length (h) in centrality and pT,max PHENIX Preliminary PHENIX Preliminary Measurements with the full PHENIX magnetic field. All species show the same increasing trend as Npart and pT,max decrease. Correlation length increases at low pT. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  15. Correlation length (f) in centrality and pT,max PHENIX Preliminary PHENIX Preliminary All species show the same increasing trend as Npart and pT,max decrease. Correlation length increases at low pT. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  16. Correlation Length vs. Centrality 0.2 < pT < 3.0 GeV/c 0.2 < pT < 3.0 GeV/c The correlation lengths are small, but cannot be explained by detector resolution effects. Correlation lengths increase from 200 to 62 GeV. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  17. Correlation Lengths: Universal Scaling 0.2 < pT < 3.0 GeV/c 0.2 < pT < 3.0 GeV/c These points have been scaled to match the 200 GeV data. Notice that the correlation lengths exhibit a universal behavior as a function of centrality. The universal curves can be described by a power law function of Npart. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  18. Universal Scaling: pT-independent 0.2 < pT < 0.75 GeV/c 0.2 < pT < 0.75 GeV/c The power law curves describing the data are independent of pT range. The scaling appears to be driven by low pT processes. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  19. Correlation length x and static susceptibility c Divergence of correlation length is an indicator of a critical temperature. PHENIX Preliminary Correlation length x(h) Divergence of susceptibility is the indication of 2nd order phase transition. No magnetic field Np PHENIX Preliminary c k=0 * T No magnetic field Np Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  20. Systematic check of the correlation length PHENIX Preliminary a 10%cent. bin width 5% cent. bin width • can absorb finite centrality bin width effects, namely, • finite initial temperature • fluctuations, while physically • important parameters are • stable. PHENIX Preliminary b Shift to smaller fluctuations x PHENIX Preliminary No magnetic field Np Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  21. <pT> Fluctuations Gamma distribution calculation for statistically independent particle emission with input parameters taken from the inclusive spectra. See M. Tannenbaum, Phys. Lett. B498 (2001) 29. Red: Random Expectation (G distribution) Blue: STAR acceptance fluctuation of: fpT=52.6 MeV, FpT=14%, s2pT,dyn=52.3 (MeV/c2), SpT=9.8% MpT = Event-by-Event Average pT Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  22. PHENIX Event-by-Event <pT> Fluctuation Results 0.2 < pT < pTmax 20-25% centrality Highlights: Non-random fluctuations are observed. Non-monotonic centrality-dependence. Strong pT-dependence. pT fluctuations appear to be driven by high pT particles. The shape can be explained using a PYTHIA-based simulation by the contribution of correlations due to jets. S. Adler et al., Phys. Rev. Lett. 93 (2004) 092301. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  23. <pT> Fluctuations: Universal Scaling? The universal curves can be described by a power law function of Npart. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  24. Two-Particle Correlations at Low pT • Most charged particle correlation results are performed in the interesting high-pT region with a trigger particle. • The low-pT region and its evolution to the high pT region is interesting too! • This study will quote correlation amplitudes in a given centrality, pT, and Df bin with no trigger particle determined using the mixed event method via: • C(Df) = (dN/dfdata/dN/dfmixed)*(Nevents,mixed/Nevents,data) • Note: No reference subtraction here. • Correlations will be plotted in pT and yT (which serves to emphasize the low pT region). • Shown are results for 200 GeV Au+Au, 62 GeV Au+Au, 200 GeV p+p, and 200 GeV d+Au collisions. yT-yT correlations are integrated over azimuth. pT=0.3 GeV  yT=1.5 pT=0.5 GeV  yT=2.0 pT=1 GeV  yT=2.7 pT=1.5 GeV  yT= 3.1 Assuming the pion mass for yT. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  25. Like-sign Near-side (Df<60o) Correlations in Transverse Rapidity |Dh|<0.7 Jets 200 GeV p+p HBT-like component here pT=0.3 GeV  yT=1.5 pT=0.5 GeV  yT=2.0 pT=1 GeV  yT=2.7 pT=1.5 GeV  yT= 3.1 62 GeV Au+Au 0-5% central 200 GeV d+Au pT-pT Correlations 0-5% central 200 GeV Au+Au Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  26. Unlike-sign Near-side (Df<60o) yT Correlations 200 GeV p+p 62 GeV Au+Au The jet structure persists, the broad peak with the HBT component on the near side does not. 200 GeV d+Au pT-pT Correlations 200 GeV Au+Au Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  27. Correlations Comparisons along a yT,1=yT,2 bin slice pT=0.25 GeV  yT=1.34 pT=0.3 GeV  yT=1.5 pT=0.5 GeV  yT=2.0 pT=0.9 GeV  yT=2.56 pT=1.5 GeV  yT= 3.1 • The 62 GeV and 200 GeV Au+Au distributions are similar. • The behavior at low pT between Au+Au and d+Au collisions is different in all 4 cases. • The influence of resonance and conversion contributions is under investigation. