Pions and kaons from stringy quark matter T.S.Bíró and K.Ürmössy , MTA KFKI RMKI Budapest, Hungary • String model, string distribution • EoS with stringy interaction • Coalescense from stringy matter • Pion and kaon pt spectra SQM 2008, Peking, China.
Pions and kaons from stringy quark matter T.S.Bíró and K.Ürmössy, MTA KFKI RMKI Budapest, Hungary String model, string distribution EoS with stringy interaction.
Dec 31, 2015
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Pions and kaons from
stringy quark matter
T.S.Bíró and K.Ürmössy,
MTA KFKI RMKI Budapest, Hungary
• String model, string distribution
• EoS with stringy interaction
• Coalescense from stringy matter
• Pion and kaon pt spectra
SQM 2008, Peking, China.
Statistical Model
How can be E / N = 6 T ?
Massive hadrons (rho?)
How can be E / N = 6 T ?
Statistical Model: hadronization point around µ = 0 (RHIC, LHC)
How can be E / N = 6 T ?
Ideal gas of radiation
How can be E / N = 6 T ?
Bag Model for QGP
How can be E / N = 6 T ?Stringy Massless QGP
How can be E / N = 6 T ?Stringy Massless QGP
322331 // nAnngσσn
Biro, Cleymans, 2008
Stringy corrections to QGP
Endline: last possible solution
Boltzmann approximation
T
µ
This branch is given by Lambert’s W
High – T equation of state
31
13144
213
:QCD lattice
~1
313
TcT
A
T
pe
Medium-high-T behavior of lattice eos
2
20
T
m
High-T behavior of lattice eos
Boltzmann approximation
Fodor Katz
High-T behavior of lattice eos
Boltzmann approximation
Fodor Katz
The zero pressure line
St. Mod.
Pressure: NP effects at any T
)(1
)()0(22)(
)()(
)()(
222
2
2
/
00
22
0
2222
T
TfT
pppp
dxxfdQQP
dQQPpdQQPpp
NPpp
T
NPP
If it were f(0) = 0, then the QGP pressure would be free of NP effects!
Thermal distribution of Q²
Q²9T²
1/16T²
Coalescense kinematics with strings
qpp
ppp
pmEEH
221
21
22
21
m
Coalescense: formula
m
mEEE
mgqmC
qpfqpf
H
with
))((
)(),(
)2/()2/(
2
21
2
21
Coalescense factor
)(~
~)(
3
222
3
q
qqC
Coalescense: string mass distribution
d
dd
m
mmmg )1(exp~)( 11
Prejudice: d = 1…3
Biro,Shanenko,Toneev: 1999
Coalescense ratio vs string mass
21
)()()()(
)(
2211EEE
H
HH
H
dmmgEGEfEf
Ef
Prejudice: d = 1…3
Goal: fit the parameters of g(m) from low pt
need for strings at low pt
)()(/)(2211EfEfEfG
HH
π
K
blue: fitted g(m)
π: <m>=0.087, d=1.187; K: <m>=0.121, d=1.595
Inetgrated String-length Distribution
K
π
dmmg )(
π: T=100 MeV, q=1.096; K: T=70 MeV, q=1.102
Comparison with RHIC Spectra
v=0.274
Max:
Antiproton spektrum (RHIC)
Max:
Kaon spektrum (RHIC)
STAR
PHENIX
TK=142MeV qK=1.059
Pion spektrum (RHIC)
Max: no data around mpion
PHENIX
Flows with p-
Flows with Kaon
vflow=0.27Tп1=107MeV
qп1=1.096
qп2=1.096
Tп2=75MeVvflow=0.55
Summary
• Strings give a realistic eos and E / N = 6T
• Above Tc there are non-perturbative
effects
• Coalescence of Tsallis-Pareto distributions
• Strings help the product formula at low pt
• Expect at LHC: same T, different q
If the accumulation of false beliefs is cleared away, Enlightenment will appear.
But, strange enough, when people attain Enlightenment, they will realize that
Without false beliefs there could be no Enlightement.
(The Teaching of Buddha)
Bibliography
• arXiv: 0801.3998, T.S.Biro and J. Cleymans: The hadronization
line in stringy matter
• hep-ph / 98083941, T.S.Biro, P.Levai, J.Zimanyi and C.Traxler:
Hadronization in heavy ion collisions, PRC59, ……, 1999
• T.S.Biro, A.A.Shanenko and V.D.Toneev: Toward Thermodynamic
Consistency of Quasiparticle Picture, Phys.Atomic Nuclei 66, 982, 2003
• J.Cleymans, H.Oeschler, K.Redlich, S.Wheaton, PRC73, 034905, 2006.
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