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Angular Correlations in STAR

Angular Correlations in STAR. Michael Daugherity for the STAR Collaboration Graduate Student - University of Texas. Fluctuations and Correlations Workshop Firenze, July 2006. Outline. Relating fluctuations and correlations Making a correlation measure from scratch

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Angular Correlations in STAR

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  1. Angular Correlations in STAR Michael Daugherity for the STAR Collaboration Graduate Student - University of Texas Fluctuations and Correlations Workshop Firenze, July 2006

  2. Outline • Relating fluctuations and correlations • Making a correlation measure from scratch • Angular correlations in STAR • Charge-dependent angular correlations Daugherity – Fluctuations and Correlations

  3. Event-by-Event Fluctuations Au-Au 130 GeV PRC 71 064906 It all started by looking at event-wise mean pt looking for anomalous events • Distribution is smooth, contrary to some phase-transition model predictions... • …but it’s broader than expected. • A measurement of non-statistical fluctuations Data mixed event reference But what causes fluctuations? How do we quantify and interpret the result? 14% increase it turns out that measuring pt fluctuations is fairly difficult… similar to z-score in statistics, counts number of σ’s away from mean Daugherity – Fluctuations and Correlations

  4. Fluctuation Measures Now we can take Pearson’s Correlation Coefficient: • the gold-standard correlation measure for the last 100 years. A large number of multiplicity, net charge, and transverse momentum fluctuation measures have been used at SPS at RHIC: ν+-,dyn, ν(Q), Φq, D, Δσ2nch, Δσ2q, Φpt, Σpt, Fpt, σ2pt,dyn, Δσpt:n, etc. Not much agreement on how to quantify fluctuations, but the essential common feature is an integral of a covariance Cov = <xy> - <x><y> = mean of products - product of means = object - reference Zero covariance means <xy> = <x><y>, thus <x><y> is our uncorrelated reference • We can understand fluctuations by measuring 2-particle correlations • Easier to interpret and relate to physical processes • Must use all pairs equally, no high-pt trigger requirement Daugherity – Fluctuations and Correlations

  5. The Big Picture <pt> at full STAR acceptance Fluctuation measure Correlation invert integrate Scale (bin size) dependence STAR Preliminary A formal relationship between fluctuation, covariance, and correlation: Defined as variance - reference PRC 71, 064906 More on fluctuations and inversion this afternoon Written as covariance between bins a and b fluctuation hep-ph/0506173 Integral of correlation J Phys G 31 809-824 sum over bins correlation 2D binning function Daugherity – Fluctuations and Correlations

  6. Correlation Measures ρ(p1,p2)= 2 particle density in momentum space ρsibling(p1,p2) Event 1 ρreference(p1,p2) Event 2 Number Correlations Covariance Δρ = object - reference Or, defining Δρ as a histogram, bin (a,b) can be written as: ε = bin width, converts density to bin counts is a per-particle measure Normalize This measure comes from a direct application of the standard correlation function, and all we have to do is count pairs We calculate this as a function of (ηΔ = η1 –η2, ΦΔ= Φ1 – Φ2), separation in pseudorapidity and azimuth (axial momentum space) Daugherity – Fluctuations and Correlations

  7. Correlation Measures What is ? ratio:explicitly cancels out acceptance and some sys error reference: acceptance and efficiency corrected, ~ flat from azimuthal symmetry and longitudinal expansion, provides per particle normalization ρsib dominated by ηΔ acceptance + permil corr signal ΦΔ ηΔ • The terminology: • correlation – measured as a function of variable x for each particle, e.g. (x1,x2) • autocorrelation – transformed to relative variable xΔ = x1 – x2by averaging along xΣ = x1 + x2, requires stationarity along xΣ • joint autocorrelation – autocorrelation as function of two different relative variables, e.g. (xΔ,yΔ) • The joint autocorrelation (ηΔ = η1 –η2, ΦΔ= Φ1 – Φ2) compactly represents the entire axial space Daugherity – Fluctuations and Correlations

