RHIC/INT Workshop on HBT - jan02
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The low-energy end of the HBT excitation functionMike 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 - jan02
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Outline
• Definition and importance of correlation function• Definitions of out, side, long… • Central collisionss systematics
• pT 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 - jan02
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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 -
• ~105 events at 2, 4, 6, 8 AGeV
RHIC/INT Workshop on HBT - jan02
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Evolution of the BP and YKP fit parameters
• Increased production of long-lived --emitters fall in
• Strong evolution of Rs (R) with beam energy
• Hadronic model with or without meanfield underpredicts (apparent) geometric size at low beam energy
E895 Collab, PRL 84 2798 (2000)
RHIC/INT Workshop on HBT - jan02
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Evolution of systematics - data and model
• Observed evolution of systematics not reproduced by model
• Dynamics driving RS(mT) may not depend on collision energy within RQMD
RHIC/INT Workshop on HBT - jan02
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Testing the model at the SPS
• For -...
• Model underpredicts apparent size below 10 AGeV...
• overpredicts size at 158 AGeV
•
• Extrapolation to RHIC???
NA44 RQMD
Rout 4.88 0.21 6.96 0.14
Rside 4.45 0.32 6.23 0.20
Rlong 6.03 0.35 7.94 0.21
I.G. Bearden et al (NA44)PRC58, 1656 (1998)D. Hardtke, Ph.D. thesis (1997)
RHIC/INT Workshop on HBT - jan02
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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 - jan02
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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=27 fm: ~ 35% reduction in RMS
RHIC/INT Workshop on HBT - jan02
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Probing freeze-out space-time structure for b0
•Source in b-fixed system: (x,y,z)•Space/time entangled in
pair system (xO,xS,xL)
out
b
K
side
x
y
U. Wiedemann, PRC 57, 266 (1998)MAL, U. Heinz, U. Wiedemann PLB 489, 287 (2000)
φβ−−φβ−=
ββ+β−φβ−+φβ−=
φβ−φβ+φ−+φ=
β+β−=
φ−φβ−φβ−β+φ+φ=
φ−φ+φ=
⊥⊥
⊥⊥
⊥⊥⊥
sin)x~t~z~x~(cos)y~t~z~y~(R
t~z~t~sin)y~t~z~y~(cos)x~t~z~x~(R
cosy~t~sinx~t~2sin)x~y~(2cosy~x~R
t~z~t~2z~R
2siny~x~siny~t~2cosx~t~2t~siny~cosx~R
2siny~x~cosy~sinx~R
LL2sl
2LLL
2ol
22212
os
22LL
22l
2222222o
22222s
! y~x~ etc. themselves functions of
RHIC/INT Workshop on HBT - jan02
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Simplifying assumption at AGS: minimal effects of flow at very low pT
out
b
K
side
x
y
U. Wiedemann, PRC 57, 266 (1998)MAL, U. Heinz, U. Wiedemann PLB 489, 287 (2000)
(several terms vanish @ pT = y = 0)
( ) ( )( ) ( )( )
φ⋅−=
φ⋅=
β+=
φ−+=
++φ−+=
β+++φ−−= ⊥
sinz~x~R
cosz~x~R
t~z~R
2sinx~y~R
x~y~2cosx~y~R
t~x~y~2cosx~y~R
2sl
2ol
22L
22l
22212
os
222122
212
s
22222122
212
o
y~x~ etc are now constants
RHIC/INT Workshop on HBT - jan02
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1st-harmonic oscillations: spatial tilt
angle S
(Beam)
Coordinate space!
x
y
z
s
2nd-harmonic oscillations fromelliptical transverse shape
b
2y~
2x~
x
y
( ) ( )( ) ( )( )
φ⋅−=
φ⋅=
β+=
φ−+=
++φ−+=
β+++φ−−= ⊥
sinz~x~R
cosz~x~R
t~z~R
2sinx~y~R
x~y~2cosx~y~R
t~x~y~2cosx~y~R
2sl
2ol
22L
22l
22212
os
222122
212
s
22222122
212
o
First-order information in HBT()
RHIC/INT Workshop on HBT - jan02
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Data: - correlation functionsAu(4 AGeV)Au, b4-8 fm
• 6 components to radius tensor: i, j = o,s,l
1D projections, =45°
2D projections
( ) ( )φ−⋅φ+=φ2ijji Rqq
e1),q(Cr
lines: projections of 3D Gaussian fit
out side long
C(q
)
E895, PLB 496 1 (2000)
RHIC/INT Workshop on HBT - jan02
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Cross-term radii Rol, Ros, Rsl quantify “tilts” in correlation functions
fit results to correlation functions
Lines: Simultaneous fit to HBT radiito extract underlying geometry
RHIC/INT Workshop on HBT - jan02
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Images of --emitting sources (scaled ~ x1014)
3 fm
x ’
y
2 AGeV
x
zS=47°
x ’
y
4 AGeV
x
zS=37°
x ’
y
6 AGeV
x
zS=33°
Large, positivetilt angles
35.1x~
y~
2
2
≈′
similar to naïveoverlap: b~5 fm
RHIC/INT Workshop on HBT - jan02
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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 (f
m)
x (fm)
+ 6 AGeV
pion momentum anisotropies due toreflection from flowing baryons
(N N)
tilt reflects x-space structureof proton flowBass et al [PLB 302 381 (93)]:
RHIC/INT Workshop on HBT - jan02
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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 calcultedby hydrodynamics
RHIC/INT Workshop on HBT - jan02
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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 - jan02
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Bertsch-Pratt projections - data and RQMD(11% T ycm0.35 pT = 0.1-0.3 MeV/c)
RHIC/INT Workshop on HBT - jan02
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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 - jan02
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HBT: probing freeze-out space-time structure I - Cylindrical sources
K
( ) ( ) ( )( ) ( )( ) ( ) ( )Kt~x~KR
Kx~KR
Kt~x~KR
2llong
2l
2side
2s
2out
2o
rr
rr
rr
β−=
=
β−= ⊥ xxx~ −≡
∫∫
⋅⋅⋅
≡)K,x(Sxd
)x(f)K,x(Sxdf
4
4
RoutRside
( ) ( )y,xx,x sideout ≠
HBT @ AGS mappedby E895 (QM99)
PRL 84, 2798 (2000)NPA 661, 444c (1999)