Transcript Signatures of new states of matter in hydrodynamic picture

Kaon and pion femtoscopy in the
hydrokinetic model of ultrarelativistic
heavy-ion collisions
Yu. M. Sinyukov
Bogolyubov Institute for Theoretical Physics,
Kiev
Talk at the X GDRE Workshop “Heavy Ion with Ultrarelativistic Energies”
SUBATRECH, Nantes, June 17 2010
OUTLOOK
•
•
0. Evidences of collective/hydrodynamic behavior of the matter formed A+A .
I. Thermalization (is early thermalization really needed?), IC, HBT-puzzle and all
that…
•
II. The transition from very initial nonthermal state in HIC to
hydrodynamic stage. Phenomenological approach.
•
III. Matter evolution at chemically equilibrated stage.
•
IV. Matter evolution at non-equilibrated stage. HydroKinetic Model (HKM).
•
V. System’s decay and spectra formation. Whether it possible to apply Cooper-Frye
prescription for continuously emitting and not equilibrated system? If possible, how?
• VI. The HKM results for the top RHIC energies. Pion and kaon femtoscopy
• VII. Energy dependence of the interferometry scales: SPS, RHIC, LHC
The evidences of space-time evolution of the thermal
matter in A+A collisions:
 Rough estimate of the fireball lifetime for Au+Au
In p+p all femto-scales are
of order 1 fm !
The phenomenon of space-time
evolution of the strongly interacting
matter in A+A collisions
Particle number ratios are well
reproduced in ideal gas model
with 2 parameters: T,
for
collision energies from AGS to
RHIC:
thermal+chemical equilibrium
s  200Gev:
A+A is not some kind of superposition of the
individual collisions of nucleons of nuclei
What is the nature of this matter at the
early collision stage?
Whether does the matter becomes thermal?
Collective expansion of the fireball.
Observation of the longitudinal boost-inv. expansion:
It was conformed by NA35/NA49 Collaborations (CERN), 1995 !
Observation of transverse (radial) collective flows:
Effective temperature for different particle species
(non-relativistic case)
:
radial collective flow
Observation of elliptic
flows:
HYDRODYNAMICS !
Expecting Stages of Evolution in Ultrarelativistic A+A collisions
t
Relatively small space-time scales
(HBT puzzle)
8-20 fm/c
Early thermal freeze-out:
T_th
Tch
150 MeV
7-8 fm/c
Elliptic flows
1-3 fm/c
Early thermalization at
0.5 fm/c
0.2?(LHC)
or strings
7
8
Collective velocities developed between
=0.3 and
=1.0 fm/c
Central
collisions
Collective velocity developed at pre-thermal stage from proper time tau_0 =0.3
fm/c by supposed thermalization time tau_th = 1 fm/c for scenarios of partonic
free streaming and free expansion of classical field. The results are compared
with the hydrodynamic evolution of perfect fluid with hard equation of state
p = 1/3 epsilon started at
. Impact parameter b=0.
Yu.S. Acta Phys.Polon. B37 (2006) 3343; Gyulassy, Yu.S., Karpenko, Nazarenko Braz.J.Phys.
37 (2007) 1031. Yu.S., Nazarenko, Karpenko: Acta Phys.Polon. B40 1109 (2009) .
Collective velocities and their anisotropy developed between
and
=1.0 fm/c
=0.3
Non-central
collisions
b=6.3 fm
Collective velocity developed at pre-thermal stage from proper time
=0.3 fm/c by supposed thermalization time tau_i = 1 fm/c for scenarios of
partonic free streaming. The results are compared with the hydrodynamic
evolution of perfect fluid with hard equation of state p = 1/3 epsilon
started at
. Impact parameter b=6.3 fm.
Basic ideas for the early stage: developing of pre-thermal flows
Yu.S. Acta Phys.Polon. B37 (2006) 3343; Gyulassy, Yu.S., Karpenko, Nazarenko
Braz.J.Phys. 37 (2007) 1031.
For nonrelativistic gas
For thermal and non-thermal expansion
at
Hydrodynamic expansion:
gradient pressure
acts
:
So, even if
:
and
Free streaming:
Gradient of density leads
to non-zero collective
velocities
In the case of thermalization at later
stage it leads to spectra anisotropy
11
Summary-1
Yu.S., Nazarenko, Karpenko: Acta Phys.Polon. B40 1109 (2009)
 The initial transverse flow in thermal matter as well as its anisotropy are
developed at pre-thermal - either partonic, string or classical field (glasma) - stage
with even more efficiency than in the case of very early perfect hydrodynamics.
 Such radial and elliptic flows develop no matter whether a pressure already
established. The general reason for them is an essential finiteness of the system in
transverse direction.
 The anisotropy of the flows transforms into asymmetry of the transverse
momentum spectra only of (partial) thermalization happens.
 So, the results, first published in 2006, show that whereas the assumption of
(partial) thermalization in relativistic A + A collisions is really crucial to explain soft
physics observables, the hypotheses of early thermalization at times less than 1
fm/c is not necessary.
12
Akkelin, Yu.S. PRC 81, 064901 (2010)
Matching of nonthermal initial conditions and hydrodynamic stage
• If some model (effective QCD theory) gives us the energy-momentum tensor at
time
, one can estimate the flows and energy densities at expected time of
thermalization
, using hydrodynamic equation with (known) source terms.
• This phenomenological approach is motivated by Boltzmann equations, accounts
for the energy and momentum conservation laws and contains two parameters:
supposed time of thermalization
and “initial” relaxation time
.
Eqs:
IC:
where
13
14
Locally (thermally & chemically) equilibrated
evolution and initial conditions (IC)
t
t out
Tch
IC for central Au+Au collisions
The “effective" initial distribution is the one which being
used in the capacity of initial condition bring the average
hydrodynamic results for fluctuating initial conditions:
x
is Glauber-like profile
I.
Initial rapidity profiles:
where
II.
is CGC-like profile
and
are only fitting parameters in HKM
Equation of state in (almost) equilibrated zone
MeV
EoS from LattQCD (in form proposed by
Laine & Schroder, Phys. Rev. D73, 2006).
