Half- Skyrmion Matter & Quarkionic Matter

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HIM-WCU workshop Hanyang U. Oct. 31 , 2009. Half- Skyrmion Matter & Quarkionic Matter. Byung -Yoon Park ( Chungnam Nat’l Univ.). Collaborators. M. Rho( Saclay , Hanyang Univ.) V. Vento(Valencia Univ.) D.-P. Min(Seoul National Univ.) H.-J. Lee( Chungbuk National Univ.). Contents. - PowerPoint PPT Presentation

Text of Half- Skyrmion Matter & Quarkionic Matter

PIONS IN SKYRME MATTER

Half-Skyrmion Matter&Quarkionic MatterHIM-WCU workshopHanyang U.Oct. 31, 2009Byung-Yoon Park(Chungnam Natl Univ.)1CollaboratorsM. Rho(Saclay, Hanyang Univ.)V. Vento(Valencia Univ.)D.-P. Min(Seoul National Univ.)H.-J. Lee(Chungbuk National Univ.)ContentsSkyrme Model ?2. Dense Skyrmion Matter3. Dense & Hot Skyrmion Matter4. Summary31. Skyrme Model?Skyrmion ModelU(x) : mapping from R3-{ }=S3 to SU(2)=S38topological soliton

1960, T. H. R. Skyrme

R ~ 1 f m M ~ 1.5 GeVBARYON ?protonneutron1919 Rutherford1932 Chadwickpionprotonneutron1935 YukawaHadronic World(Skyrmionists Viewpoint)pion1960 Skyrme6The following is the chronicle of hadronic world in the viewpoint of a skyrmionist. First there were nucleons.Then, the pion is introduced by Yukawa. At that time it was just a messenger, mediating the nuclear force among nucleons.Now, there are only pions in the hadronic world, because pions can produce the nucleons in the form of soliton.

SU(2) Collective Coord. QuantizationN, DSU(3) collectiveCoordinateQuatizationN, S, X, D, S*, X*,WN, S, X, D, S*, X*,W

Hedgehog SolitonSU(2) collectiveCoordinateQuatizationbound kaonN, S, Xc, D, S*, X*,Wc

Hedgehog SolitonSU(2) collectiveCoordinateQuatizationbound D,D*ccMulti-Skyrmion system

B=2 TorusB=3 TetrahedronB=4 CubeB=5 with Dd2 symB=6 with Dd4 symB=7 DodecahedronToroidal B=2 skyrmion

1988, Braaten & Carson, 1995, Leese, Manton & Schroers2. Dense Skyrmion Matter

2. Dense Skyrmion matter

Two skyrmions in the most attractive configuration.2. Dense Skyrmion matter1985, I. Klebanov(E/B)min=1.078 at LC=5.56Simple Cubic Skyrmion CrystalU(x+LC,y,z) =ty U(x,y,z) tyyYzxzxxxXyLCo2. Dense Skyrmion matterHalf-Skyrmion CrystalU(x+LC,y,z) =tyU(x,y,z)ty1987, A. S. Goldhaber & N. S. Manton+ additional Symmetryw.r.t.s -s(E/B)min=1.076 at LC=5.56yzxXLCs=-1s=+1(Lb/2 above)02. Dense Skyrmion matterU = exp(i F(r)t r ) ^.

Half-skyrmion?F (r ) r pU =-12. Dense Skyrmion matter

U =-1U =-1U =+12. Dense Skyrmion matter

U =-1U =-1U =+12. Dense Skyrmion matter

B=4 skyrmion2. Dense Skyrmion matter1989, L. Castellejo et al. & M. Kulger et al.yYxxXyz=LF/2 planeYozzzXzLFz=0 planeFCC Skyrmion Crystal2. Dense Skyrmion matterYX(E/B)min=1.038 at Lf=4.72ozYzzXzLFyxxyHalf-Skyrmion CC2. Dense Skyrmion matter

E/B vs. LF

2. Dense Skyrmion matter

=Chiral symmetryrestorationin dense matter?2. Dense Skyrmion matter

static soliton config.fluctuating pionsPion in the dense baryonic matter?classicaldense matterconfig.2. Dense Skyrmion matterSkyrme Model(mp=0)

\Pion fluctuation in rB=0 spaceVacuum : U=12. Dense Skyrmion matterp dynamics(r=0)

\+ p-skyrmion matterinteractions

Skyrmion matterPion fluctuations on top of the skyrmion matter2. Dense Skyrmion matter

p dynamics(r=0)\

2. Dense Skyrmion matter

p dynamics(r=0)\

2. Dense Skyrmion matterp dynamics(r=0)\

In-Medium pion decay constant ?In-Medium pion mass ?

2. Dense Skyrmion matterpion effective mass

H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A (2003)!2. Dense Skyrmion matterfpspPseudogap?Zarembo, hep-ph/0104305U still remains on the Chiral Circle But =0Chiral Symmetry Restoration2. Dense Skyrmion matter

Skyrme LagrangianTrace Anomalyof QCD2. Dense Skyrmion matterSkyrme LagrangianEllis & Lanik, PLB(1985)Brown-Rho scaling, PRL(1992)mc ~ 720 MeV, fc~240 MeV

2. Dense Skyrmion matterfccV(c)Vacuum (r=0)U=1 c=fcfpsp

U cU2. Dense Skyrmion matterNaive EstimationE/B=M2(L)c2+M4(L) +Mm(L) c3+V(c)L3

2. Dense Skyrmion matterNaive Estimation

2. Dense Skyrmion matterE/B

=0 phaseChiral phase transition=0 phase/2. Dense Skyrmion matter &

PseudogapPhase?cS PhasecSB Phasemp=02. Dense Skyrmion matterpPseudogap still remains?fpsfpss**cSB PhasePseudogapPhasecSPhasepp2. Dense Skyrmion matter3. Hot & Dense Skyrmion Matter

?2. Hot & Dense Skyrmion matterSkyrmion SoupCondiments : dilaton vector mesons Heat

Main ingredients : pions B.-Y. Park, H.-J. Lee, V. Vento, Phys. Rev. D80 (2009)2. Hot & Dense Skyrme matterSkyrmion from Instanton1989, M. F. Atiyah & N. S. Manton

time component of SU(2) gauge potential for the instanton field of charge Ntime-orderingconstant matrix to make U approaches 1 at infinityconstant rotation matrix2. Hot & Dense Skyrmion matter

E/B vs. LF

2. Hot & Dense Skyrmion matter

B.-Y. Park, D.-P. Min, V. Vento & M. Rho, Nucl. Phys. A707(2002) 381 2. Hot & Dense Skyrmion matter

B.-Y. Park, D.-P. Min, V. Vento & M. Rho, Nucl. Phys. A707(2002) 381 2. Hot & Dense Skyrmion matter

2. Hot & Dense Skyrmion matterPion Gas!P = T4p230E/B = 3PV E/B=(M2(r)+3PV)c2+M4(r) +V(c)/r 1/3

2. Hot & Dense Skyrmion matterConclusion

2. Hot & Dense Skyrmion matterSummarySkyrme Model can be applied to study dense hadronic matter hadron properties in dense matter4. SummaryThank You!

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