RHIC/INT Workshop on HBT - jan021 The low-energy end of the HBT excitation function Mike Lisa, for Roy Lacey, for the E895 Collaboration N.N. Ajitanand, J. Alexander, D. Best, P. Brady, T. Case, B. Caskey, D. Cebra, J. Chance, P. Chung, B. Cole, K. Crowe, A. Das, J. Draper, S. Gushue, M. Gilkes, M. Heffner, H. Hiejima, A. Hirsch, E. Hjort, L. Huo, M. Justice, M. Kaplan, J. Klay, D. Keane, J. Kintner, D. Krofcheck, R. Lacey, J. Lauret, E. LeBras, M. Lisa, H. Liu, Y. Liu, B. McGrath, Z. Milosevich, D. Olson, S. Panitkin, C. Pinkenburg, N. Porile, G. Rai, H.-G. Ritter, J. Romero, R. Scharenberg, L. Schroeder, B. Srivastava, N. Stone, J. Symons, S. Wang, R. Wells, J. Whitfield, T. Wienold, R. Witt, L. Wood, X. Yang, Y. Zhang, W. Zhang Auckland - BNL - CMU - Columbia - UC Davis - Harbin - KSU - LBL - St. Mary’s College - OSU - Purdue - Stony Brook

RHIC/INT Workshop on HBT - jan022 Outline Definition and importance of correlation function Definitions of out, side, long… Central collisions  s systematics p T systematics (flow) comparison to models (systematic discrepancy) Centrality dependence (assuming standard cylindrical symmetry) Non-central collisions new information available extraction of shapes at AGS possibilities for RHIC Summary

RHIC/INT Workshop on HBT - jan023 Measurement with the EOS TPC Up to ~350 particles/event (60  - ) measured over large phase space Good reaction plane resolution  p/p  3% (dominated by MCS)  5% e - contamination in  - ~10 5 events at 2, 4, 6, 8 AGeV

RHIC/INT Workshop on HBT - jan024 Bertsch-Pratt projections (11%  T y cm  0.35 p T = MeV/c)

RHIC/INT Workshop on HBT - jan025 Evolution of the BP and YKP fit parameters Increased production of long- lived  - -emitters  fall in Strong evolution of R s (R  ) with beam energy Hadronic model with or without meanfield underpredicts (apparent) geometric size at low beam energy E895 Collab, PRL (2000)

RHIC/INT Workshop on HBT - jan026 Evolution of systematics - data and model Observed evolution of systematics not reproduced by model Dynamics driving R S (m T ) may not depend on collision energy within RQMD

RHIC/INT Workshop on HBT - jan027 Testing the model at the SPS For  -... Model underpredicts apparent size below 10 AGeV... overpredicts size at 158 AGeV Extrapolation to RHIC??? NA44 RQMD R out 4.88   0.14 R side 4.45   0.20 R long 6.03   0.21 I.G. Bearden et al (NA44) PRC58, 1656 (1998) D. Hardtke, Ph.D. thesis (1997)

RHIC/INT Workshop on HBT - jan028 Central collisions even at low energies, unclear that HBT well understood/reproduced by models systematic discrepancies predicted size: too small  too large as  s grows (RQMD) predicted timescale: too large

RHIC/INT Workshop on HBT - jan029 Centrality Dependence of the Correlations (“standard” cylindrical assumption) suppressed for central collisions due to increased production of ,  Gentle fall of transverse radii as size of overlap region falls b=2  7 fm: ~ 35% reduction in RMS

RHIC/INT Workshop on HBT - jan0210 Probing freeze-out space-time structure for b  0 Source in b-fixed system: (x,y,z) Space/time entangled in pair system (x O,x S,x L ) out  b KK side x y U. Wiedemann, PRC 57, 266 (1998) MAL, U. Heinz, U. Wiedemann PLB 489, 287 (2000) ! etc. themselves functions of 

RHIC/INT Workshop on HBT - jan0211 Simplifying assumption at AGS: minimal effects of flow at very low p T out  b KK side x y U. Wiedemann, PRC 57, 266 (1998) MAL, U. Heinz, U. Wiedemann PLB 489, 287 (2000) (several terms p T = y = 0) etc are now constants

RHIC/INT Workshop on HBT - jan st -harmonic oscillations: spatial tilt angle  S (Beam) Coordinate space! x y z ss 2 nd -harmonic oscillations from elliptical transverse shape b x y First-order information in HBT(  )

RHIC/INT Workshop on HBT - jan0213 Data:  - correlation functions Au(4 AGeV)Au, b  4-8 fm 6 components to radius tensor: i, j = o,s,l 1D projections,  =45° 2D projections lines: projections of 3D Gaussian fit  outsidelong C(q) E895, PLB (2000)

RHIC/INT Workshop on HBT - jan0214 Cross-term radii R ol, R os, R sl quantify “tilts” in correlation functions   fit results to correlation functions Lines: Simultaneous fit to HBT radii to extract underlying geometry

RHIC/INT Workshop on HBT - jan0215 Images of  - -emitting sources (scaled ~ x10 14 ) 3 fm x ’ y 2 AGeV x z  S =47° x ’ y 4 AGeV x z  S =37° x ’ y 6 AGeV x z  S =33° Large, positive tilt angles similar to naïve overlap: b~5 fm

RHIC/INT Workshop on HBT - jan0216 Opposing average tilts in p, x and the physics of  flow  “antiflow” (negative tilt in p-space) x-space tilt in positive direction  non-hydro nature of  flow B. Caskey RQMD transport model: Antiflow reflects dense region z~0 (dilute large-|z| show positive flow) RQMD Au(2GeV)Au z (fm) x (fm)  + 6 AGeV pion momentum anisotropies due to reflection from flowing baryons (  N   N)  tilt reflects x-space structure of proton flow Bass et al [PLB (93)]:

RHIC/INT Workshop on HBT - jan0217 At RHIC: P. Kolb, J. Sollfrank, and U. Heinz elliptic/radial flow cannot be ignored… … but it can be included/constrained via spectra, v2 measurements can distinguish between early and late freezeout  handle on evolution timescale in addition to freezeout timescale See talk of F. Retiere transverse shapes as calculted by hydrodynamics

RHIC/INT Workshop on HBT - jan0218 Summary Early hints that things might go wrong at RHIC evolution of geometry, increasing effects of flow poorly reproduced by models at lower  s azimuthally-sensitive  - HBT - the next frontier almond-shaped source, (~ entrance-channel geometry) large positive spatial tilt angles non-hydro nature of  flow coordinate-space structure of proton flow insight necessary and available at RHIC which timescales are too short? is the nature of freezeout understood? how can hydro reproduce all else except geometry?

RHIC/INT Workshop on HBT - jan0219 THE END

RHIC/INT Workshop on HBT - jan0220 Bertsch-Pratt projections - data and RQMD (11%  T y cm  0.35 p T = MeV/c)

RHIC/INT Workshop on HBT - jan0221 HBT radii at 2 AGeV

RHIC/INT Workshop on HBT - jan0222 Evolution of (apparent) Shape: Oblate to Prolate Transition from oblate to prolate shape at AGS connects Bevalac observations to SPS Transition in character of flow/expansion: transverse  longitudinal?

RHIC/INT Workshop on HBT - jan0223 HBT: probing freeze-out space-time structure I - Cylindrical sources KK R out R side AGS mapped by E895 (QM99) PRL 84, 2798 (2000) NPA 661, 444c (1999)