The hadronization line in stringy quark matter

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The hadronization line in stringy quark matter
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Dictionary.refrence.com/search?qstringy

• Modern Language Assciation, Random House Inc.
  2008
• Resembling a string or strings, consisiting of
  strings or stringlike pieces stringy weeds a
  stringy fiber
• Coarsely or toughly fibrous, as meat
• Sinewy or wiry, as a person
• Ropy, as a glutinous liquid

• The American Heritage Dictionary of the English
  Language, Houghton Mifflin Co. 2006
• Consisting of, resembling or containing strings
  or a string
• Slender and sinewy wiry
• Forming strings, as a viscous liquid ropy.

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Dictionary.refrence.com/search?qstringy

• On-line Medical Dictionary, 1997-98 Academic
  Medical Publishing CancerWEB
• Consisting of strings or small thraeds fibrous
  filamentous as a stringy root.
• Capable of being drawn into a string as a
  glutinous substance ropy viscid gluely.
• Stringy bark, a name given in Australia to
  several trees of the genus Eucalyptus (as E.
  amygdalina, obliqua, capitellata, macrorhyncha,
  piperita, pilularis and tetradonta), which have a
  fibrous bark used by the aborigines for making
  cordage and cloth.

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The hadronization line in stringy quark matter

• T.S.Bíró, MTA KFKI RMKI Budapest, Hungary
• J. Cleymans, University of Cape Town, South Africa

• How can be E / N 6 T ?
• Stringy corrections to QGP
• High-T equation of state
• The zero pressure line

NFQCD Workshop, Yukawa Institute, Kyoto, February
13, 2008.
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Statistical Model
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How can be E / N 6 T ?
Statistical Model hadronization point around µ
0 (RHIC, LHC)
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How can be E / N 6 T ?
Massive hadrons (rho?)
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How can be E / N 6 T ?
Ideal gas of radiation
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How can be E / N 6 T ?
Bag Model for QGP
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How can be E / N 6 T ?
Stringy Massless QGP
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How can be E / N 6 T ?
Stringy Massless QGP
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How can be E / N 6 T ?
This is more generally true!

• correction depends on
• constituents are massless
• Boltzmann approximation is acceptable

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Stringy corrections to QGP
color density
free energy density fractional power
chemical potential
pressure
energy density
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Stringy corrections to QGP
Consistent solution for color density in
equilibrium
It exists only beyond an endline in T - µ
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Stringy corrections to QGP
Consistent solution for color density in
equilibrium
µ
T
c
It exists only beyond an endline in T - µ
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Stringy corrections to QGP
One massless component, Boltzmann approximation
The solution is related to Lamberts function
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Stringy corrections to QGP
Endline last possible solution
Boltzmann approximation
It is near to the zero pressure line for low
chemical potential
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Stringy corrections to QGP
End temperature last possible solution at µ 0
Boltzmann approximation
It is near to the zero pressure line for low
chemical potential
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Stringy corrections to QGP
Endline last possible solution
Boltzmann approximation
T
This branch is given by Lamberts W
µ
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The zero pressure line
Zero pressure in the Boltzmann approximation
Endline and zero pressure line are relatively
close! (T0 ? 1.04 TE)
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E/N at the zero pressure line
General relations
This is independent of the value of the string
tension!
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High T equation of state
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High-T behavior of lattice eos
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High-T behavior of lattice eos
Fodor Katz
Boltzmann approximation
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High-T behavior of lattice eos
Fodor Katz
Boltzmann approximation
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Where to stop with the Boltzmann approximation?

• Fermi integral ? Boltzmann integral for negative
  or zero µ.

The endline does not turn back!
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The zero pressure line
Fermions (quarks only) at T 0
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The endpoint at T0
6µ
3µ
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The zero pressure line
St. Mod.
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Summary

• E / N 6T only from stringy massless QGP
• fractional power is 1/3 from high-T lattice eos
• zero pressure line and endpoint of solution are
  close
• at finite baryon density and zero temperature
  the hadronization line is at mu_B 3 k_F
• at any temperature IR effects may be present
  (already a small string tension makes E / N 6T)

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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)
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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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Discussion
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FAQ

• What is actually non-ideal at T gt Tc ? (low Q2
  pairs)
• What is non-particle like (stringy) at T gt Tc ?
  (interaction)
• Are all color charges stringed at T gt Tc? No! (a
  small fraction suffices for the effect.)
• Asymptotic freedom is incomplete at any finite
  temperature. Why and what is the quantitative
  measure of this effect? ?

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Arguments

• Non-perturbative effects at arbitrary high
  temperature

• Thermal distribution of Q²
• NP order parameter
• Its thermal expectation value ? order of NP
  effects
• high-T expansion
• ? high-T NP terms in EoS (pressure, int.mesure)

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Pressure NP effects at any T
If it were P(0) 0, then the QGP pressure would
be free of NP effects!
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Thermal distribution of Q²
1/16T²
Q²
9T²
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Thermal expectation of NP order parameter
1
1
Q²
T²
?²
?²
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NP effects at high T in the EoS
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To do list

• Include massive quarks (strange)
• Compare stringy matter and quasiparticle mass
  effects to leading order at high T
• Compare stringy eos with power-law tail effects
• Compare with other simple ideas, like Q2 cutoff

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