 HBT in STAR

advertisement
 HBT in STAR
Mike Lisa*, Ohio State University
• “Traditional” HBT results: 200 GeV vs 130 GeV Au+Au collisions
• New experimental developments
• Bowler/Sinyukov Coulomb correction
• Pushing the systematics – azimuthally-sensitive HBT
• Results from 130, 200 GeV
• Interpreting asHBT results
• Hydro, Hydro+RQMD, BlastWave
• Conclusions
* Work of: Mercedes López-Noriega, Dan Magestro, Randy Wells
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
1
Reminder: p-space observables reproduced by
dynamical models, x-space not
STAR
HBT
13 February 2003
Heinz & Kolb, hep-ph/0204061
Winter Workshop - Breckenridge CO
2
“Standard” HBT:130 vs 200 GeV
• Essentially identical analysis carried out
for 200 GeV data as published 130 GeV
130
GeV
200
GeV
STAR, QM02
• (exact centrality definition, etc, being finalized)
• New: centrality dependence of
pT dependence
• mostly an overall scaling of R
• Little change with increased energy
• Transverse size slightly bigger @ low pT?
• Similar pT-dependence
• Ro/Rs problem persists
• Longitudinal radius: no change
• Sinyukov fit R L   0 mT :
T
  0cent  10 fm / c,  0periph  7.5 fm / c
• Lower-energy RHIC run needed
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
3
Recent analysis developments I
• RHIC analyses used “standard” Coulomb
correction, used by previous experiments
• “apples-to-apples” extension of systematics
A (q )
 N  (1    exp(R ij2qiq j ))
B(q)  K coul (q)
f 177c (2002)
STAR, QM01; NPA698,
• Effects of “diluting” CC (resonances, etc)
explored & reported @ QM01
• Ro affected most
K coul (q)  1  f (K coul (q)  1)
0  f  1
• Y2 data: dilution effect vs pT, centrality
• RO/RS ~ 10-15% increase when f =  ≈ 0.5
• More correct CC method of Bowler (’91)
& Sinyukov (’98), used by CERES (’02)
• Similar effect on radii as dilution with f = 



 
No Coulomb CC
“Standard”
Coulomb CC
In “right” direction, but does
not solve RO/RS problem
A (q )
 N  1    K coul (q)  1  exp(R ij2qiq j  1
B(q)
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
4
“Traditional” HBT results ~ stable
• So what’s the problem with theory?
– Timescale too long?
– Hadronic phase overestimated?
– HBT technique not understood?
• Can (HBT and other) data be consistently understood?
– What are characteristics of freezeout source @ RHIC?
• Parameterization of freezeout
• Explore with further systematics– non-central collisions
– Azimuthally-sensitive HBT
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
5
Noncentral collision dynamics
hydro evolution
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
• Dynamical models:
• x-anisotropy in entrance channel
 p-space anisotropy at freezeout
• magnitude depends on system
response to pressure
STAR
HBT
13 February 2003
Heinz & Kolb, hep-ph/01110756
Winter Workshop - Breckenridge CO
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.0 GeV/c
• system response  EoS
• early thermalization indicated
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
STAR
HBT
13 February 2003
Winter Workshop
- Breckenridge
Teaney,
Lauret, & CO
Shuryak, nucl-th/0110037
7
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
hydro only
hydro+hadronic rescatt
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
• significant (bad) effect on HBT radii
STAR
HBT
13 February 2003
STAR
PHENIX
calculation:
Winter Workshop - Breckenridge
COSoff, Bass, Dumitru, PRL 2001
8
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
• significant (bad) effect on HBT radii
• related to timescale? - need more info
STAR
HBT
13 February 2003
Winter WorkshopTeaney,
- Breckenridge
CO& Shuryak, nucl-th/0110037
9
Lauret,
Effect of dilute stage
hydro evolution
later hadronic stage?
• hydro reproduces v2(pT,m) (details!)
in-planeextended
@ RHIC for pT < ~1.5 GeV/c
• system response  EoS
• early thermalization indicated
• dilute hadronic stage (RQMD):
• little effect on v2 @ RHIC
• significant (bad) effect on HBT radii
• related to timescale? - need more info
• qualitative change of freezeout shape!!
• important piece of the puzzle!
STAR
HBT
13 February 2003
out-of-plane-extended
Winter WorkshopTeaney,
- Breckenridge
CO& Shuryak, nucl-th/0110037
10
Lauret,
Indirect indications of x-space anisotropy @ RHIC
STAR, PRL 87 182301 (2001)
• v2(pT,m) globally well-fit by
hydro-inspired “blast-wave”
T (MeV)
dashed
solid
135  20
100  24
0(c)
0.52  0.02 0.54  0.03
a (c)
0.09  0.02 0.04  0.01
S2
STAR
HBT
0.0
13 February 2003
0.04  0.01
temperature, radial flow
consistent with fits to spectra 
anisotropy of flow boost
spatial anisotropy (out-of-plane extended)
Winter Workshop - Breckenridge CO
11
Possible to “see” via HBT relative to reaction plane?
fp=90°
• for out-of-plane-extended source, expect
• large Rside at 0
2nd-order
• small Rside at 90
oscillation
Rside (small)
Rside (large)
fp=0°
2
Rs [no flow expectation]
fp
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
12
Need a model of the freezeout- BlastWave
BW: hydro-inspired parameterization of freezeout
• longitudinal direction
• infinite extent geometrically
• boost-invariant longitudinal flow
• Momentum space
• temperature T
• transverse rapidity boost
 (r , f )  ~
r    cos( 2f ) 
s
0
a
RY
b
RX
• coordinate space
• transverse extents RX, RY
• freezeout in proper time 
• evolution duration 0
• emission duration 
7 parameters describing freezeout
    0 2 
dN

