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 mission
map 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...
B. Hong et al. (FOPI)
Proceedings of International Workshop,
Poiana Brasov, Romania (1996)
P. Braun-Munzinger and J. Stachel,
NPA606, 320 (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
Prediction of 3D hydrodynamic model with phase transition
with
transition
~ emission
timescale
ec
without
transition
“e”
Rischke & Gyulassy
NPA 608, 479 (1996)
At too-high beam energy, increased timescale signal
vanishes as the plasma explodes and cools quickly
lisa:
A Bevalac TPC meets an AGS beam...
after this comes
the PID picture in
portrait mode
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
p- 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
x1,p1
Pion
Source  (x)
y2 ~ {exp(i x1p1) exp(i x2p2)
+ exp(i x2p1) exp(i x1p2)}
 
 
P( k , k )
C2 ( k1 , k 2 )   1 2
P( k1 )  P ( k 2 )
   


i( k 2  k1 )( x 2  x1 )
d x1  d x 2  ( x1 )  ( x 2 )  e
 1 


3
3
d
x

d
x


(
x
)


(
x

1
2
1
2)
3
 2
~
 1   ( Q)
3
C (Qinv)
x2,p2
Width ~ 1/R
2
1
0.05
0.10
Qinv (GeV/c)
Large acceptance many p-
But...phase space means
most are at large Q
Background (denominator)
generated with standard
event-mixing (15 previous)
R (q )
C(q) 
B(q)
single-particle acceptance
effects eliminated
4 GeV central
Finite 2-track resolution (hit merging) leads to
suppression of correlation
2-track cut for real and mixed pairs
removes low-Q suppression
Track merging/splitting effects
removed by requiring >15 wellseparated padrow crossings
Coulomb wave integration used for correction
• Gamow function
overcorrects
• 5 fm s 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
Kakija et al. (NA49) QM96
NPA 610, 248c (1996).
Gamow
5 fm s
E895 correction roughly appropriate
• RQMD p- input:
• p- -p- correlation, then corrected ~ same as treating them as p0’s
• still overcorrects at
smallest bin
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
Mpmax  Mpmax +
15
Only p- used in HBT
analysis
Restrictive cuts 
actual p- multiplicity
higher
lisa:
•
before this comes the 4panel 1d HBT with fits and
Systematics
4-panel HBT with RQMD
smooth(both in “portrait” file)
• 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
Resolution from pixel-level simulations
1
2

 2
p 
p 
2
MeV
p x  13.6
 0.113   1  0.038  ln(0.113  )   (1%  p) 
c
pz 
p z 



~ 10 MeV/c q-resolution
Multiple Coulomb Scattering
dominates resolution for p’s:
pj ~ 1.5-3.5% overall
NOTE: data not corrected for
Q-resolution
• model results smeared instead
px does NOT depend on qx 
1D fits not
affected by
resolution
(1.5-3.5%)
However, not a lot
of breathing
room....
sensitivity very
nonlinear
“Standard” Bertsch-Pratt coordinate system
C(qout , qside, qlong ) 
2
2
2
2
2
2
2
1    exp(R out
 q out
 R side
 qside
 R long
 q long
 2R ol
 q out  q long )
Q
QT
QL
p1
p2
QT
QS
p1
beam direction
QO
p2
beam direction
Bertsch-Pratt parameters - what do they measure?
2
Rs
2
~
 y
2
Ro
2
~
~
 x   t 
2
Rl
2
~
~
  z  l t 
2
R ol
~
~
~
~
 x   t    z  l t 
Spatial RMS of source
R o2
 R s2
 2
~2
 t
Can get temporal RMS
• Usually a small difference
of large numbers
• emission duration longest
at low pT
~
xx x
• 3-4 fm/c greatest seen so
far with pions
lisa:
Measuring size and lifetime with protons at low energy
this is just to show
that lifetimes CAN be
measured
PRL 71 2863 (1993)
lisa:
Q -Q
correlations forward and backwards
before this comes
similar
out thelong
plot from the NA49 thesis (in
portrait-mode file)
For present analysis at low pT, near ycm, Rol2 usually consistent with 0
3D HBT - 4, 6, 8 AGeV
central collisions
midrapidity
C(q out , q side , q long ) 
2
2
2
2
1    exp(  R out
 q out
 R side
 q side
2
2
 R long
 q long
2
 2R ol
 q out  q long )
Performed in ycm frame
• Rout Rside
• Rol  0
Projections integrated over
30 MeV/c in other components
3D HBT Excitation Function at midrapidity
Title:
3panel_c entral_midrap_0.1pt0.8_fit.eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
RQMD reproduces 3D HBT with or without meanfield
Title:
3panel_c entral_midrap_0.1pt0.8_rqmd.eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes 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
Title:
phasespac e_studied.eps
Creator:
HIGZ Version 1.23/09
Prev iew :
This EPS picture w as not s av ed
w ith a preview inc luded in it.
Comment:
This EPS picture w ill print to a
Pos tSc ript printer, but not to
other ty pes of printers.
lisa:
this has the FOUR low pt
rapidity windows for the 4 GeV
• 10% most central collisions
• (not acceptance corrected)
Scanning rapidity with low pT 4 GeV central data
Title:
4panel_4gev_low pt_fits .eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
lisa:
this is the 4panel
4gev plot (fits)
RQMD follows trends very well (with or without field)
Title:
4panel_4gev_low pt_rqmd.eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
lisa:
this is the 4panel 4gev
plot (RQMD)
4 GeV central collisions medium pT
Title:
3panel_4gev_hipi_fits .eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
Data vs RQMD - 4 GeV central medium pT
Title:
3panel_4gev_hipi_rqmd.eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
8 GeV central collisions low pT
Title:
3panel_8gev_low pt_fits .eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
Data vs RQMD - 8 GeV central low pT
Title:
3panel_8gev_low pt_rqmd.eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
8 GeV central collisions medium pT
Title:
3panel_8gev_hipi_fits .eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
Data vs RQMD - 8 GeV central medium pT
Title:
3panel_8gev_hipi_rqmd.eps
Creator:
HIGZ Version 1.23/09
Preview :
This EPS picture w as not saved
w ith a preview included in it.
Comment:
This EPS picture w ill print to a
PostScript printer, but not to
other ty pes of printers .
Particles output
by RQMD
Sources of
p-
h L,S,X
f
D
D

h’ w
Particles output
by RQMD
h L,S,X
f
D
D
Sources of p-

h’ w
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
 
xT  pT
Cos ( x  p ) 
xT  pT
Find fx-p vs pT
independent of
impact parameter
Explicit removal of x-p correlations
RQMD
x1, p 1
x2, p 2
...
Pratt CRAB code
Scramble
x1, p420
x2, p237
...
(xi xi, pi pj)
Cos(x p )  0
• 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 p-emitting source
• Static (non-longitudinally expanding) source  Ysource = 0
• Boost-invariant expansion  Ysource = Yp
• 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
Reaction plane
reconstructed by method
of Danielewicz/Odyniec
Reconstructed
reaction plane 
flat in lab
Dispersions (and
corrections) get
large for 8 AGeV,
where flow is small
Plots by C. Pinkenburg
Systematics/meta-analysis suggest approach
to maximum AGS energy interesting...
B. Hong et al. (FOPI)
Proceedings of International Workshop,
Poiana Brasov, Romania (1996)
P. Braun-Munzinger and J. Stachel,
NPA606, 320 (1996)