N.N. Ajitanand, J. Alexander, D. Best, P. Brady, T. Case, B. Caskey , D. Cebra,

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


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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


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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


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Bertsch-Pratt projections(11% T ycm0.35 pT = 0.1-0.3 MeV/c)


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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)


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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


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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)


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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


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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


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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


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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


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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()


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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)


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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


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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


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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)]:


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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


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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?


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THE END


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Bertsch-Pratt projections - data and RQMD(11% T ycm0.35 pT = 0.1-0.3 MeV/c)


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HBT radii at 2 AGeV


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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?


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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)

Documents

N.N. Ajitanand, J. Alexander, D. Best, P. Brady, T. Case, B. Caskey , D. Cebra,