An HBT Excitation Function:Experiment E895 at the AGS

Mike Lisa, The Ohio State University

• Motivation• Experiment

• Ebeam Systematics - data and RQMD– 1D midrapidity and E866

– Bertsch-Pratt/Yano-Koonin parameterizations

– x-p correlation, resonances, resolution effects

• Summary

Lawrence Berkeley Lab D. Best, T. Case, K. Crowe, D. Olson, G. Rai, H.-G. Ritter, L. Schroeder, J. Symons, T. Wienold

Brookhaven National Lab S. Gushue, N. Stone

Carnegie Mellon University M. Kaplan, Z. Milosevich, J. Whitfield

Columbia University I. Chemakin, B. Cole, H. Hiejima, X. Yang, Y. Zhang

U.C. Davis P. Brady, B. Caskey, D. Cebra, J. Chance, J. Draper, M. Heffner, J. Romero, L. Wood

St. Mary’s College J. Kintner

Harbin Institute (China) L. Huo, Y. Liu, W. Zhang

Kent State Univeristy M. Justice, D. Keane, H. Liu, S. Panitkin, S. Wang, R. Witt

Lawrence Livermore Lab V. Cianciolo, R. Sotlz

Ohio State University A. Das, M. Lisa, R. Wells

University of Auckland (NZ) D. Krofcheck

Purdue University M. Gilkes, A. Hirsch, E. Hjort, N. Porile, R. Scharenberg, B. Srivastava

S.U.N.Y. Stony Brook N.N. Ajitanand, J. Alexander, P. Chung, R. Lacey, J. Lauret, E. LeBras, B. McGrath, C. Pinkenburg

E895 mission - continuation of EOS missionmap out energy dependence of “all” physics variables

as a function of energy

Large acceptance device with good PID to characterize each event

• Lookout for signs of “anomalous” behavior in Ebeam systematics• QGP threshold at AGS?• take “condensed matter” approach• especially look at low pT

• Thoroughly test existing transport models• Bevalac experience-- easy to tune model with right mix of

wrong physics at one energy

• Continue to establish baseline systematics• how do signals change in “normal” RHI collision

Systematics/meta-analysis suggest approach to maximum AGS energy interesting...

P. Braun-Munzinger and J. Stachel,NPA606, 320 (1996)

B. Hong et al. (FOPI)Proceedings of International Workshop,Poiana Brasov, Romania (1996)

Perhaps some signals only apparent near threshold

D. Rischke, NPA 610, c88 (1996)

Magnitude, position, (existence?) of deviations due to phase transistion unclear

concentrate on data systematics

Proton sidewards flow excitation function

Analysis by H. Liu

• no sharp behavior in sidewards flow• Ebeam systematics powerful test of dynamical models

• some medium effects needed in addition to hadronic scattering

HBT systematics may also be QGP signature

Rischke & GyulassyNPA 608, 479 (1996)

At too-high beam energy, increased timescale signal vanishes as the plasma explodes and cools quickly

Prediction of 3D hydrodynamic model with phase transition

withouttransition

“”

withtransition

c

~ emissiontimescale

A Bevalac TPC meets an AGS beam...

2-year-old artist’s conception Single 8 GeV event in TPC

~ 500k-1M Au+Au collisions measured at 2, 4, 6, and 8 AGeV• continuous coverage with no low-pT threshold• good PID• ~ 1% momentum resolution

lisa:

after this comes the PID picture in portrait mode

lisa:

after this comes the PID picture in portrait mode

- sample contaminated by e- 5% level

• moving PID definition up/down, “reasonable” relaxation of DCA cut, does not change HBT signal

• at higher energy, use of pT cut reduces contamination

Ideally, HBT gives a measure of source size

C k kP k k

P k P k

d x d x x x e

d x d x x x

Q

i k k x x

2 1 21 2

1 2

31

32 1 23

13

2 1 2

2

1

1

2 1 2 1

( , )( , )

( ) ( )

( ) ( )

( ) ( )

~( )

( ) ( )

r rr r

r r

r r

r r

r

r r r r

=⋅

= ± ⋅ ⋅ ⋅∫ ⋅⋅ ⋅ ⋅∫

= ±

⋅ − ⋅ −ρ ρρ ρ

ρ

PionSource ρ( )x

C (Qinv)

Qinv (GeV/c)

