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Azimuthally Sensitive HBT Interferometry Analysis

Explore momentum and spatial anisotropies using HBT interferometry. Evaluate correlation functions and source functions vs. angle. Investigate different freeze-out characteristics and predictions for LHC. Utilize official production data for detailed analysis.

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Azimuthally Sensitive HBT Interferometry Analysis

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  1. AliFemto Meeting 19.08.2009 Azimuthally sensitive Hanbury-Brown-Twiss (HBT) Interferometry Lukasz Graczykowski, Warsaw University of Technology Johanna Gramling, University of Heidelberg Supervisor: Adam Kisiel

  2. momentum anisotropy⇒ elliptic flow(v2) spatial anisotropy⇒ HBT-Interferometry coordinatespace momentum space Reaction plane Reaction plane Time HBT-Interferometry needed for consistency checks ⇒ important constraint on models!

  3. Hanbury Brown-Twiss (HBT) Interferometry • Simple Pion-Pion Wave function (no Coulomb or strong interaction): • Correlation Function: • If source is gaussian: “out”: along pair momentum “long”: along beam axis “side”: perpendicular to out and long

  4. Azimuthally sensitive HBT Look at HBT-Radii versus angle between Reaction Plane and Pair Emission Angle Ф Large Rout, small Rside 102.5° 67.5° 157.5° 22.5° Small Rout, Large Rside Reaction plane ᶲ = -22.5° [1]

  5. Predictions for LHC [2] Predictions from hydrodynamical model: worked well for RHIC Different freeze-out characteristics in dependence of the source lifetime: Initial anisotropy can be even switched around for long lifetimes

  6. What was done: • Run Femto Analysis with kT binning: • Pythia: limited usefulness, no emission point information • EPOS(10TeV): real freeze-out coordinates, pp • Therminator(C2030): heavy ion, “natural” elliptic flow, reaction plane • Create macros to plot and fit correlation functions, radii versus considered q-range to estimate systematic errors, radii versus kT

  7. What was done: • Create new pair cut: cut on angle between reaction plane and pair emission angle, Phi • Therefore: change Event Reader, so that Reaction plane is at Phi=0 • Run Femto Analysis with Phi cut on EPOS (10TeV) and Therminator (C2030) • Create Macros • to plot and fit the correlation functions, • to plot R2 versus Phi, • to fit model source function to get input value for R‘s in different phi bins, and • compare it with hydro model prediction (for Therminator)

  8. Correlation function, gaussian fit • Difference between pp and Heavy Ion: higher amplitude for pp ⇒more challenging for heavy ions • Both not gaussian sources: fit is not perfect • Offset for EPOS for low q

  9. 2-gaussian fit for EPOS • Offset for low q disappears • 2nd gaussian term (small source size) describes nearly all of the particles, • 1st gaussian term(large source size) only a few 1: Rout=3.8 fm, Rside=2.9 fm, Rlong=6.7 fm 2: Rout=1.8 fm, Rside1.2 fm, Rlong=2.0 fm

  10. R versus qmax: estimate systematic error • Pythia: „fake“ ideal source ⇒reference case • fluctuations for very small q ranges, then stable

  11. EPOS: oscillation disappears only for large q range • Therminator: statistics too low for detailed study

  12. Source function from model Fitted with

  13. R2 versus Phi: Source function fit EPOS: no oscillations Therminator: oscillations!

  14. R2 versus Phi • EPOS: Reaction plane not provided by the model ⇒only vs emission angle, not vs Phi ⇒have to use reaction plane from Flow Analysis

  15. R2 versus Phi • Therminator: Use Monte Carlo reaction plane ⇒oscillation: as expected, but large error bars

  16. Next steps • To make useful predictions for R vs Phi: use official production for Therminator and EPOS • to get errorbars smaller than expected oscillations • To do kT- and Phi-binning at once • Use the Reaction Plane obtained by the Flow analysis(stored in AOD) to do realistic analysis of R vs Phi (also for EPOS events)

