Transcript HBT - uni-frankfurt.de

HBT t-puzzle and hadron potentials
By Qingfeng Li (FIAS)
In cooperation with: Marcus Bleicher, Xianglei Zhu,
Horst Stoecker, Hannah Petersen
Outline
•
Brief introduction to the HBT interferometry
HBT researches in nuclear physics
•
UrQMD, a Hadron-String transport model
•
The HBT results from UrQMD transport.
The HBT t-puzzle & mT-scaling.
•
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Conclusions and outlook.
Talk for INFN, University of Catania
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HBT, half century in NP
•
HBT=Robert Hanbury-Brown and Richard Q. Twiss

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 to the correlators behaved as a consequence of
B-E statistics.
In 1959, during the measurements of the ρ0 resonance (by means of
ρ0-+), Goldhaber etc (Berkeley) found an angular correlation
among identical pions, which were also explained by the B-E. What’s
more, they parameterized the observed correlation as:
•
C(Q2)=1+exp(-Q2r2)
The subsequential HBT researches in nuclear physics are based on
this Gaussian form.
2.0
1.8
R=6 fm
C(Q)
1.6
1.4
*R. Hanbury Brown and R.Q. Twiss, Philos. Mag. 45, 663 (1954).
1.2
*G. Goldhaber, S. Goldhaber, W. Lee, and A. Pais, Phys. Rev. 120, 300 (1960)
1.0
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0.0
0.1
0.2
0.3
Q (MeV/c)
0.4
0.5
3
The HBT technique
The quotient of two-particle and one-particle spectra
Experimentally:
d 6N
dp13dp23
C ( q, K )  3 3
d Nd N
dp13 dp23
q  p1  p2
K  ( p1  p2 ) / 2
2
dx dx s  x , p s  x , p 

C ( q, K ) 
 dx sx , p  dx sx , p 
1
Theoretically:
2
1
1
1
1
1
2
2
2
2
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.  the two-particle relative wave function.
The correlator is constructed with the help of the CRAB program
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The main task of HBT: to probe the QGP fireball
•
•
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
probes might be seen IF there is a (phase) transition.
long
life times in the mixed phase?
Predictions by
Rischke, Gyulassy, in
Nucl.Phys.A608:479-512,1996
Energy density
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The Parameterizations
•
•
Three-dimensional Gaussian Parameterizations
(under different coordinate systems (CMS,
LCMS, YKP, etc…)) are available.
The LCMS Gaussian Parameterization is
popular and often used. We adopt it in this
work.
The non-Gaussian effect will not be discussed in this talk.
The fitting work can be done by the ROOT or the ORIGIN software
(using -squared method)
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LCMS Gaussian Parameterization
•
=Longitudinal co-moving system (out-side-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) resonances,
different technical details of Coulomb corrections
So, we can take it as a free parameter in the fitting process.
RL,O,S are Pratt HBT-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.(Kz=0)
• Side: perpendicular to beam and average pair
momentum K.
• Out: perpendicular to Long and Side.
•
S
 