Crossover transition, LattQCD is matched with an ideal chemically equilibrated
multicomponent hadron resonance gas at
Particle number
ratios
F. Karsch, PoS CPOD07:026, 2007
are baryon number and strangeness susceptibilities
16
t
t out
Tch
x
A
“Soft Physics” measurements
x
t
Landau, 1953
Δ
ω
K
Cooper-Frye prescription (1974)
A
p=(p1+ p2)/2
QS correlation function
Long
q= p1- p2
p1
p2
Out
Space-time structure of
the matter evolution:
p
BW
18
Cooper-Frye prescription (CFp)
t
 f.o. :   t  z  const at r  const
2
2
t
z
 f.o. : (r ) at z  0
r
CFp gets serious problems:
Freeze-out hypersurface (r ) contains non-space-like
sectors
artificial discontinuities appears across  f.o.
Sinyukov (1989), Bugaev (1996), Andrelik et al (1999);
cascade models show that particles escape from the system about whole
time of its evolution.
Hybrid models (hydro+cascade) and the hydro method of continuous
emission starts to develop.
Hybrid models: HYDRO + UrQMD (Bass, Dumitru (2000))
t
t
t
UrQMD
 hadr
 hadr
 UrQMD
HYDRO
z
 hadr :   t 2  z 2  const
at r  const
r
 hadr : (r ) at z  0
The problems:
the system just after hadronization is not so dilute to apply
hadronic cascade models;
hadronization hypersurface (r ) contains non-space-like sectors
(causality problem: Bugaev, PRL 90, 252301, 2003);
The average energy density and pressure of input UrQMD gas
should coincide with what the hadro gas has just before switching.
At r-periphery of space-like hypsurf. the system is far from l.eq.
The initial
conditions
for hadronic
cascade
models
should be
based on
non-local
equilibrium
distributions
Possible problems of matching hydro with initially bumping IC
RIDGES?
The example of boost-invariant hydroevolution for the bumping IC with
four narrow high energy density tubes (r= 1 fm) under smooth Gaussian
background (R=5.4 fm)
Possible problems of matching hydro with initially bumping IC
RIDGES?
The example of boost-invariant hydroevolution for the bumping IC with ten
narrow high energy density tubes (r= 1 fm) under smooth Gaussian
background (R=5.4 fm)
Continuous Emission
t
t out
x
F. Grassi, Y. Hama, T. Kodama
(1995)
“The back reaction of the emission on the fluid
dynamics is not reduced just to energy-momentum recoiling of emitted particles on the expanding thermal medium, but also leads to a rearrangement of the medium, producing a deviation of its state from the local equilibrium, accompanied by changing of the local temperature,
densities, and collective velocity field. This
complex effect is mainly a consequence of the
fact that the evolution of the single finite system
of hadrons cannot be split into the two components: expansion of the interacting locally equilibrated medium and a free stream of emitted
particles, which the system consists of. Such a
splitting, accounting only for the momentumenergy conservation law, contradicts the underlying dynamical equations such as a Boltzmann
one.”
Akkelin, Hama, Karpenko, Yu.S
PRC 78 034906 (2008)
Hydro-kinetic approach
Yu.S. , Akkelin, Hama: PRL 89 , 052301 (2002);
+ Karpenko: PRC 78, 034906 (2008).
MODEL
• is based on relaxation time approximation for emission function of relativistic finite
expanding system;
•
provides evaluation of escape probabilities and deviations (even strong)
of distribution functions [DF] from local equilibrium;
3. accounts for conservation laws at the particle emission;
•
•
•
•
•
Complete algorithm includes:
solution of equations of ideal hydro;
calculation of non-equilibrium DF and emission function in first approximation;
solution of equations for ideal hydro with non-zero left-hand-side that
accounts for conservation laws for non-equilibrium process of the system
which radiated free particles during expansion;
Calculation of “exact” DF and emission function;
Evaluation of spectra and correlations.
Boltzmann equations and probabilities of
particle free propagation
Boltzmann eqs
(differential form)
and
are G(ain), L(oss) terms for
p. species
Probability of particle free propagation
(for each component )
84 84
Spectra and Emission function
Boltzmann eqs
(integral form)
Index
is omitted
everywhere
Spectrum
Relax. time approximation
for emission function
(Yu.S. , Akkelin, Hama PRL,
2002)
For (quasi-) stable particles
85
Kinetics and hydrodynamics below Tch =165 MeV
For hadronic
resonances
&
where
Representations of non-loc.eq. distribution function
(for quasi- stable particles)
If
at the initial (hadronisation) time
87
Iteration procedure:
I. Solution of perfect hydro equations with given
initial l.eq. conditions
88
II. Decomposition of energy-momentum tensor
89
III. Ideal hydro with “source” instead of non-ideal hydro
where
(known function)
90
Full procedure for HKM
The first correction for the
back reaction of particle
emission on the fluid dynamics
This approach accounts for
conservation laws
deviations from loc. eq.
viscosity effects in hadron gas:
91
Equation of state in non-equilibrated zone
MeV
EoS
Pressure and energy density of multicomponent Boltzmann gas
At hypersurface
the hadrons are in chemical equilibrium with some
barionic chemical potential
which are defind from particle number
ratio (conception of chemical freeze-out).
Below
we account for the evolution of all N densities of hadron
species in hydro calculation with decay resonances into expanding fluid,
and compute EoS dynamically for each chemical composition of N sorts
of hadrons in every hydrodynamic cell in the system during the
evolution. Using this method, we do not limit ourselves by chemically
frozen or chemically equilibrated evolution, keeping nevertheless
thermodynamically consistent scheme.
92
EoS used in HKM calculations for the top RHIC energy
The gray region consists of the set of the points corresponding to the different
hadron gas compositions at each
occurring during the late nonequilibrium
stage of the evolution.
System's decoupling and spectra formation