  17. Conclusion • Azimuthally sensitive HBT is an important tool: Spatial information, including the direction of reaction plane, provides information about the fireball characteristics, its lifetime and evolution ⇒Necessary to have the „whole picture“ • Used at RHIC, even more interesting at LHC • Experimental tools are now ready, all cuts and macros are there and tested • Now more detailed studies with the official production for EPOS and Therminator • Include Reaction plane obtained from Flow Analysis

  18. References [1] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett. 93, 012301 (2004). [2] A. Kisiel et al., Phys. Rev. C79, 014902 (2009)

  19. APPENDIXFITPARAMETERS

  20. Therminator - Johanna's output 3bink1 pi+ FCN=5662 FROM MIGRAD STATUS=CONVERGED 1211 CALLS 1212 TOTAL EDM=2.00171e-07 STRATEGY= 1 ERROR MATRIX UNCERTAINTY 1.4 per cent EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Norm 9.96935e-01 6.04936e-04 -0.00000e+00 9.85416e-02 2 Lambda1 2.92234e-01 2.60866e-02 -0.00000e+00 1.42193e-02 3 Rout 5.31788e+00 4.93259e-01 -0.00000e+00 -7.23399e-04 4 Rside 5.95448e+00 3.55757e-01 -0.00000e+00 -8.29856e-04 5 Rlong -8.35271e+00 8.06270e-01 -0.00000e+00 6.05170e-04 6 Routside 1.55185e+00 3.79317e+00 0.00000e+00 6.86852e-04 7 Routlong -4.17527e-06 2.61014e+00 -0.00000e+00 -1.27827e-06 8 Rsidelong 1.89963e+00 5.18460e+00 -0.00000e+00 5.72159e-04 FCN=5662.05 FROM MIGRAD STATUS=CONVERGED 480 CALLS 481 TOTAL EDM=1.01181e-09 STRATEGY= 1 ERROR MATRIX UNCERTAINTY 2.6 per cent EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Norm 9.96935e-01 5.91726e-04 5.37418e-07 -1.23403e-02 2 Lambda1 2.92046e-01 2.51512e-02 1.62322e-05 -2.69274e-03 3 Rout 5.38192e+00 4.10416e-01 4.49151e-05 2.12673e-05 4 Rside 6.09213e+00 4.15037e-01 7.37720e-05 6.43599e-05 5 Rlong 8.44318e+00 6.02137e-01 4.48533e-04 -1.07500e-05

  21. EPOS 1binkt pi+ FCN=4350.29 FROM MIGRAD STATUS=CONVERGED 677 CALLS 678 TOTAL EDM=3.23479e-08 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Norm 1.00228e+00 4.21951e-04 9.73225e-06 -4.80635e-01 2 Lambda1 5.47660e-01 3.39538e-03 6.59886e-05 -1.34154e-02 3 Rout 1.81922e+00 1.56543e-02 2.81026e-04 6.08557e-03 4 Rside 1.21306e+00 1.05184e-02 1.62590e-04 1.15685e-02 5 Rlong 2.04096e+00 1.52433e-02 2.79751e-04 1.31519e-03 6 Routside 4.58288e-01 8.62173e-02 1.22551e-03 -2.71315e-04 7 Routlong 1.24819e-06 1.30300e-01 4.19656e-03 1.47047e-04 8 Rsidelong 6.41616e-01 6.50832e-02 9.47525e-04 -3.99951e-04 FCN=4385.18 FROM MIGRAD STATUS=CONVERGED 201 CALLS 202 TOTAL EDM=7.4031e-10 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Norm 1.00221e+00 4.22758e-04 9.77048e-06 4.17058e-02 2 Lambda1 5.47164e-01 3.38966e-03 6.61832e-05 5.84055e-03 3 Rout 1.84717e+00 1.13359e-02 2.79683e-04 -1.60004e-03 4 Rside 1.26018e+00 6.74683e-03 1.60089e-04 3.38379e-03 5 Rlong 2.09146e+00 1.14935e-02 2.77598e-04 -7.32418e-04

