Download Hadron resonance gas models

Statistical Model Description of Particle Production in HIC
Krzysztof Redlich University of Wroclaw & EMMI GSI

Modelling Statistical Operator:
implementic conservation laws
canonical & grand canonical
model: comparisons with
particle yields data in:


e

e
A-A, p-p, and
collisions
Probing thermalisation with
fluctuations of net baryon number
model & experiment (STAR data)
Essential role of higher order moments and their
ratios to probe chiral cross-over transition at LHC
and RHIC
T
LHC

A-A collisions
fixed s
Quark-Gluon
Plasma
Chiral
symmetry
restored
Hadronic matter
Chiral symmetry
broken
x
B
Thermal nature of particle production in HIC
i Q
e

He
 i Q
 H  [Q, H ]  0
All properties of a thermodynamc ensemble in
thermal equilibrium are derived from part. function
Z (T ,V ,  )  Tr[e


  ( H  Q)
To get a specific value of  Qi  one fixes
]
i
from
 Qi  T  [ ln Z(T,i )]/i
The equilibrium number of particles carrying q
 N q   Ve
GC
q 
d
3
pe
- E
2 q 
 VmT e
m
K2 ( )
T
2
Statistical operator and mass spectrum
resonance dominance: Rolf Hagedorn
2
ln Z
GC
Vp
(T ,  )   2 dpdm (m)e  (
2
+ approximate
Hagedorn mass
spectrum
p 2  m2   Qm )
 (m)  m e
a m /TH
 (m)
by experimentally known mass spectrum
and include finite width of resonaces
VT
ln Z (T ,  )  2
2

ihadrons
di e
Qi 
T
s B W
 ds s K 2 ( T ) F (mi , s)
Breit-Wigner resonaces
3
Particle Yields and model parameters

Minimal setup of model parameters
particle yield
thermal density
BR
thermal density of resonances
 Ni  V [nith (T , B )    K i nithRe s. (T , B )]
K

3-parameters needed to fix all particle yields
To account for chemical off-equilibrium effects
introduce fugacity parameters in particle momentum distributions:
ni    i ni
for all particles?
J. Rafelski et. al. => introduce  on the quark level:
Density nh of hadrons composed of ku , kd , ks numbers of
k
k
k
u,d,s quarks gets a factor: nh    u u  d d  s s nh
6-parameters needed to fix all particle yields
4
Hagedorn resonance gas and particle
multiplicity ratios at RHIC
Particle multiplicity ratios
A. Andronic, P. Braun-Munzinger & J. Stachel
MODEL
DATA
P. Braun Munzinger, D. Magestro, J. Stachel & K.R
Good description of particle yields, with the statistical operator of HRG formulated
in GC- ensemble, in central heavy ion collisions from top AGS up to RHIC .
Problems with strangeness yields in non-central collisions at high energy and in
central collisions from SIS-AGS. K – yields differ by a factor of almost 20 at SIS!
5
Kinetics of abelian charges
C.M. Ko, V. Koch, Z. Lin, M. Stephanov, Xin-Nian Wang, K.R
T,V
Consider:
d  NK  
Rate equation
NK   N
 N  K 

dt
 NK   NK      N
and
N
Z
GC
Vm
K
TK 2 (
mK 
T
(T ,V ,  )  Tr[e
2

 N K    1
2
G
L

    N    N K  N  
V
V
2
Size of fluctuations
GC
K

)
N
C
K
  ( H  Q)
]

Equilibrium limit
 N K    1
2
K


 NK 
m
Vm TK 2 (
) Vc m TK 2 ( )
T
T
mK 
2
K
2
Z (T ,V )  TrS [e
C
 H
]
6
i S
i S
e He
 H  [S , H ]  0
conservation on the average
Z (T , S ,V )  Tr [e
GC
Z
GC

S 
e
S 
S S / T
Z
C
S
  ( H  S S )
exact conservation
] Z (T ,V )  TrS [e
1
Z S (T ,V ) 
2
Consider thermal system with
Total Strangenes “S”=0
A
A
A
A
nSC   Ss nGC
C
S
2
 d e
 iS
Z
GC
S
(T ,
T
0
 H
]
 i )
S= -1
S=1 VC  Vh Apart
GC
IS( s 2VC nsGC
n
1 s 1 )
GC
I 0 ( s 2VC nsGC
n
1 s 1 )
same suppression factor
1 for S and S
N
GC
N
C
suppression increases with S and with decreasing collision energy
Apart
2
part
A
7
i) Strong, quadratic dependence of |S|=1 particles with Apart at SIS
ii) strange anti-particle/particle ratios independent of Apart
 N
 
 K  C

K Y
Apart e( m B ) / T
Ap2art emk / T e( mY B )/ T
J. Cleymans, H. Oeschler & K.R.
KaoS (GSI-SIS)
8
iii) Scaling properties of particle production yields

Excellent description of kaon
production from SIS to AGS
subthreshold
J. Cleymans, H. Oeschler & K.R.
 N
K     [ K  ]  []
 
[ ]
[K ]
K N 

[N ]
[]



Scaling:
[K  ]
[ ]


[K ]
[N ]
similar scaling for [ ]/[ K  ]    [ K  ]/[ N ] : A. Andronic, P. Braun-Munzinger & K.R.
9
Strangeness Enhancement from pp to AA increases with:
i) strangeness content of the particle
ii) with decreasing collision energy
A. Tounsi & K.R
NA57
STAR
Apart
Decrease of enhancements from SPS to RHIC as predicted in the model
Consistent predictions for order of magnitude of enhancements of Omega and Xi at RHIC
Centrality dependence not correct when assuming Vcor . Apart ,however Vcordoes
not need
.
to scale linearly.