Emission function
For pion emission
is the total collision rate of the pion, carrying momentum p
with all the hadrons h in the system in a vicinity of point x.
is the space-time density of pion production caused by
gradual decays during hydrodynamic evolution of all the
suitable resonances H including cascade decays
The cross-sections in the hadronic gas are calculated in accordance
with UrQMD .
94
PARAMETERS for the RHIC TOP ENERGY
Fitting parameter at
Max initial energy
density
Glauber IC
CGC IC
16.5 GeV/fm3
19.5 GeV/fm3
Initial transverse
flows
0.22
0.21
Parameter
“absorbs” unknown portion of the prethermal flows, the viscosity effects in the QGP
and, in addition, the event-by-event fluctuations of the initial conditions which also lead to an
increase of the “effective” transverse flows in the observed inclusive spectra.
In CGC approach at RHIC energies this energy density corresponds to the
value
In CGC approach at RHIC energies the value
(T. Lappi, J.Phys. G, 2008)
is used
95
Iu. Karpenko, Yu.S. PRC 81, 054903 (2010)
The following factors reduces space-time scales of the
emission and Rout/Rside ratio:
Akkelin, Hama, Karpenko, Yu.S, PRC 78, 034906 (2008)
 essentially
non-flat initial energy density distributions (Gaussian, Glauber,
CGC);
 more
hard transition EoS, corresponding to cross-over (not first order
phase transition!);
 fairly
strong transverse flow at the late stage of the system evolution. It is
caused by:
 developing of flows at very early pre-thermal stage;
 additional developing of transv. flow due to shear viscosity (Teaney,
2003);
 effective increase of transv. flow due to initially bumping structure
(Grassy, Hama, Kodama – 2008) ;
+
 correct
description of evolution and decay of strongly interacting and
chemically/thermally non-equilibrated system after hadronisation!
Karpenko, Yu.S. PRC 81, 054903 (2010)
97
Pion, kaon and proton emission densities (Gaussian IC, vacuum c.s.)
T=80 MeV
T=145 MeV
At the point of maximal pion emission
100
Conclusion

The HKM allows one to restore the initial conditions and space-time picture of the
matter evolution in central Au + Au collisions at the top RHIC energy.