1

2

0.05 0.10

Width ~ 1/R

x1,p1

x2,p2

2~ {exp(i x1p1) exp(i x2p2)

+ exp(i x2p1) exp(i x1p2)}

Large acceptance many -

But...phase space meansmost are at large Q

Background (denominator)generated with standardevent-mixing (15 previous)

4 GeV central

)q(B

)q(R)q(C =

single-particle acceptanceeffects eliminated

Finite 2-track resolution (hit merging) leads to suppression of correlation

Track merging/splitting effects removed by requiring >15 well-separated padrow crossings

2-track cut for real and mixed pairs removes low-Q suppression

Coulomb wave integration used for correction

• Gamow function overcorrects

• 5 fm Gaussian spherical source assumed, based on results

• sensitive mainly to RMS

• applied pairwise

• used for both data and RQMD

• E877 uses identical correction; NA49 equivalent

Gamow 5 fm

Kakija et al. (NA49) QM96NPA 610, 248c (1996).

E895 correction roughly appropriate

• still overcorrects at smallest bin

• RQMD - input:• - -- correlation, then corrected ~ same as treating them as 0’s

2 GeV - fit with and without Coulomb

4 GeV - fit with and without Coulomb

6 GeV - fit with and without Coulomb

8 GeV - fit with and without Coulomb

~ logarithmic

Ebeam Ebeam

Mmax Mmax + 50

Mmax M

max + 15

Only - used in HBT analysis

Restrictive cuts actual - multiplicity higher

• Systematics smooth

• Leads to E866 data with similar coverage

• RQMD with or without meanfield reproduces data at higher energies

• 2 GeV may be interesting with more statistics

lisa:

before this comes the 4-panel 1d HBT with fits and 4-panel HBT with RQMD (both in “portrait” file)

lisa:

before this comes the 4-panel 1d HBT with fits and 4-panel HBT with RQMD (both in “portrait” file)

Resolution from pixel-level simulations2

1

22

zpp

zpp

cMeV

x )p%1()113.0ln(038.01113.0 6.13p⎥⎥⎦

⎤

⎢⎢⎣

⎡×+

⎭⎬⎫

⎩⎨⎧ ⎟

⎠⎞⎜

⎝⎛ ⋅⋅+×⋅×=δ

Multiple Coulomb Scatteringdominates resolution for ’s:δpj ~ 1.5-3.5% overall

NOTE: data not corrected forQ-resolution• model results smeared instead

δpx does NOT depend on qx

~ 10 MeV/c q-resolution

1D fits not affected by resolution (1.5-3.5%)

However, not a lot of breathing room.... sensitivity very nonlinear

beam direction

p1 p2

QT

Q

QL

beam direction

p2p1

QT

QS

QO

“Standard” Bertsch-Pratt coordinate system

)qqR2qRqRqRexp(1 longout2ol

2long

2long

2side

2side

2out

2out ⋅⋅−⋅−⋅−⋅−⋅λ+

=)q,q,q(C longsideout

Bertsch-Pratt parameters - what do they measure?

( )

( )( ) ( )t~z~t~x~R

t~z~R

t~x~R

y~R

l2ol

2l

2l

22o

22s

β−⋅β−=

β−=

β−=

=

⊥

⊥

xxx~ −≡

Spatial RMS of source

222s

2o t~RR ⋅β=− ⊥

Can get temporal RMS

• Usually a small difference of large numbers

• emission duration longest at low pT

• 3-4 fm/c greatest seen so far with pions

Measuring size and lifetime with protons at low energy

PRL 71 2863 (1993)

lisa:

this is just to show that lifetimes CAN be measured

lisa:

this is just to show that lifetimes CAN be measured

Qout-Qlong correlations forward and backwards

For present analysis at low pT, near ycm, Rol2 usually consistent with 0

lisa:

before this comes the similar plot from the NA49 thesis (in portrait-mode file)

lisa:

before this comes the similar plot from the NA49 thesis (in portrait-mode file)

3D HBT - 4, 6, 8 AGeVcentral collisions

midrapidity

=)q,q,q(C longsideout

)qqR2

qR

qRqRexp(1

longout2ol

2long

2long

2side

2side

2out

2out

⋅⋅−

⋅−

⋅−⋅−⋅λ+

Performed in ycm frame• Rout Rside

• Rol 0

Projections integrated over30 MeV/c in other components

3D HBT Excitation Function at midrapidityTitle:3panel_central_midrap_0.1pt0.8_fit.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

