Quark Model of Hadrons
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1 Quark Model of Hadrons
2 mesons baryons symmetric antisymmetric mixed symmetry Quark Model of Hadrons 2
3 Why do quarks have color? ground state baryons orbital wave function = symmetic with L=0 SU(3) f x SU(2) s octet S = 1/2 can be antisymmetric decuplet S = 3/2 cannot be antisymmetric ex. Δ ++ S z =3/2 = (u ) 3 Color wave function of baryons totally antisymmetric Quark Model of Hadrons 3 R B G
4 Light meson flavor components
5 Baryon flavor components SU(3) octet SU(3) singlet SU(3) decuplet totally symmetric wave functions
6 proton S z =+1/2 = (uud) ( ) u u d 2-dim representation Quark Model of Hadrons 6
7 Quark Model of Hadrons
8 QCD Lagrangian quark B =1/3, C =3 (u,d) : I =1/2, S =0, Y =1/3 s : I =0, S = -1, Y = - 2/3 d Y u s I 3 Quark Model of Hadrons 8
9 light quarks Λ QCD heavy quarks MeV GeV u d s c b t m q Quark Model of Hadrons
10 Dyson-Schwinger equation dressed quark propagator 0 dynamical chiral symmetry breaking gluon effective mass generated Quark Model of Hadrons 10
11 Conserved currents are not renormalized. Constituent quark mass m q 300 MeV (u, d) m s 500 MeV (s) Residual interactions are weak. except confinement Quark Model of Hadrons 11
12 (2006) Quark Model of Hadrons 12
13 color singlet-ness of hadrons quark string/ flux tube V (r) antiquark Light quarks connected by string H= p + σr with J = pr fixed Virial theorem E(J) = 2 σj or m 2 J = 4σJ (Regge trajectory) Quark Model of Hadrons 13
14 heavy quark : quarkonium Lattice QCD: Wilson loop Cornell potential quark antiquark quenched LQCD r 0 : Sommer scale G.S. Bali / Phys. Rep. 343 (2001) 1 Quark Model of Hadrons 14
15 Casimir scaling G.S. Bali / Phys. Rep. 343 (2001) 1 3x3=1-4/3 3x3=3-2/3 8x8=1-3 Quark Model of Hadrons 15
16 Confinement potential string tension confine colored subsystem no confinement between color singlet objects Lorentz property? Lorentz scalar or vector? relativistic effects? ex. spin-obit interaction Quark Model of Hadrons 16
17 Rc κ Quark Model of Hadrons 17
18 Quark Model of Hadrons 18
19 Single particle motion (s 1/2 ) 3 J = 1/2 8 J = 3/2 10 hyperfine interaction (s 1/2 ) 3 10 Σ i<j (σ i σ j ) interaction 8 Ξ Σ Λ N Ω Ξ Σ Δ SU(3) breaking Quark Model of Hadrons 19
20 HF interaction in Baryon N-Δ mass splitting (300 MeV) Δ ss ~ 50 MeV Λ Σ mass splitting (~77 MeV) from SU(3) breaking 50 MeV Λ (ud) I =0,S =0 s 50MeV x [ ( 3) + 0 * ξ ] Σ (ud) I =1,S =1 s 50MeV x [ 1 + ( 4) * ξ ] ξ - factor: s-u, s-d HF interaction is weaker than u-d. for ξ = 3/5 Σ Λ = (8/15) x150 MeV = 80 MeV
21 σ σ One gluon exchange (OgE) or color-magnetic (CM) interaction Breit-Fermi, DeRujula-Georgi-Glashow (1975) SU(3) breaking m u /m s ~ 3/5 N-Δ mass splitting (300 MeV) Δ CM ~ MeV
22 σ σ Baryon masses m q ~ 360 MeV m s ~ 540 MeV M N = 3 m q + <V cm > N = 360x MeV M Δ = 3 m q + <V cm > Δ = 360x MeV M Λ,Σ = 2 m q + m s + <V cm > Λ,Σ = 360x MeV H dibaryon : S = 2, B = 2 M H = 4 m q + 2 m s + <V cm > H = 360x x MeV ΛΛ threshold 2230 MeV 20-year searches were not successful.
23 (2) Instanton-induced-interaction (I I I) aka Kobayashi-Maskawa-'t Hooft (KMT) instanton-light-quark couplings u L instanton u R flavor antisymmetric d L I d R s L s R Quark Model of Hadrons 23
24 Instanton-induced-interaction (I I I) flavor antisymmetric u-d-s 3-body repulsion flavor antisymmetric 2-body attraction = V ij (2) (2/5) (1 - σ i.σ j ) δ (r ij ) in the baryon spin-spin interaction proportional to 1/m i m j Shuryak-Rosner (1989) Takeuchi-Oka (1989)
25 New instanton picture I I I (2-body) N-Δ mass splitting (300 MeV) Δ III ~ 125 MeV I I I (3-body) 3-body repulsion flavor singlet (u-d-s) for H dibaryon M H > m ΛΛ threshold flavor singlet u d s u ds u d s
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