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Fitted HBT radii versus space-time variances in flow-dominated models

Fitted HBT radii versus space-time variances in flow-dominated models. Mike Lisa Ohio State University. Frodermann, Heinz, MAL, PR C73 044908 (2006); nucl-th/0602023. Outline. motivation: possible problems in comparing models to data new formula for “fitting” model calculations

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Fitted HBT radii versus space-time variances in flow-dominated models

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  1. Fitted HBT radii versus space-time variances in flow-dominated models Mike Lisa Ohio State University Frodermann, Heinz, MAL, PRC73 044908 (2006); nucl-th/0602023 WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  2. Outline • motivation: possible problems in comparing models to data • new formula for “fitting” model calculations • application to two common models • conclusions WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  3. The many estimates of length scale • HBT radii : parameters of Gaussian fits • 3D fit to 3D CF R • experimental procedure • 1D fit to projections of 3D CF  R1D(and 3 ’s) • questionable shortcut • FWHM of 1D projections R* • Space-time variances R-hat • quick to calculate if SP(x) Gaussian, then C(q) Gaussian* and R = R1D= R* = R-hat *Coulomb ignored throughout WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  4. dN/dx STAR Phys. Rev. C 71 (2005) 044906 Retiere & MAL PRC70 044907 (2004) Kisiel, Florkowski, Broniowski, Pluta PRC73 064902 (2006) The many estimates of length scale • But neither S(x) nor C(q) is “ever” Gaussian if SP(x) Gaussian, then C(q) Gaussian* and R = R1D= R* = R-hat *Coulomb ignored throughout WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  5. Paic and Skowronski J. Phys. G311045 (2005) “typical” study from STAR 6 6 6 Ro (fm) Rs (fm) Rl (fm) 4 4 4 Fit with ad-hoc alternate forms ? what to do with the parameters? STAR Phys. Rev. C 71 (2005) 044906 0.1 0.2 surely the way of the future... imaging qmax (GeV/c) “fit-range study” syst. err. What do experimentalists do? • But neither S(x) nor C(q) is “ever” Gaussian if SP(x) Gaussian, then C(q) Gaussian* and R = R1D= R* = R-hat *Coulomb ignored throughout WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  6. hydro cascade • Hirano: R1D • Soff: R-hat • Zschiesche R* • Heinz: R-hat • AMPT R • MPC R-hat • RQMD R • HRM R What do theorists do? • But neither S(x) nor C(q) is “ever” Gaussian • How much does this (rather than physics) dominate model comparisons? if SP(x) Gaussian, then C(q) Gaussian* and R = R1D= R* = R-hat WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  7. RQMD - some difference  R-hat  R AMPT - huge difference Hardtke & Voloshin PRC61 024905 (2000) Lin, Ko, Pal PRL89 152301 (2002) It can matter(how much, is model-dependent) • AMPT, RQMD, HRMreproduce HBT radii best. • Only these use “right” method • coincidence? WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  8. Our plan • Examine two popular models which have published R-hat • Blast-wave • Heinz/Kolb B.I. hydro • Compare R versus R1D versus R-hat • for fits (R and R1D), perform experimentalist’s “fit-range study” • But first... an explanation of our “fit” procedure... WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  9. Blastwave hydro CE EOS out side long The “data” to be “fit” • Straight-forward to calculate CF WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  10. Analytic calculation of radii (“fit”) 3D functional form: • only good for C>1 • not for noisy data F.O.M. to minimize: WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  11. Analytic calculation of radii (“fit”) 3D • non-homogeneous linear equations • invertable to find parameters P • as per data, we take  = fixed (not ´) • (its value does not matter) WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  12. Analytic calculation of radii (“fit”) 1D Similarly, for R1D... • rather than one 4x4 set of equations for 4 parameters... • 3 sets of 2x2 equations for 6 parameters • similar technique used by Wiedemann, others WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  13. projection of 3D CF projection of 3D fit BW projections - approximately Gaussian kT=0 kT=0.3 GeV/c L projection appears least Gaussian WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  14. “HBT radii” from variances radii from ‘fit’ using various q-ranges STAR Au+Au @ 200 GeV 0-5% Phys. Rev. C 71 (2005) 044906 BW - 1D studies pT=0.1 Ro Rs RL o • Transverse radii: R1D R-hat • Longitudinal • R1D R-hat • signif. fit-range systematic s L pT=0.9 qmax (GeV/c) Ro Rs RL o s L KT (GeV/c) WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  15. “HBT radii” from variances radii from ‘fit’ using various q-ranges STAR Au+Au @ 200 GeV 0-5% Phys. Rev. C 71 (2005) 044906 BW - 3D studies  Ro Rs RL • -coupling / 3D structure Ro fit range systematic • still, BW agreement w/data persists qmax (GeV/c)  Ro Rs RL KT (GeV/c) WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  16. CE Hydro projections - Gaussian fits “look bad” kT=0.3 GeV/c kT=0.6 GeV/c • CF projections appear Gaussian • projections of 3D Gaussian fit match poorly • (unseen) 3D q structure of CF drives fit WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  17. “HBT radii” from variances radii from ‘fit’ using various q-ranges STAR Au+Au @ 200 GeV 0-5% Phys. Rev. C 71 (2005) 044906 CE Hydro - 3D studies  Ro Rs RL larger fit-range systematic (side is least affected, despite “looking” worst in projections) significant difference b/t R, R-hat “fitted” R agree better with data qmax (GeV/c)  Ro Rs RL KT (GeV/c) WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  18.  Ro Rs RL Ro Rs RL KT (GeV/c) KT (GeV/c) Hydro using 2 EoS “CE” EoS assuming Chem. Equilib until FO - original publications - More realistic “NCE” EoS • similar non-Gaussian effects • NCE always compared better to data,for R-hat and (by construction) for yields. • apples::apples comparison further improves agreement  STAR data  Variance  3D “fit” WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  19. Blast-wave “CE” EoS “NCE” EoS   Ro Rs RL Ro Rs RL  Ro Rs RL KT (GeV/c) KT (GeV/c) KT (GeV/c) BW & Hydro • Qualitatively sim non-Gauss effects • magnitude much smaller for BW • conclusions about BW agreement ~same (still “good” but  will increase) • hydro agreement (for Ro, Rl) improvesin apples::apples comparison WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

  20. Summary / Conclusions • Variety of length-scale estimators are compared to experimental HBT radii • danger of apples::oranges comparison • magnitude of difference is model-dependent • analytic calculation of “fit” parameters in models • R versus R1D versus R-hat • non-Gaussian features generate differences, fit-range systematic • R≠R1D : importance of global 3D fit (as experimentally done) • R < R-hat in temporal components (long & out) • agreement w/hydro much improved in apples::apples • impact on “puzzles” • effect significantly smaller for BW WPCF 2006, Sao Paulo Brazil - lisa Non-gaussian effects

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