quark model of hadrons
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Quark Model of Hadrons
Quark Model of Hadrons
Makoto Oka
PART II of the Lecture
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Quark Model of Hadrons 2
SU(3) Symmetry mesons
baryons
symmetric
mixed symmetry
antisymmetric
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Quark Model of Hadrons 3
Color and Statistics 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 antisymmetricex. Δ++ Sz=3/2 = (u⇑)3
Color wave function of baryons totally antisymmetric R
GB
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Light meson flavor components
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Baryon flavor components
SU(3) singlet
SU(3) octet
SU(3) decuplet
totally symmetric wave functions
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Quark Model of Hadrons 6
Proton wave function proton Sz=+1/2 = (uud) (⇑⇑⇓)
2-dim representation
u ud
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Quark Model of Hadrons
Quark Model Powerful tool to understand hadron spectrum, structures and dynamics. With proper dynamical contents, it is applicable to multi-quark systems, such as 2-baryons, pentaquarks.
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Quark Model of Hadrons 8
Quarks in QCD
QCD Lagrangian
quarkB =1/3, C =3
(u,d) : I =1/2, S =0, Y =1/3
s : I =0, S = -1, Y = - 2/3
Y
I3
ud
s
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Quark Model of Hadrons
Quarks in QCD
Quark masses and scale of QCD
1 10 100 1 10 100 MeV GeV u d s c b t
mq
ΛQCDlight quarks heavy quarks
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Quark Model of Hadrons 10
Constituent Quark
dynamical chiral symmetry breaking
dressed quark propagator gluon
effective mass generated0
Dyson-Schwinger equation
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Quark Model of Hadrons 11
Constituent Quark
Conserved currents are not renormalized.I , Y , C charges do not change.
Constituent quark mass mq ≈ 300 MeV (u, d) ms ≈ 500 MeV (s) Residual interactions are weak. except confinement
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Quark Model of Hadrons 12
(2006)
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Quark Model of Hadrons 13
Color Confinement
color singlet-ness of hadrons
Light quarks connected by string H= p + σr with J = pr fixed Virial theorem E(J) = 2 √σJ or mJ
2 = 4σJ (Regge trajectory)
quark antiquark
string/ flux tubeV (r)
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Quark Model of Hadrons 14
Color Confinement
quark antiquark
quenched LQCDr0: Sommer scale
heavy quark : quarkonium
Lattice QCD: Wilson loop Cornell potential
G.S. Bali / Phys. Rep. 343 (2001) 1
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Quark Model of Hadrons 15
Casimir scaling
3x3=1 - 4/3
3x3=3 - 2/3
8x8=1 -3
Color ConfinementG.S. Bali / Phys. Rep. 343 (2001) 1
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Quark Model of Hadrons 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
Color Confinement
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Quark Model of Hadrons
Charmonium and bottomium
Potential model approach
Rc�and κ�fit to the running coupling constant
17
S.N. Mukherjee, et al., Phys. Rep. 231 (1993)
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Quark Model of Hadrons
S.N. Mukherjee, et al., Phys. Rep. 231 (1993)
18
Charmonium and bottomium
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Quark Model of Hadrons 19
Baryon Spectrum
Single particle motion(s1/2)3 J = 1/2 8 J = 3/2 10hyperfine interaction
(s1/2)3
8
10
NΛΣΞ Δ
Σ∗Ξ∗Ω
Σi<j(σi・σj) interaction
SU(3) breaking
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HF interaction in Baryon N-Δ mass splitting (300 MeV) ↔ Δss ~ 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
Baryon Spectrum
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One gluon exchange (OgE) or color-magnetic (CM) interaction Breit-Fermi, DeRujula-Georgi-Glashow
(1975)
N-Δ mass splitting (300 MeV) ↔ ΔCM ~ 18.75 MeV
SU(3) breaking mu/ms ~ 3/5
Origin of (σ・σ) Interaction
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Baryon masses mq ~ 360 MeV ms ~ 540 MeV MN = 3 mq + <Vcm>N = 360x3 – 150 ≈ 930 MeV
MΔ = 3 mq + <Vcm>Δ = 360x3 + 150 ≈ 1230 MeV MΛ,Σ = 2 mq + ms + <Vcm>Λ,Σ
= 360x2 + 540 – 90 ≈ 1170 MeV H dibaryon : S = –2, B = 2 MH = 4 mq + 2 ms + <Vcm>H
= 360x4 + 540x2 – 450 ≈ 2070 MeV ΛΛ threshold 2230 MeV 20-year searches were not successful.
Origin of (σ・σ) Interaction
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Quark Model of Hadrons 23
Instanton Induced Interaction
(2) Instanton-induced-interaction (I I I)aka Kobayashi-Maskawa-'t Hooft (KMT)
instanton-light-quark couplings
IuL
dL
sL
uR
dR
sR
instanton
flavor antisymmetric
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Instanton-induced-interaction (I I I) flavor antisymmetric u-d-s 3-body repulsion flavor antisymmetric 2-body attraction
= Vij(2) (2/5) (1 - σi .σj ) δ (rij) in the baryon
proportional to 1/mimj Shuryak-Rosner (1989)Takeuchi-Oka (1989)
spin-spin interaction
Instanton Induced Interaction
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I I I (2-body)
N-Δ mass splitting (300 MeV) ↔ ΔIII ~ 125 MeV
I I I (3-body)
3-body repulsion flavor singlet (u-d-s) for H dibaryon MH > mΛΛ threshold
uds
uds
uds
flavor singlet
New instanton picture