Transcript HBT puzzle, a puzzle approaching a new world

HBT with UrQMD
---two-pion correlation
by Qingfeng Li @ FIAS,
(AvH fellow, Host: Horst Stoecker)
Closely cooperate with: Marcus Bleicher, Xianglei Zhu, H. Appelshaeuser
Horst Stoecker, Hannah Petersen
Also thanks to: UrQMD-group, NA49, NA57,CERES-Collaborations
M. Lisa, S. Pratt, T. Humanic, Nu Xu
Outline





HBT? What’s HBT?
UrQMD Model Calculations.
HBT puzzle(s)
Model explanations on the HBT puzzle
Summary and outlook
Key words: HBT puzzle, Corona effect, potentials, resonance decay
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What’s HBT?



HBT=Robert Hanbury-Brown and Richard Q. Twiss
What did they do?
In 1950’s, in order to measure stellar radii through the
angle subtended by nearby stars, Robert invited Richard to
develop the mathematical theory of intensity interference.
They found by astro-observation that two-photons
arriving
R=6 fm
to the correlators behaved as a consequence of B-E
statistics.
In 1959, in order to discover the ρ0 resonance (by means of
ρ0-+), Goldhaber etc, performed an experiment in
Berkeley (but failed), however, they found an unexpected
angular correlation among identical pions! Which were also
explained by the B-E. What’s more, theyQ (MeV/c)
parameterized the
observed correlation as:
C(Q2)=1+exp(-Q2r2)
2.0
1.8
C(Q)
1.6

1.4
1.2
1.0
0.0
0.1
0.2
0.3
0.4
0.5
Which decided the track of subsequent HBT research in nuclear physics.
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What’s the ‘crucial’ goal of high
energy HICs?
 The new phase: QGP from QCD
theory
 How to detect it?
 The relative ‘direct’ approach is
to detect the electromagnetic
radiation which it emits, BUT,
with a huge amount of noise.
 J/ suppression; Strangeness
enhancement; energy loss of
hard partons; density effect on
vector mesons;DCC (disoriented
chiral condensates ); etc, etc…
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Why the HBT technique is
important to probe the QGP?
 We know, the transition can only take place
in a very small space-time.
 Correlations of two final-state particles are
closely linked to the space-time of the
region of homogeneity (the relevant volume
for particles of a given velocity, not the entire
source, which can give partly the message
of the source.
 A non-trivial structure in the excitation
function of HBT might be seen IF there is a
(phase) transition.
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HBT shows the message at freezeout
mb
ulo
Co
HBT
r i ng
e
t ad ro n i
t
z
a
a H
a
c
t n
QGP i
s
o
e
o r
n
o
R
F-O
Ur
QM
D
C
F-S
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Why do we use UrQMD model?
 Hydronamics failed to explain the decrease
of HBT radii with kT (see, e.g. nucl-th/0305084)
 Might be due to the Corona effect at late
stage?
 Transport model, considering the full
rescattering process, might throw light on
what other mechanisms generate the
observed kT-dependence of the HBT radii
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What’s the HBT technique?
The quotient of two-particle and one-particle spectra
d 6N
dp13 dp23
C ( q, K )  3
d N d 3N
dp13 dp23
q  p1  p2
K  ( p1  p2 ) / 2
The two-particle correlator C(q,K) is related to the emission function S(x,K),
Which is the Wigner phase-space density of the particle emitting system
and can be viewed as the probability that a particle with average momentum K
is emitted from the space-time point x in the collision region.
For identical bosons,
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C (q, K )  1 
|  d 4 xS ( x, K )eiq x |2
|  d 4 xS ( x, K ) |2
Qingfeng Li for Palaver 2006
HBT-a very simple picture
From
Braz. J. Phys. vol.35 no.1 São Paulo Mar. 2005
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Gaussian Parameterization
 To better understand the three-dimensional
spatio-temporal source distribution.
Although the realistic source deviates from
a standard Gaussian, it provides the
standard description of experimental data.
 There exist quite a few different types of
Gaussian parameterization under different
coordinate system (CMS, LCMS, YKP, etc…).