Assume:
Vcor  ( Apart / 2) V0 with   1
10
Canonical statistical model in pp collisions:
Using Canonical description of strangeness
and Grand Canonical for baryon number
and electric change conservations in p-p
collisions is a good approximation
Using correlation volume instead of
strangeness undersatuaration factor
could be equivalent: see also
I. Kraus H. Oeschler; F. Becattini et al.
P. Braun-Munzinger et al. from “QGP” 3
11
Canonical statistical model in pp collisions:
Using Canonical description of strangeness
and Grand Canonical for baryon number
and electric change conservations in p-p
collisions is a good approximation
LHC H. Oeschler et al.
Observed deviations from Thermal
Model predictions !!
P. Braun-Munzinger et al. from “QGP” 3
12
Fixing thermal parameters:
p-p
C-C Si-Si
J. Cleymans et al.
Pb-Pb
I. Kraus et al.
Temperature approximately independent of system size and centrality
Strong variation of baryon chemical potential with centrality and system size
for mid-rapidity data
13
Energy dependence of thermal parameters
at chemical freeze-out
J. Cleymans et al.
A. Andronic et al.
14
Particles excitation functions in HG model
Braun-Munzinger, Cleymans, Oeschler &K.R.
Andronic, Braun-Munzinger &Stachel (09)
Nu Xu & K.R. H.Oeschler et al.
Problem with
canonical
description of
HADES data: data
deviate by factor
five from model
predictions!!
HADES
15
The Yields of anti-hypernuclei at RHIC
N. Sharma et al., A. Andronic et al.

First observation
of hypernuclei 1952
by Danysz and Pniewski
 First observation of
anti-hypernuclei by
STAR in AU-AU coll.
 Can we understand
yields within the SM?
Statistical Model Results
3
 p
 
 p
2
3


He
p



exp(

[6


2

]
/
T
)


B
S
3
 He
 p 
3
He
 exp(6 B / T )
3
He
Coalesence Model Results
3
He p pn  p 

 
3
He ppn  p 
3
3

3

2
pn  p  

 
He pn  p  
He
16
 
Charm production in e e annihilation
Jet structure of hadrons production
Flavor content of the jets:
up type quarks  (u, c)
down type quarks  (d , s, b)
Can we quantify light and heavy flavor particles within Statistical Model ??
17
Most hadronic events in high energy e+e􀀀 collisions are two-jet events
Each jet represents an independent fireball
T  158  0.5 V  30  1
 S  0.8  2 / dof  558 / 28
Problem: Open Charm and Bottom
shows dramatic deviations from data
 N B  mod el / data  1020
2-jets with Q  0
 N D   mod el / data  102
Subtract the contributions from
charm and bottom to lighter particles
e.g. C,B contributions to
   11.7%, K   30.0%
K *0 (892)  16.5%,  (1020)  68.0%
2-jets with Q  0 sub. decays of “C” and “B”
T  169  0.5 V  18  1
 S  0.68  2 / dof  686 / 28
18
Canonical effects and charm/bottom mesons
Qi
di
3

d
p exp(  ( Ei  bi   i )
3 
(2 )
zi
I
(
2
V
x
)
Z
Q 1
 N i QQi 1  V  ziQi 1
Qi 1
x
I
(
2
V
x
)
Z 1   zi
Q
Charge of the particle
Charge of the system
x  Z 1Z1
i
Q0
Total charge of the system
And small 2Vc x  1
 Ni QQi0 1  V  zi V  Z1
Strong Suppression of thermal
particle phase-space
Q  1
 Ni 
Q 1
Qi 1
V  zi

V  Z 1
Strong Enhancement of thermal
particle phase-space
19
Charm and Bottom particles at LEP, 91 GeV
D
DS*
D0

S
D
D*
 c1
J /
'
B
BS 0 B* Y
 c
Ds1
 0B
Open charm and bottom well described by thermalisation of thermal fireball with
overall Charm= 1 and Bottom= 1
J / ,  ' and  c are entirely coming from Bottom’s decays and agree with model
Hidden charm, Y is of non-thermal origin, thus, it does not fit to model systematic!20
Production cross section of  relative to J / 
'
A. Andronic, F. Beutler, P. Braun-Munzinger, J. Stachel &K.R.
NA50
The ratio for the Tevatron energy was derived
from the CDF data on J /  and  '
and is for pt  1.25 GeV :
'
We have extrapolated the  measurements
from pt  2 GeV down to 1.25 GeV
Strong suppression of  / ( J /  ) ratio
in PbPb relative to pA , pp and pp
different production mechanism in
elementary and heavy ion collisions
'
RHIC
CDF
The nuclear modification canceled
'
out in the  / ( J /  ) ratio as the pp
value is the same as in the pA
Data pA compilation by:
Good agreement of Statistical Model
and data in PbPb collisions
21
STAR DATA ON MOMENTS of B  p  p FLUCTUATIONS
 NB  NB  M B
Phys. Rev. Lett. 105, 022302 (2010)