  8. Correlation Analysis • A quick recap before moving on • Fluctuation measures all depend in some way on covariance (correlations) of particles, but no agreement on normalization and other factors • Relating fluctuation to correlations places the results in a larger context • Correlations can be defined with straightforward statistics, and have a direct physics interpretation • By looking at all possible pairs we measure correlations that are minimum-bias, model-independent, and require no high-pt trigger • Next up, two examples of correlation analysis • Proton-Proton • the essential reference before tackling Au-Au • well known and described physics in terms of soft transverse strings and semi-hard scattering • Hijing • what changes from p-p to Au-Au, and what changes with centrality? • does quenching describe the data well? Daugherity – Fluctuations and Correlations

  9. Proton-Proton minimum-bias; i.e. no high-pt trigger We can even separate them Spectrum on transverse rapidity using two-component model hard soft yt2 STAR Preliminary yt ~ ln pt pt ~ 2.0 pt ~ 1.0 pt ~ 0.5 yt1 Correlation on transverse rapidity We expect to see STRINGS (soft, Lund-model) and MINIJETS(semi-hard, back-to-back scattering) proton-proton 200 GeV axial STAR Preliminary STRING 1D Gaussian “away-side” ridge MINIJET “same-side” jet cone Daugherity – Fluctuations and Correlations

  10. Proton-Proton hep-ph/0506172 away-side – ΦΔ ~ π MINIJETS same-side –small opening angle yt2 • This is a minimum-biasjet, no trigger particle required • we can see jets down to 0.5 GeV STAR Preliminary yt1 STRINGS HBT string fragments – 1D Gaussian on ηΔ Daugherity – Fluctuations and Correlations

  11. HIJING proton-proton Au-Au 200 GeV Quench Off peripheral (70-80%) mid (40-50%) central (0-5%) • We can do the same soft/hard cuts and see the same string and minijet components as in p-p • Hijing predicts very little change with centrality, soft component a bit smaller in central, but no major modifications • The jet quenching does reduce the hard component, but again no modifications to correlation structures central – quench on http://www.rhip.utexas.edu/~daugherity/analysis/hijing/index.html Daugherity – Fluctuations and Correlations

  12. Au-Au 130 GeV ~300k events 0.15 < pt<2 GeV/c |h|<1.3, full f=2p merging & HBT cuts applied 40-70% 17-40% 5-17% 0-5% ? p-p 200 GeV PRC, in press (nucl-ex/0411003) Features: peak at small relative angles cos(fD) - momentum conservation at low pt cos(2fD) - elliptic anisotropy Now remove the (ηΔ-independent) sinusoids to isolate the small-angle peak Daugherity – Fluctuations and Correlations

  13. Au-Au 130 GeV 40-70% 17-40% 5-17% 0-5% elongation along ηΔ narrowing along ΦΔ sinusoids removed Widths p-p 130 GeV Au-Au mid-central ση σΦ Daugherity – Fluctuations and Correlations

  14. Au-Au 62 GeV proton-proton • Correlation structure evolves smoothly from p-p to central Au-Au • We see strings disappearing and minimum-bias jets being modified 80-90% 70-80% 60-70% 50-60% 90-100% ΦΔ ηΔ STAR Preliminary 30-40% 20-30% 10-20% 5-10% 0-5% ΦΔ ηΔ Daugherity – Fluctuations and Correlations

  15. Au-Au 200 GeV Similar to 62 GeV, but strings damp out more quickly, and broadening along ηΔ is more dramatic 80-90% 70-80% 60-70% 50-60% 90-100% ΦΔ ηΔ STAR Preliminary 30-40% 20-30% 10-20% 5-10% 0-5% ΦΔ ηΔ Daugherity – Fluctuations and Correlations

  16. Au Soft, away-side recoil, cos(fD) minijet Au Gluon bremsstrahlung/ medium dragging calculations: (Armesto, Salgado, Wiedemann, hep-ph/0405301) p-p z 130 GeV Au-Au mid-central 100 GeV jet Hubble expansion HI  h f p-p Possible interpretation… Interaction with longitudinally expanding medium carries radiated gluons and hadron fragments along pseudorapidity Fragmentation asymmetry reverses from p-p to Au-Au dramatic evolution with centrality Daugherity – Fluctuations and Correlations

  17. Axial Correlations Recap • The dominant feature is a jet-like correlation that broadens with centrality • consistent with coupling to longitudinally expanding medium • Minimum-bias correlations reveal dynamics of low-Q2 partons • new access to non-perturbative interactions • These correlations have significant energy and centrality dependence • This rich structure drives observed multiplicity fluctuations • Measuring the correlations directly gives new insight into the physics behind the fluctuations Up Next: measuring charge-dependentcorrelations Daugherity – Fluctuations and Correlations