Yano-Koonin parametrization
Nucl-ex/0505014
From one- to two- to three dimensional parameterization
(e.g. nucl-th/0510049 for reviews)
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LCMS Gaussian Parameterization
 =Longitudinal co-moving system (outside-long)
2
C(qO , qS , qL )  1   exp(RO2 qO2  RS2qS2  RL2qL2  2ROL
qOqL )
 is the incoherence or chaoticity factor, lies between 0 (complete coherence)
and ±1 (complete incoherence) in the real reactions.
it will be affected by many factors other than
the quantum statistics (bosons: 1, fermions: -1 ),
for example,
 misidentified particles(contamination),
the (long-lived) resonance,
different technical details of Coulomb corrections
RL,O,S are Pratt radii, Rol is the cross term and vanishes at mid-rapidity.
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The out-side-long system sketch
 Long: parallel to beam, and the
longitudinal components of the pair
velocity vanishes.(Pz=0)
 Side: perpendicular to beam and
average pair momentum K. S
 Out: perpendicular to Long and Side.
L
O
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K
The survey of Pratt radii
RL,RO, and RS
 R~R(KT, Eb, b, (A,B), y, , (m1,m2))
Quite a few model endeavors:
Hydrodynamics models: matter in the collision region is taken as an ideal,
locally thermalized fluid with the zero mean free path;
(hydro+/PYTHIA+)UrQMD, RQMD: hadronic dynamics model with string degree of freedom.
Having potentials for baryons at low beam energies.
From UrQMD ver2.0, the PYTHIA (v6.1) was added in order to consider the
hard process.
MPC: Molnar’s Parton Cascade, (with the stiffest effective EoS)
AMPT: A Multi-Phase Transport model (hadron+string+parton)
HRM: Hadronic Rescattering Model (no strings/partons)
etc…
Next, we show the results of the source of
two negatively (except otherwise stated) charged pions using UrQMD model.
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How to calculate numerically?
 Standard UrQMD (v2.2) output of freeze-out
particles
(http://www.th.physik.uni-frankfurt/~urqmd)
 CRAB (v3.0) used to analyze the (threedimensional LOS) correlation of two identical
particles.
(http://www.nscl.msu.edu/~pratt/freecodes/crab/home.html)
 Three-dimensional Gaussian fitting.
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1,Good agreement
2,Deviations shown
at small kT for RL and RS
R.vs.KT@AGS
(6A GeV)
(10.7A GeV)
(8A GeV)
R i (fm)
(4A GeV)
(2A GeV)
Eb
O
L
10
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
data:
;
S
th:
th.
<11%T
<5% T
0
100
200
300
400
0
100
200
300
400
0
kT (MeV/c)
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100
200
300
400
500
KT  ( pT 1  pT 2 ) / 2
The mass dependence of lifetime of
better agreement
resonances
M
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(4A GeV)
(6A GeV)
(10.7A GeV)
(8A GeV)

R i (fm)
The green lines:
We consider the
Mass dependence
Of lifetime of
Resonances.
(2A GeV)
Eb
O
L
10
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
8
6
4
2
0
data:
fm
;
S
th:
th.
fm
fm
fm
fm
0
Phase shifting?
100
200
300
400
0
100
200
300
400
kT (MeV/c)
Qingfeng Li for Palaver 2006
0
100
200
300
400
500
R.vs.KT@SPS-NA49
Eb
good agreement
S
O
L
(20A GeV)
10
NA49 data:
8
;
th:
6
4
2
(30A GeV)
10
0
8
6
4
2
<7.2% T
(40A GeV)
8
6
4
2
0
(80A GeV)
R i [fm]
0
8
6
4
2
(160A GeV)
0
8
<10% T
6
4
2
0
0
100
200
300
400
0
100
200
300
400
0
100
kT [MeV/c]
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200
300
400
500
R.vs.KT@RHIC
s
L
NN 10
O
exp.:
8
(30 GeV)
Large deviation shown in RO
;
S
th.:
6
<15% T
4
2
15%T
(62.4 GeV)
8
<15% T
6
4
2
0
8
(130 GeV)
R i (fm)
0
<10% T
6
4
2
0
(200 GeV)
8
<5% T
6
4
2
0
0
200
400
600
800 0
200
400
600
800 0
200
kT (MeV/c)
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400
600
800
R.vs.b@RHIC
s  200
GeV
25
+15 fm
RO in central
collisions.
20
+10 fm
th.
R O (fm)
15
0-5%
10-20%
30-50%
50-80%
+5 fm
10
5
exp.
