Mesonic Bound States Above Tc
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Mesonic Bound States Above Tc
The Problem of Mass
Chang-Hwan Lee @
QM2005@Budapest
in collaboration with
G.E. Brown, M. Rho,(partly, H.-J. Park, E. Shuryak)
NPA 740 (2004) 171; 747 (2005) 530 hep-ph/0503016nucl-th/0507011; nucl-th/0507073
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Plan of Talk
Below Tc : Chiral Symmetry Restoration
Above Tc: colorless Mesonic Bound States
Brown/Rho Scaling
Vector Manifestation a la Harada/Yamawaki
What can we learn from lattice calculations ?
Implications for RHIC: Scaling decay width & Delayed-decay of mesons
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Dropping Masses a la Brown/Rho Scaling
Harada/Yamawaki & Harada/Sasaki/Rho
Vector Manifestation.
Below Tc: Chiral Symmetry Restoration
Fixed Point of RG approach gives
vanishing coupling, vanishing mass
towards chiral symmetry restoration point.
both mass & decay-width scale !
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Tc
M
below TcChiral Symmetry Restoration
Q) What happens above Tc ?
Hadronization ?
Vector Manifestation RG
fixed point
Vanishing coupling
RHIC
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Matter formed at RHIC is not weakly interacting quasi-particle gas.
Above Tc:
Ideal Liquid at RHIC (Shuryak’s talk)
Can hadronic modes survive after phase transition ?
How can these modes connected with chiral symmetry restoration below Tc ?
Question
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Mesonic bound states above Tc:
Hatsuda & Kunihiro, PRL 55 (1985) 158 (para pion & sigma)Asakawa, Hatsuda, & Nakahara, NPA 715 (2003) 863cBrown, Lee, Rho, & Shuryak, NPA 740 (2004) 171
Quark-antiquark bound states exists above Tc.QM2005
- Poster by Kitazawa (with Kunihiro, Nemoto) hep-ph/0505070, …- talk by Mannarelli (with Rapp)
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What is the binding energy if we take the potential extracted from lattice free energy ?Assumption: finite value of V1 at r=∞ is absorbed into the
renormalized thermal mass of quarks.
Potential from Bielefeld Lattice Results
cf) Wong, hep-ph/0408020; combination of V & F
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Above Tc: Running coupling at large diatance
Lattice Calculation by F. Zantow et al. (Bielefeld)
Strong coupling regime above Tc
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mq=1.4 GeV
Heavy quark potential (renormalized) from Bielefeld lattice
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Mass of Bound States (with heavy quark potential)
Solid lines are just to guide you.
thermal quark mass
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color-magnetic effects (cf K-electron)
With chirally restored u, d quarks (helicity eigenstates)
alpha =velocity of particles (c=1 unit)
32 degrees of freedom (including plasmino) close to lattice result 37 at Tc !
Modification for light quarks in chiral limit
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With modified potential (chiral limit)
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heavy quark potential
chiral limit
chiral limit
heavy quark potential
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Unorthodox phase structure (Hypothesis)
Masses of colorless pion, sigma-like modes above Tc go to zero at T = Tc;+
QGPIdeal Liqui
d
Mesons disappe
ar
Tc Tzb
a1M2mq*
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Lattice Results from Miller: Gluon Condensate
Soft glue
Hard glue
Hard glue is responsible for ldea
l liquid
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Scaling decay width (nucl-th/0507073)
dominant decay is around & below T=120 MeV
No decay near Tc !
Vector manifestation by Harada & Yamawaki
Implications for RHIC
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Tc : chemical equilibrium
Equilibrium is already established above Tc at RHIC
STAR: Peripheral collisions: Tchemical freeze out = Tc
Delayed decay of rho at T=120 MeV
PRL 92 (2004) 092301
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Peripheral collisions: Tchemical freeze out = Tc
4 x 10-4 with vacuum mass( Braun-Munzinger et al. )
With massless mesonic bound states at Tcthis ratio is governed mainly by degrees of freedom
3 (rho0)3(pi) + 18 (pi from rho)
= 0.14
nucl-th/0507073 : 0.14 ≤ (rho0/pi-) ≤ 0.21
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Our analysis (chiral symmetry restoration + Bielefeld Lattice Result) indicates masslessmesonic bound states at Tc;+.
mass & width (simultaneous scaling):delayed rho decay is consistent with rho/pi ratio in peripheral collisions in STAR.
Conclusions
Thanks to Bielefeld Lattice Group (F. Zantow) for providing us their results.