~ exp  
2 
d
 2 
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
13
BlastWave fits to published RHIC data
• pT spectra constrain (mostly) T, 0
central
midcentral
peripheral
• (traditional) HBT constrains R, 0, 
– (fit to STAR-HBT only)
• v2(pT,m) constrains a, RX/RY
Central
Midcentral
Peripheral
T (MeV)
108  3
106  2
95  3
0
0.88  0.01
0.87  0.01
0.81  0.02
a
0.06  0.01
0.05  0.01
0.04  0.01
RX (fm)
12.9  0.4
10.2  0.5
8.0  0.1
RY (fm)
12.8  0.4
11.8  0.6
10.0  0.2
0 (fm/c)
8.9  0.3
7.4  0.7
6.5  0.4
 (fm/c)
0.0  9.0
0.8  1.8
0.09  0.6
2 / ndf
80.5 / 101
153.7 / 92
74.3 / 68
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
14
Minbias observations at 130 GeV
“raw”
•  flat within errors
• Significant (& “allowed”) oscillations
observed in HBT radii
• RP/binning correction* significant
• produces RL2 oscillation from
“nowhere”? – is it real?
preliminary
2
RO
after RP/binning
correction
R S2
2
R OS
(*) [Heinz, Hummel, MAL, Wiedemann PRC 044903 (2002)]
STAR
HBT
13 February 2003
- Breckenridge
CO
R. Wells,Winter
PhD Workshop
thesis, Ohio
State, 2002
R 2L
15
asHBT versus BlastWave
• Minbias asHBT well-reproduced with
same BlastWave from minbias v2(pT,m)
• Ry = 11.4 fm
s2 = 0.045
• Rx = 10.8 fm
• 0 = 8.3 fm/c
•  = 0 ( → ~1.5 fm/c w/ Bowler CC))
• Consistent picture – convincing argument
for flow scenario
• Saturation ????
Au+Au 130 GeV
minbias
• asHBT: geometry dominates dynamics
• Source out-of-plane extended
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
16
Azimuthal HBT: hydro predictions
RHIC (T0=340 MeV @ 0=0.6 fm)
• Out-of-plane-extended source (but flips
with hadronic afterburner)
• flow & geometry work together to
produce HBT oscillations
• oscillations stable with KT
(note: RO/RS puzzle persists)
STAR
HBT
13 February 2003
& Kolb, hep-ph/0204061
Winter Workshop - Breckenridge Heinz
CO
17
Azimuthal HBT: hydro predictions
RHIC (T0=340 MeV @ 0=0.6 fm)
• Out-of-plane-extended source (but flips
with hadronic afterburner)
• flow & geometry work together to
produce HBT oscillations
• oscillations stable with KT
“LHC” (T0=2.0 GeV @ 0=0.1 fm)
• In-plane-extended source (!)
• HBT oscillations reflect competition
between geometry, flow
• low KT: geometry
• high KT: flow
STAR
HBT
sign flip
13 February 2003
& Kolb, hep-ph/0204061
Winter Workshop - Breckenridge Heinz
CO
18
Further systematics in Au+Au 200 GeV
Centrality cuts
kT-integrated
12 f bins
kT cuts
Mid-central
4 f bins
• Oscillation phases: out-of-plane extended source
• Source size increases, oscillations decrease with increasing centrality
• 0th and 2nd harmonics only
• Average size (0th harmonic) falls with kT
• Mild evolution of 2nd harmonic with kT
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
19
“Grand summary”
Fourier Coefficients
n=0
n=2
• Centrality- and kT- dependence
of the f-dependence summarized
concisely by Fourier coefficients
2

