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Su Houng Lee 1. Mesons with one heavy quark 2. Baryons with one heavy quark 3. Quarkonium

Heavy quark system and OPE. Su Houng Lee 1. Mesons with one heavy quark 2. Baryons with one heavy quark 3. Quarkonium Arguments based on two point function  can be generalized to higher point function. QCD Chiral symmetry breaking Confinement. Phenomenology One heavy quark

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Su Houng Lee 1. Mesons with one heavy quark 2. Baryons with one heavy quark 3. Quarkonium

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  1. Heavy quark system and OPE Su Houng Lee 1. Mesons with one heavy quark 2. Baryons with one heavy quark 3. Quarkonium Arguments based on two point function  can be generalized to higher point function

  2. QCD Chiral symmetry breaking Confinement Phenomenology One heavy quark Two heavy quark Heavy quark

  3. 1. Mesons with one heavy quark

  4. Heavy quark propagator Perturbativetreatment are possible because

  5. One Heavy quark and one Light antiquark Perturbative treatment are possible when which breaks down at x=0 due to light quark propagator

  6. Contribution from light quark condensate converges for large

  7. Chiral order parameters D(2400) D(1870)

  8. Chasher-Banks formula

  9. Chasher-Banks formula –correlator with h-quark

  10. Chasher-Banks formula – with heavy quark

  11. Direct observation of chiral symmetry restoration in medium 0+ D(2400) Belle G > 200 MeV D p Hayashigaki (00) 0- D(1870) Weise, Morath, Lee (99) • QCD sum rule approach: Hayashigaki, Weise, Morath, Lee Generalization to other channels: Kampfer et a. (10), Mishra et.al., Z. Wang

  12. near mass shell  Heavy quark symmetry D* D D0 D1 but no convergence  model approach

  13. Bs1(5830) Bs(58xx)? B(57xx)? B1(5721) xxx 345 xxx? 396 Bs*(5415) Bs(5366) B*(5325) B(5279) 46 46 Qqquark system in vacuum and medium: Chiral symmetry Ds1(2460) D1(2420) D(2400) 2318 ? Ds(2317) 348 413 349 530 448 ? D*(2112) D*(2007) Ds(1968) D(1870) 144 137 0- 0+ 1- 1+ 0- 0+ 1- 1+

  14. 2. Baryons with one heavy quark

  15. Chasher-Banks formula - <LL-L*L* >

  16. 3. Quarkonium

  17. System with heavy quark anti-quark Perturbative treatment are possible when

  18. Perturbative treatment are possible when

  19. = Subtlety for bound states Applequist, Dine, Muzinich (78), Peskin (79), Basis for pNRQCD ........ Separation scale

  20. Mass shift: QCD 2nd order Stark Effect : Peskin 79 e > Lqcd • OPE for bound state: m infinity Separation scale For small T  modify matrix element • Attractive for ground state

  21. G0 <a/p B2>T <a/p E2>T G2 Summary of analysis of Stark effect+ QCD sum rule (Morita-Lee) • Due to the sudden change of condensate near Tc • Abrupt changes for mass and width near Tc

  22. QCD sum rule for Quarkonia in medium • QCD sum rule for Quarkonia at nuclear matter: • Klingl, Kim, SHL,Weise (99), Hayashigai (99) • Contribution from complete dim 6 operators: Kim SHL (01) • mass shift at nuclear matter: -7 MeV (dim 4) • -4 MeV (dim4+ dim6) • QCD sum rule + MEM at finite temperature: Gubler, Oka, Morita • looking forward to further work

  23. <E2>, <B2> vs confinement potential • Local vs non local behavior Time W(S-T)= exp(-s ST) OPE for Wilson lines: Shifman NPB73 (80) T S W(S-T) = 1- <a/p E2> (ST)2 +.. W(S-S) = 1- <a/p B2> (SS)2 +.. Space W(S-S)= exp(-s SS) Space • Behavior at T>Tc W(SS)= exp(-s SS) <a/p B2>T W(ST)= exp(-g(1/S)T) <a/p E2>T

  24. Early work on J/y at finite T (Hashimoto, Miyamura, Hirose, Kanki) s String Tension: QCD order parameter T/Tc

  25. Analytic approaches Chiral symmetry breaking Confinement JPARC One heavy quark Two heavy quark Heavy quark Lattice calculation

  26. Summary • All Chiral symmetry order parameters zero eigenvalue solutions in QCD 2. Correlators with one Heavy quark: lead to sum rules relating well known chiral operators to spectral density + others that will be worked out. b) Obtain Weinberg type sum rule c) Nuclear target ? Heavy ion at JPAR Correlators with heavy quarks only : Quarkoniumin medium will give new insights into confinement problem

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