  22. 2gauss pi+ FCN=4179.04 FROM MIGRAD STATUS=CONVERGED 1099 CALLS 1100 TOTAL EDM=9.54225e-09 STRATEGY= 1 ERROR MATRIX UNCERTAINTY 1.0 per cent EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 Norm 1.00082e+00 4.49272e-04 3.05669e-10 2.41608e-01 2 Lambda1 1.89081e-01 1.43163e-02 3.60251e-08 -4.89928e-04 3 Rout1 3.80723e+00 2.61132e-01 1.13517e-06 -3.47922e-04 4 Rside1 2.96375e+00 2.27850e-01 4.75580e-07 -1.20118e-04 5 Rlong1 6.74693e+00 5.60299e-01 3.32776e-06 -2.10935e-04 6 Lambda2 4.97050e-01 6.30413e-03 3.10301e-08 2.92020e-02 7 Rout2 1.77891e+00 1.35259e-02 6.35758e-08 -1.15208e-02 8 Rside2 1.21307e+00 8.24245e-03 2.62120e-08 -8.02389e-03 9 Rlong2 2.00400e+00 1.44306e-02 5.76168e-08 -7.57453e-03

  23. EPOS R versus Phi MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 p0 4.80516e+05 3.31808e+02 6.95453e+01 -1.32853e-07 2 p1 1.04843e+01 1.15311e-02 2.41836e-03 1.20857e-03 yslong=10.4843 xosf=90 yosf=-0.0370067fm FCN=1194.52 FROM MIGRAD STATUS=CONVERGED 194 CALLS 195 TOTAL EDM=7.61535e-10 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 p0 1.04127e+00 8.78625e-03 2.98181e-05 -3.68707e-03 2 p1 5.38176e-01 1.16931e-02 9.31568e-05 -9.05181e-04 3 p2 4.40603e+00 2.58022e-01 2.06276e-03 3.63476e-06 4 p3 2.29851e+00 1.45247e-01 1.40058e-03 1.50833e-04 5 p4 5.56283e+00 3.42828e-01 2.29094e-03 1.40966e-04 6 p5 1.76821e-02 7.89819e-02 1.33294e-03 -6.81168e-05 still working... xoutf=135 youtf=4.40603fm

  24. FCN=74155.2 FROM MIGRAD STATUS=CONVERGED 42 CALLS 43 TOTAL EDM=7.65585e-10 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 p0 4.01573e+05 2.27183e+02 2.22373e+01 -1.26715e-07 2 p1 1.66879e+01 1.37560e-02 1.34701e-03 -3.80663e-03 ysout=16.6879 xsidef=135 ysidef=2.29851fm FCN=424435 FROM MIGRAD STATUS=CONVERGED 42 CALLS 43 TOTAL EDM=7.3555e-09 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 p0 1.07781e+06 6.48134e+02 1.42709e+02 -2.68883e-07 2 p1 2.25505e+00 1.95147e-03 4.30976e-04 -6.86460e-02 ysside=2.25505 xoutf=135 youtf=5.56283fm FCN=481059 FROM MIGRAD STATUS=CONVERGED 43 CALLS 44 TOTAL EDM=4.90629e-10 STRATEGY= 1 ERROR MATRIX ACCURATE EXT PARAMETER STEP FIRST NO. NAME VALUE ERROR SIZE DERIVATIVE 1 p0 4.73634e+05 3.34134e+02 6.93974e+01 6.35024e-08 2 p1 1.01163e+01 1.13817e-02 2.36536e-03 3.97518e-03 yslong=10.1163 xosf=135 yosf=0.0176821fm

  25. Therminator: use MC Reaction plane • ⇒oscillation, as expected, but large errors

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