The instanton and the phases of QCD
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1 The instanton and the phases of QCD Naoki Yamamoto (University of Tokyo) Introduction contents QCD phase structure from QCD symmetries (1) QCD phase structure from instantons (2) Summary & Outlook (1) T. Hatsuda, M. Tachibana, G. Baym & N.Y., Phys. Rev. Lett. 97 (2006) (2) N.Y., JHEP 0812 (2008) 060. 九大若手研究会 量子色力学の相構造研究の現状と展望 Dec
2 QCD phase diagram T Early universe Quark-Gluon Plasma RHIC/LHC Hadrons? Neutron star & quark star Color superconductivity m B
3 QCD phase structure from QCD symmetries
4 Ginzburg-Landau (GL) approach Symmetry of the system & order parameter 1. Topological structure of the phase diagram 2. Order of the phase transition 3. Critical behaviors e.g.) Ising model Z(2) symmetry : m -m Order parameter: m (magnetization) unbroken phase (T>T c ) 2nd order phase transition broken phase (T<T c )
5 Chiral vs. Diquark condensates QCD symmetry : Axial anomaly Chiral field: Diquark field: u,d,s r,g,b E p F p -p F
6 Ginzburg-Landau potential Pisarski-Wilczek ( 84) Axial anomaly (instanton-induced int.) Iida-Baym ( 00) Hatsuda-Tachibana- Yamamoto-Baym ( 06)
7 Chiral-super interplay (Nf=3) 1st order 2nd order Natural parameter relations:
8 QCD phase diagram (Nf=3) T : 1 st order : 2 nd order 2nd critical point driven by the axial anomaly (instanton) μ See also, Kitazawa, Koide, Kunihiro & Nemoto ( 02)
9 Realistic QCD phase structure? T m u,d,s = 0 (3-flavor limit) T m u,d = 0, m s = (2-flavor limit) T μ 0 m u,d <m s (realistic quark masses) μ Critical point Asakawa & Yazaki, 89 2nd critical point Hatsuda, Tachibana, Yamamoto & Baym 06 μ
10 QCD phase structure from instantons
11 Instantons and chiral symmetry breaking Instanton? Mechanism for chiral symm. breaking/restoration instanton liquid (metal) instanton molecule (insulator) T=0 T>Tc Origin of Nambu-Jona-Lasinio (NJL) model Schäfer-Shuryak, Rev. Mod. Phys. ( 97) nonlocal NJL model See, e.g., Hell-Rößner-Cristoforetti-Weise, arxiv: Then, χsb in dense QCD from instantons?
12 Low-energy dynamics in dense QCD Dense QCD : U(1)A is asymptotically restored. NG boson field: Low-energy effective Lagrangian of η c.f. Manuel-Tytgat, PL( 00) Son-Stephanov-Zhitnitsky, PRL( 01) Schäfer, PRD( 02) convergent!
13 Coulomb gas representation : topological charge : 4-dim Coulomb potential Instanton density, topological susceptibility Witten-Veneziano relation: N.Y., JHEP ( 08)
14 Renormalization group analysis Fluctuations: RG scale: Change of potential after RG: RG trans.: kinetic vs. potential D=2: potential irrelevant vortex molecule phase potential relevant vortex plasma phase D 3: potential relevant plasma phase
15 Phase transition induced by instantons D-dim sine-gordon model: System parameter α Topological excitations Order of trans. 2D O(2) spin system vortex 2nd 3D compact QED magnetic monopole crossover 4D dense QCD instanton crossover Note: weak coupling QCD: Unpaired instanton plasma in dense QCD Coexistence phase: Actually, N.Y., JHEP ( 08)
16 Phase diagram of instantons (Nf=3) T instanton molecule QGP instanton liquid χ SB CFL instanton plasma m B
17 Some comments Effects of instantons may be also important in hot QCD. QCD critical point at high T from PNJL model with gd K. Fukushima, PRD ( 08), N. Bratovich, T. Hell, S. Rößner + W. Weise ( 08) QCD critical points can disappear due to the medium effects on instantons!
18 Large Nc? qq scattering Double-line notation qq scattering Diquarks are suppressed at large Nc! Deryagin-Grigoriev-Rubakov ( 92) Shuster-Son ( 00) Ohnishi-Oka-Yasui ( 07) See, also, McLerran-Pisarski ( 07)
19 Summary & Outlook 1. Chiral-super interplay driven by the instanton 2nd critical point at low T and high μ Continuity of χsb phase and CSC phase 2. Instanton plasma from low μ to high μ The instantons play crucial roles everywhere! 3. Future problems Real location of the 2nd critical point? How to detect it in lab. exp. or observation of NS? AdS/CFT application to phases of dense QCD?
20 Back up slides
21 QCD phase diagram at large Nc Gluodynamics (~Nc 2 ) dominates independent of μb (~Nc). McLerran-Pisarski, NPA ( 07) see also, Horigome-Tanii, JHEP ( 07)
22 Hadron-quark continuity Continuity between hadronic matter and quark matter (Color superconductivity) Phases Hadrons (3-flavor) Color superconductivity Symmetry breaking Order parameter Elementary excitations SU(3) L SU(3) R SU(3) L+R Chiral condensate NG bosons (π etc) Vector mesons (ρ etc) Baryons SU(3) L SU(3) R SU(3) C U(1) B SU(3) L+R+C Diquark condensate NG bosons Gluons Quarks Conjectured by Schäfer & Wilczek, PRL 1999
23 Prediction for the location of the critical point Taken from hep-lat/ , M. Stephanov
24 Order of the thermal transition Z(3) GL theory O(4) GL theory SU L (3)xSU R (3) GL theory
25 Ginzburg-Landau theory of tricritical/critical point Taken from Quark-Gluon Plasma Yagi, Hatsuda and Miake (Cambridge Univ. Press, 2005)
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