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  28. Like-sign Near-side (Df<60o) yT Correlations 200 GeV Au+Au 0-5% 10-15% 20-25% The primary features persist from central to peripheral collisions. Correlations for the most peripheral collisions are similar to d+Au collisions. This statement is true for all 4 cases. 30-35% 40-50% 60-70% Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  29. Correlations Comparisons along a yT,1=yT,2 bin slice pT=0.25 GeV  yT=1.34 pT=0.3 GeV  yT=1.5 pT=0.5 GeV  yT=2.0 pT=0.9 GeV  yT=2.56 pT=1.5 GeV  yT= 3.1 The integrated correlation amplitudes vary little over a wide range of centralities (and pair occupancies). Later, background and flow-subtracted peak amplitudes will be measured. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  30. Charge Difference Correlations: C(LS)-C(US): Near Side 200 GeV p+p 62 GeV Au+Au, 0-5% Central Calculated by subtracting the correlation amplitude of unlike-sign pairs from that of like-sign pairs. It is expected that primarily HBT remains in this case at low yT. The remaining peak is much broader in Au+Au collisions and shifted in yT compared to p+p and d+Au collisions. The location of the peaks in yT agree with STAR results. 200 GeV Au+Au, 0-5% Central 200 GeV d+Au Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  31. Charge Difference Correlations: C(LS)-C(US): Away Side 200 GeV p+p A similar peak with similar properties compared to the near-side is seen on the away-side, but with a lower integrated correlation amplitude. 62 GeV Au+Au, 0-5% Central 200 GeV d+Au 200 GeV Au+Au, 0-5% Central Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  32. Charge Difference Correlations Comparisons along a yT,1=yT,2 bin slice The near and away side charge difference correlations are qualitatively similar. The p+p and d+Au charge difference correlations do not decrease significantly at low yT. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  33. Near-Side Peak Amplitude vs. Centrality 200<pT,1<500 MeV/c, 200<pT,2<500 MeV/c |Dh|<0.1 |Df|<60o Azimuthal correlation functions were measured for all like-sign pairs with both pairs in the pT range from 200-500 MeV (yT<2). The near-side peak was fit to a Gaussian convoluted with a Background*cos(2Df) flow term (Au+Au only). For |Dh|<0.1, the like-sign pairs are correlated in Qinvariant space, the unlike-sign pairs are not. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  34. Near-Side Peak Amplitude vs. Centrality 200<pT,1<500 MeV/c, 200<pT,2<500 MeV/c |Dh|<0.1 |Df|<60o These 2 species lie on a universal curve. The universal curves can be described by a power law function of Npart. Look for Cu+Cu data soon… Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  35. Near-Side Peak Amplitude vs. pT pT,min<pT,1<pT,max, pT,min<pT,2<pT,max Points plotted in the center of each pT bin. |Dh|<0.1 |Df|<60o pT bin widths have been chosen such that the mean number of pairs per event is the same in each bin. Central Au+Au flow- and background-subtracted amplitudes decrease exponentially with pT while the p+p and d+Au amplitudes remain flat. The amplitude increase above 1 GeV is due to the contribution of hard processes. No evidence for excess contributions from hard processes is seen in Au+Au collisions in the pT=0.5-1.0 GeV/c range. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  36. Just for Fun: A Critical Exponent Analysis • Let’s assume that the increased fluctuations are indicative of critical behavior. Then, it is expected that a) the system can be described by critical exponents, and b) all systems can be described by the same set of critical exponents. Recall that • The critical exponent for compressibility is represented by the symbol g and is described by • Replacing and solving for 1/kNBD gives (A=constant, T=Temperature, V=volume) Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  37. N.B.D. 1/k+1/m All systems have been scaled to match the 200 GeV Au+Au points for emphasis. All four systems exhibit a power law behavior with respect to Npart. All systems appear to follow a universal curve within errors. The fit assumes that Npart,c~0 The value of the critical exponent is g=1.24±0.13 (p=1/3) for all species. This is consistent with g for common gas-liquid phase transitions, which are typically between 1.2 and 1.3. 