1 / 27

Tilted Pion Sources and Azimuthal Dependence of HBT Radii

Tilted Pion Sources and Azimuthal Dependence of HBT Radii. Mike Lisa. Formalism: R 2 ( f )  spatial correlation tensor implicit & explicit f -dependence a dominant and overlooked correlation  striking experimental signal toy models, RQMD pion flow and spatially tilted sources

kylene
Download Presentation

Tilted Pion Sources and Azimuthal Dependence of HBT Radii

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Tilted Pion Sources and Azimuthal Dependence of HBT Radii Mike Lisa • Formalism: R2(f)  spatial correlation tensor • implicit & explicit f-dependence • a dominant and overlooked correlation  striking experimental signal • toy models, RQMD • pion flow and spatially tilted sources • preliminary observation of tilted source @ AGS nucl-th/0003022 MAL, U. Heinz and U.A. Wiedemann March 2000

  2. Extracting & summarizing source information central Au+Au@2AGeV y=ycm0.35 pT=0.1-0.3 GeV/c Gaussian parameterization in Bertsch-Pratt decomposition vanish for azimuthally symmetric sources March 2000 E895 Collab. PRL 84 (2000)

  3. Space-time interpretation of R2ij for cylindrically symmetric sources mass-shell constraint q·K=0: mixes spatial, temporal information explicit dependence separates and y (fm) implicit dependence Q Q O T carries dynamical information and typically dominates p Q p S 2 1 x (fm) beam towards viewer point out: “x” is “out”, “y” is “side” and “z” is “long” (not “real” x,y,z) March 2000

  4. The next challenge — f-dependent interferometry side y K out f reaction plane x b Two coordinate systems connected by a pair-dependent rotation reaction-plane-fixed March 2000

  5. Connecting the BP correlations to the source in its natural frame Spatial correlation tensor ! U. Wiedemann PRC57 (1998) 266 explicit and implicit (Smn(f)) f dependence March 2000

  6. Constraints on implicit f-dependence Smn(f) General symmetry: Mirror reflection in reaction plane Vanishing points @ ycm General symmetry: Point reflection about origin: determines f y K reaction plane x Symmetry @ ycm (Kz=0): Point reflection about 2D origin: b Allf-dependence of Smn due to x-K correlations March 2000

  7. Neglecting implicit f-dependence Note: usually, neglecting x-K correlations is “boring”, but we show that there is something exciting that was overlooked until now! Implicit f-dependence weak compared to explicit f-dependence • trivially true at K 0 • Negligible if x-K correlations (due to transverse flow, opaqueness) small compared to thermal smearing • no restriction on longitudinal flow • may be checked via consistency relations  Wiedemann Heiselberg L/H/W • Contrast with KT dependence from azimuthally symmetric case • implicit KT dep. need not vanish @ KT=0 • explicit KT-dependence weighted with (generally small) bt • explicit KT-dependence vanishes at K 0 Smn(f) = Smn “Same source viewed from all anglesf” March 2000

  8. Neglecting implicit f-dependence, and focussing on ycm 5 nonvanishing components Smn encode all spacetime geometry driving R2ij(f) Smm: lengths of homogeneity S13: correlation between x & z  Spatial tilt angle y x qs z (Beam) Reaction plane • No radii vanish, even at ycm and pT=0 • first harmonic oscillations @ ycm!!! • natural consistency relations to check influence of Smn(f) March 2000

  9. Simple case - ellipsoidal source w/ no flow Using CRAB, generate c.f.’s in 8 bins of z x March 2000

  10. A series of tilted ellipsoids in relative momentum measure a single tilted ellipsoid in coordinate space! z 2D projections of correlation functions x -80 0 -80 0 -80 0 emission angle coordinate space March 2000

  11. Adding longitudinal flow Same model but with additional boost Still “same source(s) viewed from different f z-flow effects |pz|<40 MeV/c March 2000

  12. RQMD@AGS: “Single-pion tilts” (effective source tilts bigger) 4 AGeV 2 AGeV 0-2 fm 4-6 fm 8-10 fm • big! • positive! • not overly sensitive to b • sensitive to dynamics • falling with Ebeam March 2000