Mean
M B  N p    N p 

Variance
 B 2  ( N B )2 

Skewness
S B  ( N B )3  / B 3

Kurtosis
 B  ( N B )  / B  3
4
4
Properties of fluctuations in HRG
F. Karsch & K.R.
 B( n )
 n ( P(T ,  B ) / T 4 )

(B / T )n
Calculate generalized susceptibilities:
from Hadron Resonance Gas (HRG) partition function:
P HRG  Pmesons  Pbaryons and Pbaryons  T 4 F (m / T ) cosh(3q / T )
baryons
 B( 4)
1
(2 )
B
 B(3)
1
(1)
B
( 4)

resulting in:  B B2  B( 2 )
B
 B(2)
 B(3)
 coth(  B / T ) and
 tanh(  B / T )
(1)
(2)
B
B
 B2
 B(2)
 (1)
M B B
S B B 2
 B(3)
 ( 2)
B
Compare this HRG model predictions with STAR data at RHIC:
Comparison of the Hadron Resonance Gas Model
with STAR data

Frithjof Karsch &K.R.
K.R.

RHIC data follow
generic properties
expected within
HRG model for
different ratios of
the first four
moments of baryon
number fluctuations
Can we also quantify the energy dependence of each moment separately
using thermal parameters along the chemical freezeout curve?
Mean, variance, skewness and kurtosis obtained
by STAR and rescaled HRG


STAR Au-Au s  200
M p  p  8.5
STAR Au-Au s  200
M p  p  1.8 these data,
due to restricted
phase space:
Account effectively
for the above in the HRG model
by rescaling the volume
parameter by factor 1.8/8.5
QCD phase boundary & Heavy Ion Data

Particle yields and their
ratios, well described by
the Hadron Resonance
Gas

QCD phase boundary
appears near freezeout
line
Thus: HRG has to be a good description
of regular part of QCD partition
function in hadronic phase
Thus: HRG has to describe LGT
thermodynamics
Kurtosis as an excellent probe of deconfinement
S. Ejiri, F. Karsch & K.R.
1 c4

9 c2
Kurtosis
R4,2
B

HRG factorization of pressure:
PB (T , q )  f [T ,  (m)]cosh(3q / T )

F. Karsch, Ch. Schmidt

consequently: c4 / c2  9 in HRG
2
In QGP, SB  6 / 
Kurtosis=Ratio of cumulants
c4q / c2q 
B
The R4,2
measures the quark
content of particles carrying
baryon number
 ( N q )4 
 ( N q )2 
 3  ( N q )2 
excellent probe of deconfinement
Higher moments of baryon number fluctuations
J. Engels, F. Karsch, B. Friman, V. Skokov & K.R.

If freeze-out in heavy ion
collisions occurs from a
thermalized system close
to the chiral crossover
temperature, this will lead
to a negative sixth and
eighth order moments of
net baryon number
fluctuations.
These properties are
universal and should be
observed in HIC
experiments at LHC and
RHIC
Figures: results of the PNJL model
obtained within the Functional
Renormalisation Group method 28
Fluctuations of 6th and 8th order moments exhibit strong
variations from HRG results:
Their negative values near chiral transition to be seen in
heavy ion collisions at LHC and RHIC
The range of negative fluctuations near chiral cross-over: PNJL model results with
quantum fluctuations being included : These properties are due to O(4) scaling ,
thus should be also there in QCD.
29
Conclusions


The Hagedorn partiction function of the Hadron Resonance
Gas is a very good approximation of the regular part of the
QCD partiction function:
=> it reproduces bulk of particle yields meassured
form SIS up to LHC energy
=> it reproduces net proton fluctuations up to 4th order
measured at RHIC
=> It reproduces fully ratios of different
susceptibilities obtained on the lattice
=> it reproduces thermodynamics up to very near
T_c obtained on the lattice for different quark
masses
The 6th and 8th order moments of baryon number
fluctuations are excellent probes of chiral cross-over
30
transition in HIC at the LHC and RHIC
Centrality dependence of baryon chemical potential
For NA57 the temperature is fixed to T  168 MeV from central
Pb-Pb collisions: ( the value consistent with recent analysis of A. Andronic et al.)
31
Strangeness enhancement from p-Be to
central Pb-Pb collisions at s  17.3 GeV
NN
Canonical model with exact strangeness conservation at fixed T  168 MeV
and  B being centrality dependent provides good description of NA57 data if the
correlation volume scales as:
V  ( A / 2) with   1/ 3
part
32
Multistrange particle enhancement at RHIC
Calculations done at fixed T  164MeV ,   20MeV (Nu Xu et al.) for all centrality
Overall agreement is not satisfactory, particularly for Lambda yields
33