q  K 
qO 
K
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L
O
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K
8
Coulomb potential modification of the final state
interaction (FSI)
Bowler-Sinyukov Method:
C (qO , qS , qL )  (1   )
2
 K coul (qinv )(1  exp( RO2 qO2  RS2 qS2  RL2 qL2  2 ROL
qO qL ))
Kcoul(qinv) is the Coulomb
correction factor and only
depends on invariant relative
momentum qinv.
It affects K-K but not -
correlation obviously.
qinv  q 2  E 
2
The  source will mainly
be discussed in this talk
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Experimental status…
Experiments:
SIS
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From M. Lisa, in Annu. Rev. Nucl. Part. Sci. 2005. 55:357–402
AGS
SPS
RHIC
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The investigation of HBT radii RL,RO, and RS
•
R~R((A,B), (m1,m2),KT, Eb, b, y, )
Quite a few model endeavors:
Hydrodynamics models: Standard: matter in the collision region is taken as an ideal,
locally thermalized fluid with the zero mean free path;
updated ones: To consider viscosities, more dimensions,
To polish the freeze-out, etc.
MPC: Molnar’s Parton Cascade, (with the stiffest effective EoS)
HRM: Hadronic Rescattering Model (no strings/partons)
(hydro+/PYTHIA+)UrQMD, RQMD: hadron-string dynamics model.
Optional effective potentials for baryons at low beam energies.
From UrQMD ver2.0, the PYTHIA (v6.1) was added in order to consider the
hard process. (http://www.th.physik.uni-frankfurt/~urqmd)
AMPT: A Multi-Phase Transport model (hadron+string+parton)
etc…
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The HBT t-puzzle at RHIC
AMPT:HBT is sensitive to
the parton-scattering
Cross sections.
HRM: considering only
the hadron rescattering
(with sudden collisions ),
no parton degree of
freedom
From M. Lisa, in Annu.
Rev. Nucl. Part. Sci.
2005. 55:357–402
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The UrQMD model
UrQMD : Ultra-relativistic Quantum Molecular Dynamics
•It is a non-equilibrium transport model
•It includes 55 baryon species (with mass up to 2.25GeV) and 32 meson species (with
mass up to 1.91GeV)
•Particles interact via:
- Mean Field modification
- Collisions (with measured and calculated cross sections)
•Particles produce via:
- Formation and decay of resonance
- Excitation and fragmentation of string
• It provides full phase-space dynamics of heavy-ion collisions
• it can be used to study HICs at energies from SIS to RHIC
(Ca+Ca Eb=160A GeV)
•An important News: the newest version 2.3 has been released. (http://th.physik.unifrankfurt.de/~urqmd/)
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Treatment of the “pre-formed” hadrons
before string fragmentation
•
•
•
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At high SPS and RHIC energies, particle production is
dominated by this string mechanism.
The formation time of the hadron is determined by the
“yo-yo” mode. During this time, the particles are taken
as “pre-formed”. The transport of the “pre-formed”
particles is treated to be “free-streaming”.
The reduced cross sections are only included for leading
hadrons.
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Why do we use the UrQMD model?
•
•
•
Hydrodynamics failed to explain the decrease of HBT
radii with KT (see, e.g. nucl-th/0305084)
Microscopic Transport Model, considering the full
rescattering process of hadrons, might throw light on
what other mechanisms generate the observed KTdependence of the HBT radii
The time-related HBT puzzle
mb
ulo
Co
HBT
i ng
er
t ad ron i
t
z
a
a H
a
c
t n
QGP
s
i o
e
o r
n
o
R
F-O
Ur
QM
D
C
F-S
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Part I: the survey of the HBT parameters
from UrQMD cascade calculations
from AGS, SPS to RHIC energies
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UrQMD vs. data @ AGS
Au+Au
(6A GeV)
data:
;
S
th:
th.
E802
(10.7A GeV)
(8A GeV)
R i (fm)
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
E895
(4A GeV)
(2A GeV)
Eb
•Good agreement
•Deviations at
small kT for RL
and RS
0
100
200
300
400
0
100
200
300
400
0
100
200
300
400
<11%T
<5% T
500
kT (MeV/c)
KT  ( pT 1  pT 2 ) / 2
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UrQMD @ SPS-NA49
R L (fm)
Deviation
for RO
and RS!
(160A GeV)
(80A GeV)
(40A GeV)
(30A GeV)
(20A GeV)
10
8
6
4
2
NA49 data:
0
;
th:
400
0
R O (fm)
8
6
4
2
0
R S (fm)
8
6
4
2
0
0
Pb+Pb
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200
400
0
200
400
0
200
200
400
kT (MeV/c)
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0
200
400
600
<7.2% T
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UrQMD @ SPS-CERES
(40A GeV)
(80A GeV)
(160A GeV)
R L (fm)
10
CERES data:
8
;
Deviation
for RO
and RS!
th:
6
4
2
R O (fm)
0
8
6
4
Similar to last slide
2
0
R S (fm)
8
6
4
2
0
0
Pb+Au
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200
400
0
200
400
0
200
400
kT (MeV/c)
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600
<5% T
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R.vs.KT@RHIC
s
L
NN 10
O
exp.:
(30 GeV)
8
;
S
Deviation
for RO!
th.:
6
4
2
<15% T
15%T
(62.4 GeV)
8
6
<15% T
4
2
0
8
(130 GeV)
R i (fm)
0
6
<10% T
4
2
0
(200 GeV)
8
6
<5% T
4
2
0
0
Au+Au
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200
400
600
800 0
200
400
600
800 0
200
400
600
800
kT (MeV/c)
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Excitation Function of (RO2-RS2)1/2 , Vf, f
V f  2  RL RS2
Vf and f at AGS deviate
from data
Calculated f ~0.7±0.3 fm
3/ 2
6
5000
2
2
2 1/2
3
2000
(R O -R S )
3
V f (fm )
4
3000
(fm)
5
4000
1000
1
(b)
(a)
0
0
1
10
100
1000
10000
Eb (A GeV)
1.5
 f (fm)
It is related to duration
time (in the absence of
flow)
1.0
Exp.
UrQMD(v2.2, Cas)
kT=100 MeV/c
Energy Region
AGS/SPS(NA49)/RHIC
kT=200 MeV/c
0.5
kT=100 MeV/c
HBT t-puzzle is seen at
all energies!
SPS(CERES)
kT=200 MeV/c
(c)
0.0
1
10
100
1000
Eb (A GeV)
10000
support an universal
kinetic decoupling criterion
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f 
Vf
N

