Michael Daugherity University of Texas at Austin for the STAR Collaboration

1. Anomalous centrality variation of minijet angular correlations in Au-Au collisions at 62 and 200 GeV from STAR Michael Daugherity University of Texas at Austin for the STAR Collaboration

2. Overview • We report a survey of minimum-bias two-particle correlations in Au+Au collisions • These are sensitive to minijets, elliptic flow, resonances, HBT, etc. allowing a novel comparison of correlation amplitudes and ranges • Each correlation source has a unique distribution on relative (η,φ) making decomposition possible • We observe a surprising trend in minijet correlations minijet: Same-side jet-like correlations with no trigger particle M. Daugherity, STAR Collaboration

3. Correlation Measure • and measure pair density ρ • Covariance = object - uncorrelated reference (mixed-event pairs) • The denominator provides per-particlenormalization: • Correlations are directly comparable regardless of event multiplicity • This is done with all possible pairs • No trigger particle is specified. We use the correlation definition Axial Autocorrelations large azimuth peak φΔ = φ1 - φ2 We use the notation Example: jets small angle peak same - mixed proton-proton minijets ηΔ = η1 - η2 mixed measured as a function of relative η and φ φΔ ηΔ M. Daugherity, STAR Collaboration

4. J of Phys: Conf 27 (2005) 98 Proton+Proton Components yt2 yt1 transverse correlations axial correlations typical jet trigger pT (Gev/c) 4 3 2 1 0.5 φΔ ηΔ yt ~ ln(pt) STAR Preliminary These structures define minijet correlations soft component hard component φΔ φΔ ηΔ ηΔ Longitudinal Fragmentation (“strings”) 1D Gaussian, US pairs HBT peak at origin, LS pairs Minijets 2D Gaussian at origin, away-side peak actually cos(φΔ) M. Daugherity, STAR Collaboration

5. Fit Function (in 5 Easy Pieces) Proton-Proton fit function STAR Preliminary = + φΔ φΔ φΔ ηΔ ηΔ ηΔ dipole longitudinal fragmentation 1D gaussian HBT, res., e+e- 2D exponential Minijet Peak 2D gaussian Away-side -cos(φ) cos(2φΔ) • Au-Au fit function • Use proton-proton fit function + cos(2φΔ) quadrupole term (“flow”). • This gives the simplest possible way to describe Au+Au data. quadrupole Note: from this point on we’ll include entire momentum range instead of using soft/hard cuts φΔ ηΔ M. Daugherity, STAR Collaboration

6. proton-proton 200 GeV Data Analyzed 1.2M minbias 200 GeV Au+Au events, and 13M 62 GeV minbias events (not shown) Included all tracks with pT > 0.15 GeV/c, |η| < 1, full φ note: 38-46% not shown 84-93% 75-84% 65-75% 55-65% 46-55% φΔ ηΔ STAR Preliminary 19-28% 28-38% 9-19% 5-9% 0-5% φΔ ηΔ We see the evolution of correlation structures from peripheral to central Au+Au M. Daugherity, STAR Collaboration

7. 200 GeV Model Fit model 84-93% 75-84% 65-75% 55-65% 46-55% φΔ ηΔ STAR Preliminary 19-28% 28-38% 9-19% 5-9% 0-5% φΔ ηΔ M. Daugherity, STAR Collaboration

8. 200 GeV Residual Fit residual = data - model 84-93% 75-84% 65-75% 55-65% 46-55% φΔ ηΔ STAR Preliminary 19-28% 28-38% 9-19% 5-9% 0-5% φΔ ηΔ We have a good fit with the simplest possiblefit function. Other than adding the cos(2φΔ) quadrupole term, no other modification was necessary. Residuals at 62 GeV are comparable. M. Daugherity, STAR Collaboration