The analysis, which is based on a detailed reproduction of the pion and kaon
momentum spectra and measured femtoscopic scales, demonstrates that basically
the pictures of the matter evolution and particle emission are similar at both
Glauber and CGC IC with, however, different initial maximal energy densities: it is
about 20% more for the CGC IC.

The process of decoupling the fireballs created in Au + Au collision lasts from
about 8 to 20 fm/c, more than half the fireball’s total lifetime. The temperatures in
the regions of the maximal emission are different at the different transverse
momenta of emitting pions: T ≈ 75–110 MeV for pT = 0.2 GeV/c and T ≈ 130–135
MeV for pT = 1.2GeV/c.

A comparison of the pion and kaon emissions at the same transverse mass
demonstrates the similarity of the positions of emission maxima, which could point
out to the reason for an approximate mT-scaling.
Iu. Karpenko, Yu.S. PLB 688, 50 (2010)
Pion spectra at top SPS, RHIC and two LHC energies in HKM
Long- radii at top SPS, RHIC and two LHC energies in HKM
Side- radii at top SPS, RHIC and two LHC energies in HKM
Out- radii at top SPS, RHIC and two LHC energies in HKM
Out- to side- ratio at top SPS, RHIC and two LHC energies
in HKM
Emission functions for top SPS, RHIC and LHC energies
The
ratio as function on in-flow and energy
At some p
2
1
2
1
Conclusion
 The main mechanisms that lead to the paradoxical behavior of the interferometry
scales, are exposed.

In particular, decrease of
ratio with growing energy and saturation of
the ratio at large energies happens due to a magnification of
positive
correlations between space and time positions of emitted pions and a developing of
pre-thermal collective transverse flows.
BACK UP SLIDES
Saddle point approximation
Spectrum
Emission
density
where
Normalization condition
Eqs for saddle point
Physical
conditions at
Dnepropetrovsk May 3 2009
:
112
NPQCD-2009
Cooper-Frye prescription
Spectrum in
new variables
Emission density
in saddle point
representation
Temporal
width of
emission
Generalized
Cooper-Frye f-la
113
Dnepropetrovsk May 3 2009
NPQCD-2009
Generalized Cooper-Frye prescription:
t
0
Escape probability
r
114 114
Yu.S. (1987)-particle flow conservation; K.A. Bugaev (1996) (current form)
Nov 3-6
RANP08
Momentum dependence of freeze-out
Here and further for
Pb+Pb collisions we use:
Pt-integrated
initial energy density
EoS from Lattice QCD
when T< 160 MeV, and
EoS of chemically frozen
hadron gas with 359
particle species at T< 160
MeV.
Nov 3-6
115
RANP08
The pion emission function for different pT in hydro-kinetic model (HKM)
The isotherms of 80 MeV is superimposed.
The pion emission function for different pT in hydro-kinetic model (HKM).
The isotherms of 135 MeV (bottom) is superimposed.
Transverse momentum spectrum of pi− in HKM, compared with the
sudden freeze-out ones at temperatures of 80 and 160 MeV with arbitrary
normalizations.
Conditions for the utilization of the generalized
Cooper-Frye prescription
i)
For each momentum p, there is a region of r where the emission function has a
sharp maximum with temporal width
.
ii) The width of the maximum, which is just the relaxation time ( inverse of collision
rate), should be smaller than the corresponding temporal homogeneitylength of the
distribution function:
1% accuracy!!!
iii) The contribution to the spectra from the residual region of r where the saddle point
method is violated does not affect essentially the particle momentum spectrum.
iiii) The escape probabilities
for particles to be liberated just from the
initial hyper-surface t0 are small almost in the whole spacial region (except peripheral
points)
Then the momentum spectra can be presented in Cooper-Frye form despite it is, in fact,
not sadden freeze-out and the decaying region has a finite temporal width . Also, what
is very important, such a generalized Cooper-Frye representation is related to freeze-out
hypersurface that depends on momentum p and does not necessarily encloses the initiall
dense matter.
119
Dnepropetrovsk May 3 2009
NPQCD-2009
A
“Soft Physics” measurements
x
t
Landau, 1953
Δ
ω
K
Cooper-Frye prescription (1974)
A
p=(p1+ p2)/2
QS correlation function
Long
q= p1- p2
p1
p2
Out
Space-time structure of
the matter evolution:
p
BW
120
Conclusions
The CFp might be applied only in a generalized form, accounting for the
direct momentum dependence of the freeze-out hypersurface corresponding
to the maximum of the emission function at fixed momentum p in an appropriate
region of r.
121