Vf
N N N  N  
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See, D. Adamova etc,
PRL90, 022301 (2003)
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Part II: The importance of MeanField Potential of formed particles
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EoS
•
•
It is well-known that, in low-energy nuclear
physics, the mean-field effect is essential.
Phenomenologically, the mean field includes:
- bulk term (density related)
- surface term
- Yukawa term
- Pauli term
- symmetry term
- momentum dependent term
In addition, the Coulomb potential for charged particles
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Example I: the importance to the -/+ ratio
3.5
3.5
Au197F1
FOPI exp.
3.0
3.0
2.5
2.0
2.0
-
 

2.5
The Importance of
Coulomb
&
Symmetry
Potentials!
=(5N2+NZ)/(5Z2+NZ)
1.5
1.5
1.0
1.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Eb [A GeV]
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Example II: to solve the Flow “puzzle” at low energies
v2 
px2  p y2
px2  p y2
At Eb<10 A GeV,
the flow can be well
reproduced with
a specified potential.
PRC74，064908（2006）
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Evidence in HBT RO/RS ratio at AGS…
Pot.: SM-EoS
with Lorentz boost
(M. Isse etc
Phys.Rev.C72:064908 (2005) )
For simplicity, pot.s of all
Baryons are set as
nucleons. No meson pot.s
Coul. Pot is optional.
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Part III: To consider a potential for
“pre-formed” hadrons
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How to consider the “pre-formed”
hadronic potential?
•
•
①
②
③
④
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To modify the interactions at early stage, more collisions (by
considering a shorter formation time or larger cross sections for
“pre-formed” particles) or a mean-field potential for “pre-formed”
hadrons might be taken into account. The former idea has been
checked in the AMPT and the HRM models. Here we would like to
consider the latter idea.
As the first step,
the density dependent term used for formed baryons is used for
“pre-formed” particles.
The “pre-formed” mesons act like “pre-formed” baryons but with a
reduction factor (2/3) due to the quark-number difference.
The potential interaction between formed and “pre-formed”
particles is neglected.
The “pre-formed” particles also contribute to the hadronic density
(for “pre-formed” mesons, the 2/3 factor is considered).
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After considering the “pre-formed” hadronic potential...
See the
two-bumps
See the stronger
flow at large pt
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To solve the HBT t-puzzle
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Not only for the  source…
The marked area
illustrates the uncertainties
from non-Gaussian effect
and corrections on FSI
mT  m 2  kT2
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Why so ?
Under the assumptions of thermalization and
Gaussian-source shape, the HBT radii can be
expressed analytically as
RO term can be expanded as：
Due to the strong phase-correlation induced by
the potentials, the term -2<Txt> might be
comparable to the term <t2t2>.
An important consensus:
Due to the strong x-t correlation, RO/RS1 does not mean t0
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Improvement to the mT-scaling
Left Plots:
Without “pre-formed” hadron potential:
RL: of kaons and Lambdas: Large
RO: of all particles
: Large
RS: of Lambdas
: Large
Right Plots:
With “pre-formed” Hadron potential:
RL: of Kaons and Lambda: follow
RO: of all particles
: follow
RS: of pions and Kaons : follow
the mT-scaling
T.Csorgo etc, PRC 54, 1390(1996)
Without the consideration of the FSI in hydro-dynamics
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Conclusions and outlook
The investigations based on UrQMD show:
============================================
• UrQMD cascade calculations can (semi-)quantitatively fit data
•
•
•
In addition to flow effect, the late stage of HICs affects to some extent the
KT dependence of the HBT radii
The model calculations support a nearly energy independent mean free
path (~1fm) at pion freeze-out
HBT t-puzzle is also seen by the comparison of our UrQMD cascade
calculations with data.
============================================

The inclusion of potential interactions of both formed and “pre-formed”
particles pushes down the calculated HBT radius RO and pulls up the RS
so that the HBT t-puzzle disappears throughout the energies from AGS,
SPS, to RHIC. Furthermore, the rapidity distribution of particle
multiplicities, the transverse momentum dependence of elliptic flow, and
the mT-scaling can be better explained.
============================================
•
The form of the potential for the new phase is simple and rough (ideally,
the EoS of the new phase should be based on the first-principle lattice
QCD calculations.
Hydro+UrQMD hybrid model ?
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Thanks
[email protected]
[email protected]
For details, please read:
arXiv:0802.3618v1, Phys. Lett. B663,395-399,(2008).
arXiv:0709.1409v2, Phys. Lett. B659,525-530,(2008)
arXiv:0706.2091v2,
J. Phys. G 34, 2037 (2007)
arXiv:nucl-th/0612030v1, J. Phys. G 33, 537 (2007)
arXiv:hep-ph/0608189v1, Phys. Rev. C 74, 064908 (2006)
arXiv:nucl-th/0602032v2, Phys. Rev. C 73, 064908 (2006)