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Angular Correlations in STAR

Delve into the analysis of angular correlations in STAR Collaboration focusing on fluctuation measures and correlation analysis. Understand how to quantify fluctuations using correlation coefficients and explore the relationship between fluctuations and correlations.

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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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