RQMD reproduces 3D HBT with or without meanfieldTitle:3panel_central_midrap_0.1pt0.8_rqmd.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

3D Excitation Function

• No jumps in any 3D parameter

• no large sensitivity to meanfield

• l parameter in RQMD fits somewhat unstable

large errors indicated

Momentum resolution more impt to 3D correlation functions

• included in all model comparisons

Long-lived resonance contribution in RQMD

• most impt at low pt and midrapidity

Any strong variations somewhere on phase space? study/test HBT systematics in small chunks

• 10% most central collisions• (not acceptance corrected)

Title:phasespace_studied.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

lisa:

this has the FOUR low pt rapidity windows for the 4 GeV

lisa:

this has the FOUR low pt rapidity windows for the 4 GeV

Scanning rapidity with low pT 4 GeV central dataTitle:4panel_4gev_lowpt_fits.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

lisa:

this is the 4panel 4gev plot (fits)

lisa:

this is the 4panel 4gev plot (fits)

Title:4panel_4gev_lowpt_rqmd.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

lisa:

this is the 4panel 4gev plot (RQMD)

lisa:

this is the 4panel 4gev plot (RQMD)

RQMD follows trends very well (with or without field)

Title:3panel_4gev_hipi_fits.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

4 GeV central collisions medium pT

Title:3panel_4gev_hipi_rqmd.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

Data vs RQMD - 4 GeV central medium pT

Title:3panel_8gev_lowpt_fits.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

8 GeV central collisions low pT

Title:3panel_8gev_lowpt_rqmd.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

Data vs RQMD - 8 GeV central low pT

Title:3panel_8gev_hipi_fits.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

8 GeV central collisions medium pT

Title:3panel_8gev_hipi_rqmd.epsCreator:HIGZ Version 1.23/09Preview:This EPS picture was not savedwith a preview included in it.Comment:This EPS picture will print to aPostScript printer, but not toother types of printers.

Data vs RQMD - 8 GeV central medium pT

Particles outputby RQMD

Sources of -

ρ’

ρ’

Particles outputby RQMD

Sources of -

Effect of manual decays

Position-Momentum correlations

• Rescattering, decays, decompression, lead to correlation between x and p

• Strength of correlation grows with pT

• Leads to smaller apparent source parameters in HBT measurements

RQMD v2.3

Slightly stronger correlation with meanfield in RQMD

TT

TTpx px

pxCos

⋅⋅=−

rr)(ϕ

Find x-p vs pT

independent ofimpact parameter

Explicit removal of x-p correlations

RQMDx1, p1

x2, p2

...Pratt CRAB code

Scramblex1, p420

x2, p237

...

(xi xi, pi pj)

0)(Cos px → −

• pairs more spatially separated on average reduced correlation weighting

• Exactly same points used same bin-to-bin fluctuations

x-p correlations affect higher pT pairs

Dynamic -emitting source

• Static (non-longitudinally expanding) source Ysource = 0• Boost-invariant expansion Ysource = Y

• timescale decreases slightly at higher energy (3-4 fm/c at SPS)• locally spherical source with energy-independent scale

Summary• HBT excitation function measured over large region of phase space

• present analysis restricted to low pT

• No surprising jumps in HBT systematics• but would like more statistics at 2 AGeV

• Systematics consistent with measurements at max AGS energy

• standard hadronic model (RQMD) reproduces data well• No large sensitivity to meanfield effects

• Flow effects affect fit radii at larger pT• E895 low pT measurements sensitive to geometry

• MCS-dominated resolution reduces measured 3D radii by as much as 20%

• Bertsch-Pratt• Rout ~ Rside

• decreases with energy due to resonances and resolution

• Yano-Koonin• locally spherical with non-zero lifetime

• non-boost-invariant longitudinal flow of source seen

Reconstructedreaction planeflat in lab

Dispersions (andcorrections) getlarge for 8 AGeV,where flow is small

Plots by C. Pinkenburg

Reaction plane reconstructed by method of Danielewicz/Odyniec

Systematics/meta-analysis suggest approach to maximum AGS energy interesting...

P. Braun-Munzinger and J. Stachel,NPA606, 320 (1996)

B. Hong et al. (FOPI)Proceedings of International Workshop,Poiana Brasov, Romania (1996)