0.2 < pT < 3.0 GeV/c g=1.24±0.13 Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  38. Critical Exponents vs. p and Npart,c Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  39. Conclusions • PHENIX has presented a survey of multiplicity fluctuations as a function of collision species, collision energy, centrality, and pT range. • The fluctuations increase with a power law behavior as centrality decreases. • All species measured can be described by a universal power law curve. • PHENIX has presented a survey of correlation length measurements using multiplicity fluctuations • Correlation lengths at low pT exhibit a maximum at Npart=100. • Correlation lengths are smaller than similar measurements at the AGS. • Correlation lengths increase with decreasing beam energy. • Correlation lengths increase at low pT. • Correlation lengths as a function of Npart (Npart>100) for all species can be described by a universal power law curve. • PHENIX has presented a survey of two-particle pT correlations at low pT in Au+Au, d+Au, and p+p. • Significant differences in like-sign near-side correlations are seen between p+p and d+Au at low pT. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  40. Good luck to our host country! Photos from Round 1: Italy 1, USA 1 Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  41. Auxiliary Slides Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  42. <pT> Fluctuations: Universal Scaling? The universal curves can be described by a power law function of Npart. Residual STAR vs. PHENIX differences may be attributed to acceptance. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  43. Acceptance and Occupancy Corrections: Results Extrapolated to 2p Acceptance Multiplicity fluctuations are acceptance dependent. PHENIX results shown here are projected to 2p acceptance to facilitate direct comparisons to other measurements. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  44. A Survey of N.B.D. 1/k Preliminary Request PHENIX Preliminary • Inclusive charged hadron fluctuations. • These values are corrected to remove the contribution due to impact parameter (geometrical) fluctuations and projected to 2p in azimuth for direct comparisons to NA49. • Here, the Poissonian (random) limit is 1/k0. • Large non-random fluctuations are observed that decrease with centrality. PHENIX Preliminary Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  45. Jet Simulation Results: PHENIX at sqrt(sNN) = 200 GeV The Sprob parameter is initially adjusted so that FpT from the simulation matches FpT from the data for 20-25% centrality (circled). It is then FIXED and finally scaled by RAA for all other centralities. This decrease is due to the signal competing with the MpT width increase for low N. PHENIX Data: nucl-ex/0310005 This decrease due to jet suppression? 200 MeV/c < pT < pTmax 20-25% centrality Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  46. Impact Parameter Fluctuations: HIJING 1.37 Corrections for geometry fluctuations are estimated using HIJING 1.37 run a) with a fixed impact parameter, and b) with an impact parameter covering the range of the 5% centrality bin. Estimations match the 1% centrality data. Estimated systematic errors are 12-15% (included in all further data points. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  47. Relations to the observable N.B.D k Two point correlation function in one dimensional case in a fixed T Two particle correlation function Fluctuation caused by centrality bin width Relation to N.B.D. k Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  48. Susceptibility Susceptibility is defined by the response of phase for the external field. In the static limit of k = 0, χ cannot be extracted separately without temperature control, but χT value can be obtained by the mean multiplicity μ and α and ξ. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  49. Correlation Length Excitation Function The correlation lengths measured here are small. However, they are an order of magnitude larger than the two-track resolution (when projected to the detector radius). Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

  50. Near-Side Peak Width vs. Centrality 200<pT,1<500 MeV/c, 200<pT,2<500 MeV/c |Dh|<0.1 The standard deviation of the Gaussian fit to the flow- and background-subtracted near-side peaks for all like-sign pairs within the pT range 200-500 MeV/c. The 200 GeV Au+Au peaks broaden significantly towards the most central collisions. The d+Au peak is much more narrow than the p+p peak. Jeffery T. Mitchell (BNL) – Fluctuations and Correlations Workshop, Florence, Italy – 7/8/06

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