9. Quadrupole Component Instead of removing a background, we can make a measurement Data cos(2φΔ) component Amplitudes 200 GeV 62 GeV • 62 and 200 have the same shape • Substantial amp. changewith energy φΔ φΔ ηΔ ηΔ STAR Preliminary STAR Preliminary v2{2} v2{2D} v2{4} D. Kettler, T. Trainor arXiv:0704.1674 accepted to J Mod Phys E flow data from PRC 72 014904 The η-dependence of correlations separates quadrupole from other components 9 M. Daugherity, STAR Collaboration

10. Minijet Same-Side Peak Peak Amplitude Peak η Width Peak φ Width Statistical and fitting errors shown Systematic error is 9% of correlation amplitude STAR Preliminary STAR Preliminary STAR Preliminary 200 GeV 62 GeV peripheral central X-axis shows mean participant path-length • Observations • Amplitude and η widths start small and experience a sharp transition • Transition occurs at ~55% centrality at 200 GeV, is more central (~40%) for 62 • φ width has a verydifferent centrality dependence M. Daugherity, STAR Collaboration

11. Binary Scaling Peak Amplitude Peak η Width Peak φ Width STAR Preliminary STAR Preliminary STAR Preliminary 200 GeV 62 GeV constant widths small increase before transition Large increase in amplitude and η width are unexpected minijet amplitude assuming binary scaling in Kharzeev and Nardi model Deviations from binary scaling represent new physics unique to heavy ion collisions M. Daugherity, STAR Collaboration

12. HIJING Minijets Peak Amplitude Peak η Width Peak φ Width STAR Preliminary STAR Preliminary STAR Preliminary 200 GeV 62 GeV HIJING 1.382 default parameters, 200 GeV, quench off Quench on causes slight amplitude decrease The observed minijets correlation is actually far greater than predicted by HIJING (factor of 4) M. Daugherity, STAR Collaboration

13. Consistency Check Does interaction between same-side peak and cos(φΔ) terms cause the transition? Result 200 GeV: standard, two-stage fit Two-stage fit: STAR Preliminary cos(φΔ) cos(2φΔ) fix cos(φΔ) and cos(2φΔ) on away-side then fit remaining terms ν ν The results are consistent Cancellation in fit terms does not cause the amplitude increases. minijet peak minijet η width ν ν M. Daugherity, STAR Collaboration

14. Transition Does the transition from narrow to broad ηΔ occur quickly or slowly? data - fit (except same-side peak) 83-94% 55-65% 46-55% 0-5% STAR Preliminary STAR Preliminary STAR Preliminary STAR Preliminary ηΔ width Large change within ~10% centrality Smaller change from transition to most central Low-pT manifestation of the “ridge” Shape changes little from peripheral to the transition The transition occurs quickly M. Daugherity, STAR Collaboration

15. Scaling What is the best way to compare different energies? Does the transition scale? Peak Amplitude Peak Amplitude Peak η Width Peak η Width Bjorken Energy Density Npart STAR Preliminary STAR Preliminary STAR Preliminary STAR Preliminary 200 GeV 62 GeV 200 GeV 62 GeV εBJ εBJ Npart Npart Depends strongly on formation time (used 1 fm/c), difficult to compare energies. Peripheral bins are compressed. Peak η Width Peak Amplitude Transverse Particle Density STAR Preliminary STAR Preliminary 200 GeV 62 GeV S = overlap area Minijet parameters seem to scale with system density M. Daugherity, STAR Collaboration

16. Yield Estimates Kharzeev and Nardi two-component model (PLB 507 (2001) 121) “Hard” scattering fraction = (hard) / (soft + hard) = In 200 GeV central Au+Au, x ~ 0.1 and ν ~ 6. Estimate of total yield fraction = 0.6 / 1.5 ~ 1/3 Correlations from this analysis • Units: # correlated pairs per particle • # pairs = (Nch) * (Peak Volume) > 7,000 pairs in central collisions • Pair combinatorics require estimate of average number of structures per event to extract yield with more structures giving greater yield. • Assuming number of structures follows binary collision scaling gives yield fraction of 32% • 1/2 binary scaling gives 23%, 1/10 gives 10% • This correlation represents a significant • fraction of the total yield. Peak Volume STAR Preliminary 200 GeV 62 GeV 8x increase See also T. Trainor, arXiv:0710.4504, accepted to J Mod Phys E M. Daugherity, STAR Collaboration