+0 fm
0
+15 fm
+15 fm
20
+10 fm
+10 fm
R L (fm)
R S (fm)
15
10 +5 fm
+5 fm
5
+0 fm
+0 fm
0
100
200
300
400
500
600
200
300
400
kT (MeV/c)
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500
600
Shifted lines by 5 fm
R.vs.(A,B)@RHIC
GeV
s  200
20
Au+Au/p+p
Cu+Cu/p+p
16
+10
+10
12
R i ratio
8
4
+5
+5
+0
+0
(b)
(a)
0
200
Au+Au/Cu+Cu
s
6
NN
300
600
exp.
RL:
RO:
2
0
100
500
=200 GeV
th.
4
400
RO in central
Au+Au,
Cu+Cu,
and
p+p
collisions.
(c)
200
300
400
500
RS:
600
kT (MeV/c)
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Surface-like
emission
String problems
10
Circles:
R.vs.Eb@small KT
R s (fm)
8
kT=100 MeV/c
Squares: kT=200 MeV/c
6
4
2
0
8
exp (stars):
kT~150: E2,4,6,8,
4
2
E20,30,40,80,160 (NA49)
kT~170: s130
0
kT~200: E10.7,s62.4,s200
8
R L (fm)
How to improve the HBT radii at
AGS and SPS energies?
---the mass dependence of
the resonance lifetimes.
But: the RO/RS changes little
R o (fm)
6
E40,80,160 (CERES)
6
4
2
0
1
10
100
Eb (A GeV)
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1000
10000
The Volume ~ E
5000
Circles: kT=100 MeV/c
4000
Stars: exp.
3000
3
V f (fm )
Roughly, the evolution
of Vf can be reproduced
However, the decrease
of Vf at AGS is not
obtained.
Squares: kT=200 MeV/c
V f  2  RL R
3/ 2
2000
2
S
1000
0
1
10
100
1000
Eb (A GeV)
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10000
What’s
the (classical) HBT puzzle?
 Model calculations of RO/RS or (RO2-RS2)1/2
are obviously larger than the experimental
data 8 Circles: k =100 MeV/c
It is related to duration time
(in the absence of flow):
T
Squares: kT=200 MeV/c
6
 
4
2
(R O -R S )
2 1/2
(fm)
Stars: exp. data
2
0
1
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10
100
1000
10000
Eb (A GeV)
Qingfeng Li for Palaver 2006
( RO2  RS2 )
2
How to improve it?
---hadronic potentials
should also be studied
more carefully?
Flow ‘puzzle’---thanks Hannah and
Xianglei
v2 
p p
2
y
p p
2
y
2
x
2
x
At Eb<10 A GeV,
the flow can be well
reproduced with
a specified potential.
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The time evolution of the HBT radii
and the puzzle
SPS-E40 @ central collisions
10
8
1.5
6
tf=15 fm/c
1.0
tf=40 fm/c
4
1000
R O /R S
tf=5 fm/c
R L (fm)
In the late stage,
HBT puzzle occurs.
2.0
Exp
tf=2000 fm/c
0.5
800
1/2
pionm
pionp
<N>
600
400
Eb=40 A GeV
200
R O (fm)
s =200 GeV
0
0.0
8
8
6
6
4
4
2
2
0
0
0
100
200
300
400
0
100
kT (MeV/c)
0
0
10
20
30
40
t (fm/c)
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R S (fm)
2
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200
300
400
Corona effect
/rescattering
Corona effect
s1/2=200 GeV
Au-Au results are rescaled
RL
RO
RS
in p+p coll.
Standard
p-mixed
Exp.
in Au+Au coll.
p-mixed
2
R (fm)
p-mixed: after consider
the random mixture of
the momenta of freeze-out
pions, kT-dependence of
HBT radii vanishes largely
(the space-momemtum
correlations)
3
1
The corona effect determines
the kt-dep of HBT radii.
0
200 300 400 500 200 300 400 500 200 300 400 500
kT (MeV/c)
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But, if the rescattering is
not sufficient …
 Weaker stopping power
 Equally, larger transparency
 Might influence the configuration of
the pion source
 What to change the rescattering
effect during the HICs? Roughly
saying, potentials and collisions.
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The (argued) ‘disadvantages’
in the UrQMD calculations
 No potentials for baryons in the
above calculations (only cascade
mode used).