 R  pT ,f   cosnf 
R  ,n pT    2
R p ,f   sin nf 

  T
2
  o, s, l
  os
central
midcentral
peripheral
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
20
“Grand summary”
Fourier Coefficients
n=0
n=2
• Centrality- and kT- dependence of
the f-dependence summarized
concisely by Fourier coefficients
2

 R  pT ,f   cosnf 
R  ,n pT    2
R p ,f   sin nf 

  T
2
  o, s, l
  os
• Hydro predictions (*): b = 6 fm
“RHIC” source
“LHC” (IPES) source
central
midcentral
peripheral
• Scale of homogeneity lengths off
• Phase/magnitude of oscillations
from “RHIC” source in the ballpark
• significance ?
STAR
HBT& Kolb,
(*) Heinz
hep-ph/0204061
13 February
2003
Winter Workshop - Breckenridge CO
21
Evolution of spatial anisotropy
• Extraction of full freezeout
scenario underway
• Timescales short, flow dominant
• Out-of-plane-extended freezeout
geometry for all centralities
– further constraint on evolution
timescale (and dynamic models!!)
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
22
• HBT systematics from 200 GeV similar to 130 GeV
– New, more correct CC ~ 10-15% effect on Ro
• Dynamic models (hydro, hydro+RQMD)
– soft p-space signals 
– soft x-space signals X
– worse agreement with hadronic stage included
• BlastWave – toy model, but…
– consistent framework to extract main features of freezeout
– can initial state effects describe all signals as consistently?
– in particular, short timescales 0,  -- perhaps the problem
• asHBT
STAR
HBT
– probes details of anisotropic geometry/flow interplay
– consistent w/ BW expectations (& further constrains f.o. picture)
• (ditto for non-identical particle correlations)
– f.o. source out-of-plane extended
• (model-dependent in principle, but robust in fact)
• another constraint on evolution duration
– detailed systematics from 200 GeV run
• hydro suggests this can reveal important physics
• tighter model constraints
• 2003
new level of presentation
(FCs) for
asHBT
13 February
Winter Workshop
- Breckenridge
CO
23
Backups follow
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
24
Next slides
• Show Fabrice’s BW fits of published data
• Show BW vs Randy’s stuff
– Rx=Ry and rho_a = 0 cases too
• Show Dan’s 3 centrality bins with 12 phi bins
– 2nd order harmonics only
• Show Dan’s centrality/kT dependence
• Show “1-page summary,” with Heinz/Kolb on top
• Show Dan’s figure 4
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
25
Symmetries of the emission function
I. Mirror reflection symmetry w.r.t. reactionplane
(for spherical nuclei):
S( x, y, z, t ;Y , KT , )  S( x, y, z, t ;Y , KT ,)

~
x ~
x (Y , KT , )  1  ~
x ~
x (Y , KT ,)
with
1  (1)
 2   2
II. Point reflection symmetry w.r.t. collision center
(equal nuclei):
S( x, y, z, t ;Y , KT , )  S( x, y, z , t ;Y , KT ,   )
 ~
x ~
x (Y , KT , )  2  ~
x ~
x (Y , KT ,   )
with
STAR
HBT
2  (1)
13 February 2003
 0    0
Winter Workshop
Breckenridge CO
Heinz, Hummel,
MAL, -Wiedemann,
PRC66 044903 (2002)
26
Fourier expansion of HBT radii @ Y=0
Insert symmetry constraints of spatial correlation tensor into Wiedemann relations
and combine with explicit -dependence:
Rs2 (f)
 Rs2,0 
2   n  2, 4,6,... Rs2, n  cos(nf)
Ro2 (f)
 Ro2,0 
2   n  2, 4,6,... Ro2, n  cos(nf)
2
2   n  2, 4,6,... Ros
, n  sin( nf)
2
Ros
(f) 
Rl2 (f)