  18. from PLB 407 174: “Observation of Charge-Ordering in Particle Production in Hadronic Z0 Decay” + - + - + - + - p+ p- p+ p- η -2 0 2 Charge-Dependent Correlations • We can access additional dynamics by considering the relative charge of particle pairs: • Like Sign (LS = ++ and --) pairs include quantum interference correlations and boson enhancement from identical particles • Unlike Sign (US = +- or -+) pairs are produced nearby from quark-antiquark pairs and resonance decays • We expect to see a short-range enhancement of US pairs. Charge-ordering In string fragmentation models, the charge-ordered particles are also ordered in η: Daugherity – Fluctuations and Correlations

  19. CD References peripheral mid central CI Proton-Proton STAR Preliminary = CD US LS No structure on ΦΔ Gaussian on ηΔ HIJING • p-p shows charge-ordering signal as Gaussian on ηΔ with no structure on ΦΔ • Hijing also shows charge-ordering along ηΔ and no change with centrality Daugherity – Fluctuations and Correlations

  20. STAR 130 GeV Charge-Dependent most peripheral central PLB 634 347 Same plots viewed from above… The 130 GeV data show changes in structure with centrality, need finer centrality bins to see more… Daugherity – Fluctuations and Correlations

  21. Au-Au 62 GeV proton-proton • Good agreement between p-p and peripheral bin • Smooth evolution to symmetric exponential signal 80-90% 70-80% 60-70% 50-60% 90-100% ΦΔ ηΔ STAR Preliminary 30-40% 20-30% 10-20% 5-10% 0-5% ΦΔ ηΔ Daugherity – Fluctuations and Correlations

  22. Au-Au 200 GeV • Similar to 62 GeV results • 1-D Gaussian on ηΔ disappears more quickly 80-90% 70-80% 60-70% 50-60% 90-100% ΦΔ ηΔ STAR Preliminary 30-40% 20-30% 10-20% 5-10% 0-5% ΦΔ ηΔ Daugherity – Fluctuations and Correlations

  23. Charge-Dependent Summary • The largest correlation amplitude observed at RHIC • Smooth evolution all the way from proton-proton to central Au-Au peripheral Au-Au mid Au-Au proton-proton central Au-Au • Evidence for charge-ordering moving from one-dimensional string to a surface • The 1-D signal becomes symmetric on ηΔ and ΦΔ in central Au-Au • Inconsistent with resonance gas or string fragments • Evidence for attenuation through an opaque medium • The change from Gaussian to exponential implies pair loss increasing with opening angle, consistent with attenuation through a medium Daugherity – Fluctuations and Correlations

  24. Summary: Angular Correlations p-p 200 GeV Au-Au 200 GeV minijet pt > 0.5 GeV minijet correlations no pt cut peripheral central pt < 0.5 GeV elongation ‘string’ net-charge correlations charge-ordering peripheral central LS - US 1D 2D Daugherity – Fluctuations and Correlations

  25. Conclusions • Fluctuations and correlations provide different manifestations of underlying dynamics; correlations are more readily interpreted. • Correlations show that multiplicity and <pt> fluctuations at RHIC are driven by minijets, while net-charge fluctuations are related to charge-ordering • String fragmentation and minimum-bias jet correlations smoothly and dramatically evolve from p-p to central Au-Au. • Our observations are consistent with the following interpretation: • semi-hard processes measured in p-p are embedded in an increasingly dense and thick longitudinally expanding medium in Au-Au. • hadronization via longitudinal strings in p-p becomes insignificant in Au-Au where the bulk medium hadronizes isotropically along the axial surface. Daugherity – Fluctuations and Correlations

  26. The Big Picture • We have developed a general and powerful method for measuring two-particle correlations • These number correlations were found by counting pairs, but covariance derivation allows for easy extension to any arbitrary function • …so we can directly measure the correlations relating to any non-statistical fluctuation • Results are model independent and minimum-bias, includes important measurements of low-Q2 dynamics • other correlation measurements done at RHIC require jet hypothesis and trigger bias or are limited in phase-space The Bottom Line: A lot of work has been invested on integral measures of fluctuations, but differential measures of correlations show dramatic novel behavior and access new physics Daugherity – Fluctuations and Correlations

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