 No string-string interaction
although the string degree of freedom
exists.
 Or, no deconfined quarks nor gluons
and the interactions between them.
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Potential contributions
 The contributions of nuclear potentials are
important at low beam energies (Eb<AGS).
 Besides B-B Coulomb interaction, we
further considered the Coulomb potential
between B-M and M-M.
(see PRC 72, 034613 (2005); J. Phys. G 32, 151 (2006); J. Phys. G 32,407(2006) )
 So far, the potentials in UrQMD are non-relativistic
and needed to update for investigations especially
at SPS and RHIC. ---one more question: the
calculation time becomes too long for HBT
calculations (to guarantee a good statistics)
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Potential contribution to the
Correlation function
AGS, Eb=4 A GeV
2.0
qL; qO,qS<5 MeV/c
1.6
Cascade
Cascade
SM-EoS
SM-EoS
qO; qS,qL<5 MeV/c
C
Potential leads to
larger incoherence
in the direction
x and z, and,
Ro, Rl decrease.
Then,
how about Ro/Rs ratio?
out,
side,
out,
side,
long, Cascade
long, SM-EoS
1.8
qS; qO,qL<5 MeV/c
1.4
1.2
1.0
0
30
60
90
0
30
q (MeV/c)
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60
90
120
Potential contribution
at AGS(Eb=4 A GeV)
8
8
6
6
4
4
2
2
0
0
8
1.2
6
0.9
exp.
nnn
nnn+(Mres)
4
2
0.6
wnw
wnw+(Mres)
0
0
100
200
300
400
500
100
200
300
0.3
400
kT (MeV/c)
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500
R O /R S
R S (fm)
R L (fm)
AGS-E4
R O (fm)
10
10
The potential
contributes to
a higher Rs,
lower Ro,
and thus
better Ro/Rs
More collisions by setting zero
formation time for strings
SPS-E160
2.0
zero formation time for strings
default UrQMD cal.
out
side
C
It is very time consuming
e.g. :
SPS-E160:3events/h
1.5
RHIC-s200:1event/d
The difference
Between
C(qo) and C(qs)
almost disappears
after considering
zero formation time
for string.
1.0
0
20 40 60 80 100 120 0
20 40 60 80 100 120
q (MeV/c)
A larger early pressure especially in the sideward direction leads to larger Rs
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Ro/Rs
at SPS(Eb=160 A GeV)
2.0
SPS-E160
But it looks that
the Ro/Rs keeps
increasing slowly
with beam energy.
the hadronic
potential might
not fully Explain the
HBT puzzle at RHIC?
1.5
RO/RS
The consideration
of potential interaction
also give a better
Ro/Rs at SPS
1.0
nnn
nnn+(Mres)
RHIC-s200
0.5
wnw+(Mres)
nnn+f=0
100
200
kT (MeV/c)
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300
Leads to much
smaller
Ro/Rs ratio mainly
due to a larger Rs.
400
Readjust the formation time?
data
0
Zero-formation time
Qingfeng Li for Palaver 2006
How to solve the HBT puzzle
---
reduce (or 0) string formation time for more pressure?
(tremendous number of collisions
make it almost impossible to
calculate the HBT interferometry at RHIC)
the idea in HRM and checked
for elliptic flow and HBT at SPS in UrQMD
---consider Partons?
the idea in AMPT
Not yet in UrQMD model
qMD,
---consider optical potential for pions (chiral symmetry)
 with the help of another model:
see PRL94, 102302(2005), PRC73, 024901(2006)
and, I want to stress that the hadronic potential should be also paid attention.
In my opinion, these explanations are not contradictive: the detailed interactions between
particles should be considered more carefully.
The origin of the HBT puzzle might be
f’+U=C
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multi-faceted. To consider both sides of BUU:
Qingfeng Li for Palaver 2006
Summary and outlook
 Good (quantitatively) agreement of the calculated
HBT radii with data from AGS to RHIC.
 The decay of resonances affects the HBT radii
(mainly at low kT).
 HBT puzzle is also seen by the comparison of our
calculations with data, especially at RHIC energies
 A relativistic EoS for nuclear matter should be
updated in UrQMD model.
 Is it necessary to consider new degree of freedom
in our UrQMD model?
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My e-mail address: [email protected]
[email protected]
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