Rl2,0 
2   n  2, 4,6,... Rl2,n  cos(nf)
Rol2 (f) 
2   n 1,3,5,... Rol2 , n  cos(nf)
Rsl2 (f)
2   n 1,3,5,... Rsl2 , n  sin( nf)

Note: These most general forms of the Fourier expansions for the HBT radii
are preserved when averaging the correlation function over a finite,
symmetric window around Y=0.
Relations between the Fourier coefficients reveal interplay between flow and
STAR geometry, and can help disentangle space and time
HBT
13 February 2003
Winter Workshop
Breckenridge CO
Heinz, Hummel,
MAL, -Wiedemann,
PRC66 044903 (2002)
27
Bowler CoulombCorrection vs +Work in progress: finalizing resolution effects, etc.
Low kT
STAR
HBT
13 February 2003
High kT
Winter Workshop - Breckenridge CO
28
“Traditional HBT” - cylindrical sources
C(qo , qs , ql )  1    e 
Decompose q into components:
qLong : in beam direction
qOut : in direction of transverse momentum
qSide :  qLong & qOut
K
 q o2 R o2  q s2 R s2  q l2 R l2
 
 
  

~2
K  ~
x out   t 

2 
2
~
R s K  x side K

~2
2
Rl K  ~
x long  l t
R o2

 

K
 
  

K
x out , x side   x, y 
Rout
Rside
(beam is into board)
STAR
HBT
13 February 2003
~
xx x
d 4 x  S( x, K )  f ( x )

f 
4
d
 x  S( x, K )
Winter Workshop - Breckenridge CO
29
Anisotropic sources Six HBT radii vs f
side
•Source in b-fixed system: (x,y,z)
•Space/time entangled in
pair system (xO,xS,xL)
R s2
~2
~2
y
K
fp
x
 x sin f  y cos f  ~
x~y sin 2f
2
out
2
b
~
~
~
R o2  ~
x 2 cos2 f  ~y 2 sin 2 f  2 t 2  2 ~
x t cosf  2 ~y t sin f  ~
x~y sin 2f
~
~
R l2  ~z 2  2L ~z t  2L t 2
~
~
2
R os
 ~
x~y cos 2f  12 ( ~y 2  ~
x 2 ) sin 2f   ~
x t sin f   ~y t cosf
~
~
~
~
2
R ol
( ~
x~z  L ~
x t ) cosf  ( ~y~z  L ~y t ) sin f   ~z t  L t 2
~
~
R sl2  ( ~y~z  L ~y t ) cosf  ( ~
x~z  L ~
x t ) sin f
• explicit
and implicit (xx(f)) dependence on f
STAR
HBT
!
13 February
2003266 (1998). Winter Workshop - Breckenridge CO
Wiedemann,
PRC57
~
xx x
d 4 x  f ( x, K )  q( x )

q 
4
d
 x  f ( x, K)30
Recent analysis developments II
Quick slide on pT vs kT cuts
if Mercedes gets me a plot…
Otherwise, forget it..
Not that important
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
31
Need a model of the freezeout- BlastWave
BW: hydro-inspired parameterization of freezeout
• longitudinal direction
• infinite extent geometrically
• boost-invariant longitudinal flow
• Momentum space
• temperature T
• transverse rapidity boost
 (r , f )  ~
r    cos( 2f ) 
s
0
a
RY
b
RX
• coordinate space
• transverse extents RX, RY
2
• freezeout
in
proper
time
f  2



r
cos
f
r
sin
s
   0 s 
 
• ~revolution
duration
RY 
 RXduration
  
• emission
7 parameters describing freezeout
1
2
1  exp (~
r  1)/ as  0  
dN
( ~
r)

~ exp  
2 
d
 2 
STAR
HBT
13 February 2003
Winter Workshop - Breckenridge CO
32
Download