17. Summary • We measure 2D angular autocorrelations on (η,φ) to study minijets in Au+Au collisions and make two primary observations: • Transition • Minijet correlations follow binary scaling in peripheral Au+Au collisions and deviate at a sharp transition point • The transition points for 62 and 200 GeV occur at about the same value of transverse particle density • Yield • Beyond the transition point the peak amplitude and η width increase dramatically • The same-side correlations include a large number of hadrons, estimated at up to ~1/3 of the particle yield in central Au+Au collisions M. Daugherity, STAR Collaboration

18. Backup Slides

19. Yt-Yt Correlations proton-proton By looking in yt-yt space we can find where these new correlations are in momentum Corresponding to excess minijet amplitude and width, we see a sudden onset of localized growth on yt < 2.5 → pt < 0.8 M. Daugherity, STAR Collaboration

20. Away-side STAR Preliminary ϕΔ ηΔ • Momentum conservation for an (other-wise) independent-particle many-body system produces a cos(φΔ) component whose amplitude is constant for our measure. • Instead, the amplitude exactly follows the minijet peak amplitude We have found the away-side jet! Instead of suppression we can now study momentum transport M. Daugherity, STAR Collaboration 20

21. Away-side Since φ is periodic, any AS Gaussian at φΔ=π will also need to copied to φΔ= -π and φΔ= 3π. I tried replacing cosine term with Gaussians at odd multiples of π, and letting ROOT freely fit the amplitude and width. The result was indistinguishable from a cosine. cosine Gauss at 3π sum of Gaussians Gauss at π Gauss at -π • The data demand a cos(φΔ) shape. • A model with away-side Gaussians is statistically indistinguishable, though it has one extra parameter. M. Daugherity, STAR Collaboration

22. Longitudinal Fragmentation We follow the 1D Gaussian along ηΔ which is seen in p-p collisions and described by the Lund String Model amplitude width 62 200 • But from studying the charge-dependence, we know that we are seeing two distinct processes. • longitudinal fragmentation: soft hadronization process, charge-dependent, energy-independent, monotonically decreasing with centrality. • A second process that is charge-independent, energy-dependent, non-monotonic with centrality. Seems to have constant mean at nu ~ 3.5, width decreases with energy • *The other charge-dependent results are interesting, but that’s another story. charge-dependent term M. Daugherity, STAR Collaboration

23. Finer Centrality Bins Fine bins test, 200 GeV, all parameters As a test, I tried offsetting and doubling the number of centrality bins around the step for 200 GeV. Here the red points are the “fine bins” test: Let’s zoom in on the minijet parameters: Results are consistent and support a sudden turn-on M. Daugherity, STAR Collaboration

24. Why minijets? We hypothesize that the transition is due to particles associated with minijets rather than a new physical process • The ΦΔ width doesn’t change at the transition • The pT correlation amplitude trend doesn’t change, the widths change slightly M. Daugherity, STAR Collaboration

25. What about the sharp peak? • Many different processes compete near φΔ = ηΔ = 0: • e+e- pairs from γ conversion (big) • HBT / Coulomb correlations (big) • resonance decay (small, <10% of peak) • tracking inefficiencies: splitting, merging, crossing, etc. (small) • high pt jets (very small for minbias) • plus other structures that we want • Four general approaches: • kill these structures with cuts • use simulations to model the big contributors • ignore the bins near the origin • fit a sharp exponential I tried them all and got the sensible result: No matter how you handle the bins near the origin the large-scale structure doesn’t change Or, what happens at the origin, stays at the origin… M. Daugherity, STAR Collaboration