tsallis distribution in high- energy heavy ion collisionsg.g. barnaföldi: tsallis distribution in...
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Tsallis Distribution in High-Energy Heavy Ion Collisions
Gergely Gábor Barnaföldi KFKI RMKI of the HAS
in collaboration
T.S. Bíró, G. Kalmár, K. Ürmössy, P. Ván
Non-Ideal Plasma Physics Workshop, 1st-2nd December 2010, Moscow, Russia
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 2
O U T L I N E
● Motivation: just some of them...
● Where to apply Tsallis-Pareto statistics?
● Can non-extensive thermodyn. resolve this?
● Problems of high & low-pT hadron spectra
● Tsallis-Pareto in proton-proton collisons
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 3
Non-extensive thermodynamics (Non-extensive thermodynamics (Based on: T.S. Biró: EPL84, 56003,2008) ) associative composition rule, (non-additive) : associative composition rule, (non-additive) :
Then should exist a strict monotonic function, X(x) 'generalised logarithm' Then should exist a strict monotonic function, X(x) 'generalised logarithm' (an entropy-like quantity), for which:(an entropy-like quantity), for which:
Example: (i) Classical thermodynamics:Example: (i) Classical thermodynamics:
(ii) Tsallis distribution(ii) Tsallis distribution
Basics of non-extensive thermodynamics
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 4
Extensive vs. non-extensive
C. Tsallis: EPJ A40 257 (2009)
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 5
M O T I V A T I O N
● New LHC pp data (CMS)
JHEP 1002:041(2010)
fitted Tsallis distribution for pT spectra:
Parameters:
0.9 TeV T= 130 MeV, q=1.13 2.36 TeV T= 140 MeV, q=1.15 n := (q-1)-1
● RHIC analysis on AuAu data (y=0) Cooper-Frye model: K. Ürmössy, T.S. Bíró: PL B689 14 (2010)
Parameters:
200 GeV T= 51 MeV, q= 1.062 (fit for pT < 6 GeV/c)
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New data at LHC energiesSee: ALICE: Prague Jet workshop & CMS: QCD-10-008
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Comparision in xT: old/new data by Tevatron
See: CDF: PRD 79 112005 (2009) & CMS QCD-10-008
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A new question on the market...
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 9
● Old interpretation 'thermal' & 'non-thermal' models
PT
Incl
. C
ross
Sec t
ion
Thermal Nonthermal
4-6 GeV/c
RHIC/LHC energies
High & low pT hadron spectra
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 10
● A suggested new way: Tsallis (like) distribution
PT
Incl
. C
ross
Sec t
ion
T,q T', q'
4-6 GeV/c
RHIC/LHC energies
Tsallis can fit the distribution
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 11
Scale evoution can resolve the gap...
● Suggested interpetation: Tsallis + evolution
PT
Incl
. C
ross
Sec t
ion
T(Q)q(Q)
T(Q), q(Q)
4-6 GeV/c
RHIC/LHC energies
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 12
●Hadronization: requires a model, based on local parton-hadron duality (kvantum numbers & momenta connected to a cone around or to the leading particle.)
● Parton/hadron shower evolution comes from statistical processes (step-by-step MC evolution). → microscopical
● Fragmentation function (FF) carries integrated (phenomenological) information on how parton fragment into hadron. → integradted distribution
● Measurement lepton-antilepton annihilation, HIC, etc...
Hadronization processes & fragmentation
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 13
1- z1- z 1- z'1- z' 1- z''1- z''
zz
Z'Z'
Fragmentation processes in parton model
In a pQCD based parton model, fragmentation functions (FF) gives how parton (a) fragment into a hadron (h), D
h / a(z,Q2).
DGLAP scale evolution:
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 14
Z
X
i
kj
Fragmentation via associative composition
Program:Program:
1) Search and fit Tsallis distribution 1) Search and fit Tsallis distribution to data.to data.
2) Search for physical meaning of 2) Search for physical meaning of T and q parameters.T and q parameters.
3) Components of the sub-systems 3) Components of the sub-systems are e.g. 'splitting functions' Pare e.g. 'splitting functions' P
q gq g, P, P
g gg g
4) Test: BFKL / DGLAP-like evolution 4) Test: BFKL / DGLAP-like evolution equation ansatz can be inserted.equation ansatz can be inserted.
D(x,QD(x,Q22) ~ f(E,T,q) * f(ln(Q) ~ f(E,T,q) * f(ln(Q22))))
D(x,QD(x,Q22) ~ f(E,T(ln(Q) ~ f(E,T(ln(Q22)),q(ln(Q)),q(ln(Q22))))))
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 15
● TEST on CDF ch. hadron data in pp @ 1.96 TeV |y|<1
● DGLAP motivated evolution: n = (q0-1)-1 –2*log(log(Q))
Joint model: Tsallis with evolution
T = 10.64 q
0= 1.116
NO
evolu
t ion
T = 3.95 q
0= 1.116
Wit
h e
volu
tion
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 16
● More TEST:
0.2 - 7 TeV
midrapidity
data
● C.m. Energy
dependence
of the T & q
parameters
Joint model: Tsallis with evolution
T q
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 17
● TEST on various midrapidity data @ different cm
● The q-T plane
2n d joint model: Tsallis on q-T plane
T q
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 18
Test of the Tsallis based FF
● Tsallis T & q parameters in different channels
● Test of the model: pQCD vs. Tsallis based FF● pQCD based parton model
PRC65 034903 (2002) ● Scalig Tsallis parameters ● DGLAP evolution ● Sum Rule for normalization
GGB et al: Gribov '80 (2010)
Spectrum in pp collisions
q(Q
2 )
T(Q2) [GeV]
T(Q
2 ) [G
eV]
Q2 [GeV2]
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 19
● pQCD based parton model:
QCD at T → 0 temperature
power law distribution
strong dependence on FF
good for high-pT hadrons
● Quark-coalescence model
Thermal, finite temperature
exponential distribution e-m / T
parton-hadron duality
good for high-pT hadrons
P. Lévai, GGB, G. Fai: JPG35, 104111 (2008)
Further motivation...
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 20
S U M M A R Y
● High & low pT spectra has different distribution..
...however hadronization should not work differently.
● Non-extensive (non-equilibrium) thermodynamic
Can be applied generally. Based on composition rules, evolution eq. can be obtain even for non-thermalised case.
● Tests and models with Tsallis assumptions
Seems working for hadron production up to intermediate pT,
and extension to the highest pT region is still question,
however evolution need to be included.
.
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 21
… so we hope...
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G.G. Barnaföldi: Tsallis Distribution in High-Energy Heavy Ion Collisions 22
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