topological structure of dense hadronic matter
DESCRIPTION
May 2006 Trieste. Topological Structure of Dense Hadronic Matter. V. Vento Universitat de València. Colaborators: Heejung Lee (APCTP), Byung-Yung Park (Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and Mannque Rho(Saclay). Introduction A theory for Nuclear Structure - PowerPoint PPT PresentationTRANSCRIPT
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Topological Structureof
Dense Hadronic Matter
May 2006Trieste
V. VentoUniversitat de València
Colaborators: Heejung Lee (APCTP), Byung-Yung Park(Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and
Mannque Rho(Saclay)
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1. Introduction2.A theory for Nuclear Structure3.Dense Skyrmion Matter4.Pions in Dense Skyrmion Matter5.Sliding Vaccua6.Vector Mesons 7.Ongoing work8.Concluding remarks
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1. Introduction
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TheoryEffectiveRelevant degrees of freedom?
Dynamics?
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Effective Theory
QCD
Observation
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Quantum Chromo-Dynamics
Effective Theoryat zero
Temp./Density
Effective Theoryat finite
Temp./Density
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2. A theory for Nuclear Structure
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Skyrme’s Old Idea 1960, T. H. R. Skyrme
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Skyrme’s Old Idea
U(x) : mapping from R3-{ }=S3 to SU(2)=S38
topological soliton
1960, T. H. R. Skyrme
R ~ 1 f m M ~ 1.5 GeV BARYON
1983 Adkins,Nappi,Witten,….
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Two SkyrmionsProduct Ansatz 1984 Orsay group, VV,..
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1988, Braaten,Carson,…. Manton and collaborators
Toroidal B=2 Skyrmion
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Multi-Skyrmion Systems(surface of constant baryon number density)
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Quantization is progressingManton (B=2), Carson (B=3), Walhout (B=4), Irwin (B=4 to 9), Krusch (general formalism!)
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3. Dense Skyrmion MatterB.-Y. Park, D.-P. Min, M. Rho, V. Vento,
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z
Skyrmion Crystal1985, CC, I. Klebanov, 1987, Half-Skyrmion BCC, A. S. Goldhaber & N. S. Manton1989, FCC & Half-Skyrmion CC, L. Castillejo et al., M. Kugler et al.
o
o
o
o
o
o o
z
zx
yx
oy
2LFCC
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E/B vs. LF
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<tr(U)>
Chiral symmetryrestoration
in dense matter?
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3. Pions in Dense Skyrmion Matter B.-Y. Park, H.-J. Lee, M. Rho, V. Vento
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Skyrme Model(m=0)\
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dynamics(=0)\
+ -skyrmion matterinteractions
Skyrmion matter
Pion fluctuations on top of the
skyrmion matter
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dynamics(=0)\
Wavefunction renormalization constant Z-1
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nuclear matter density
-N sigma term
Chiral Symmetry Restoration
pion properties in dense medium?
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GellMann-Oakes-Renner Relation
Chiral symmetry restoration
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GellMann-Oakes-Renner Relation
pion condensation?
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Pion effective mass
Pseudogap phase?
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Pion velocity in medium
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f
Pseudogap?
Zarembo, hep-ph/0104305
U still remains on the Chiral Circle
But <U>=0Chiral Symmetry
Restoration
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Zarembo, hep-ph/0104305
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4. Sliding Vacuua B.-Y. Park, H.-J. Lee, M. Rho, V. Vento
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Skyrme Lagrangian
Trace Anomalyof QCD
m ~ 720 MeV, f~240 MeV
Ellis & Lanik, PLB(1985)
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f
V
Vacuum (=0)U=1=f
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Naive Estimate
E/B=M2(L)2+M4(L) +Mm(L) 3+V()
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E/B
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In-medium quantities
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5. Vector Mesons
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Hidden Local Gauge Symmetry
dilaton
Trace Anomaly
rho & omega vector mesons
HLG
+ Vector Meson Dominance
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KSRF relation : mV=afg222
Bando, Kugo, Yamawaki, Phys. Rep. (1988)
pions, chi, rho and omega
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E/B
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<> & <> without Omega
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<> & <> with Omega
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6. Ongoing work
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position
orientation
size
Introduce variables describing the single skyrmion dynamics
Classical mechanicsStatistical mechanicsQuantum mechanics
Skyrmion from Instanton1989, M. F. Atiyah & N. S.Manton
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time component of SU(2) gauge potential for the instanton field of charge N
time-orderingconstant matrix to make U approach 1 at infinity
constant rotation matrix
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E/B vs. LF
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7. Concluding remarks
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The skyrmion role in dense matter
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1. Construct dense skyrmion matter 2. Fluctuations
on top of this skyrmion matter.
Properties and Dynamics of hadronsin dense medium.
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Skyrme model
• Universal theory of baryons and mesons • Nuclei and meson fluctuations • Nuclear matter and mesons in the medium …….. Nuclear physicists dream!
Caveats:• Still very primitive! Crystal structures
which should be Fermi liquids Quantum effects!• Approach to QCD