  13. Opposing average tilts in p, x and the physics of p flow RQMD w/ meanfield: Au(2GeV)Au, b=3-7 fm transport model exhibits weak p “antiflow,” similar to observation (Kintner et al. PRL 78 4165, 1997) • coordinate-space tilt in positive direction • Antiflow reflects dense low-|z| region • p from dilute large-|z| show positive flow Bass et al [PLB 302 381 (93), PRC 51 3343 (95)]: pion anisotropies ~ 2 AGeV due to reflection (pND pN) not absorption (pNNDN NN) experimental handle through tilt? March 2000

  14. RQMD w/ meanfield: Au(2GeV)Au, b=2-8 fm, pT<300 MeV/c long out side ol os sl positive x-z correlation negative tilt? Clue: oblate source S11>S33 In terms of prolate source: March 2000

  15. Prolate/oblate sources and large/small tilts z z q q sz sx x x sz sx selects solution with |q| < 45o Viewed as prolate source Viewed as oblate source sx sz q sx sz q + 90o sz < sx q < 0 sz > sx q > 0 March 2000

  16. Smn measures Gaussian curvature in b-fixed Cartesian system... pair separation distributions Hardtke & Voloshin [PRC 61 024905 (2000)]: HBT radii from Gaussian fits sensitive to close pairs Radii reflect Gaussian curvature near origin in Drout, Drside, Drlong For most sources, and March 2000

  17. …but source is tilted in this system + has longitudinal flow effects. Dz/2 Dz/2 fit to pair distribution in Dz-Dx with tilted ellipsoid no qz cut |qz|<25 MeV cut March 2000

  18. Preliminary E895 DATA 2 AGeV 4 AGeV March 2000

  19. No-flow toy model 2 GeV cut 22 4 GeV cut 20 -0.8 0 -0.8 0 -0.8 0 -0.8 0 -0.8 0 -0.8 0 -80 0 -80 0 -80 0 March 2000

  20. Rough idea of extracted shapes of average effective source “to scale” 2 AGeV st = 3.5 fm/c sx’ = 4.2 fm sy = 5.8 fm sz’ = 5.5 fm qs = 50o y z y z x’ x x’ x 4 AGeV st = 3.3 fm/c sx’ = 3.9 fm sy = 4.8 fm sz’ = 4.8 fm qs = 37o March 2000

  21. Summary • R2ij(f) spatial correlation tensor Smn, encodes source information in natural frame • implicit dependence Smn(f) due to transversex-p correlations (flow, opaqueness…) • complicate relation between R2 and Smn: higher harmonics to both • presence of significant implicit dependence checkable via consistency relations • explicitf-dependence (due to spacetime geometry) dominates implicit @ low pT • Smn(f) Smn: 5 nonvanishing components @ ycm encode: • 4 spacetime homogeneity lengths • S22-S11 (transverse elliptic shape)  2nd-order oscillations in Ro2, Rs2, Ros2 • spatial tilt of source in reaction plane - “the last static component” • S13 striking 1st-order oscillations in Rol2, Rsl2 • Tilt @ AGS • large and positive • measurable (and measured!!) • experimental handle on physics of flow dynamics (rescatt., meanfield) March 2000

  22. Tilts at RHIC? Theoretically, and experimentally, “challenging” • But try! • RQMD evolves too quickly w/ E • Never know what else... RQMD@RHIC b=3-8 fm c/o N. Xu, R. Snellings @ SPS: Rside ~ 30% too big I.G. Bearden et al (NA44) PRC58, 1656 (1998) March 2000 E895, QM99

  23. y x Qy z (Beam) Reaction plane March 2000

  24. Constraints on Smn(f) General symmetry: Mirror reflection in reaction plane Symmetry @ ycm (Kz=0): Point reflection about 2D origin: Vanishing points Harmonic coefficients General symmetry: Point reflection about origin: March 2000

  25. Prolate/oblate sources and large/small tilts March 2000

  26. First Harmonics at Midrapidity?? - Ain’t that Impossible?Is “up” different than “down”? March 2000

  27. Howd’ja get more f-bins? 3) binning in instead of 1) a bit more statistics 2) tweaked reactionplane resolution (C. Pinkenburg) & HBT cuts K p1 py pairs straddling f-boundaries never used p2 all pairs wind up in somef-bin px f - boundaries binning with f1, f2 also led to increased sensitivity to oscillations in Rside as compared to Rout March 2000

More Related