Masayasu Harada (Nagoya Univ.)

1. D Meson Mass Splitting obtained in a model based on the Hidden Local Symmetry Masayasu Harada(Nagoya Univ.) at “Heavy Quark Physics in QCD” (KEK, September 7, 2009) based on M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, 074002 (2004) M.H., Work in progress

2. 1. Introduction

3. ☆ Discovery of New D Mesons (2003～)

4. new D mesons ・・・ inconsistency with the experiment ◎ Masses of DsJ(0+, 1+) ⇔ quark model ・・・ predictions by quark model ・・・ experiment S.Godfrey and N.Isgur, PRD 32, 189 (1985)

5. ☆ several proposal ◎ 4-quark picture ・ K. Terasaki, PRD 68, 011501 (2003) ・ S. Yasui and M. Oka, PRD76, 034009 (2007) ・・・ ◎ 2-quark picture • semirelativistic potential model ・ T. Matsuki and T. Morii, PRD 56, 5646 (1997) ・ T. Matsuki, T. Morii and K. Sudoh, PTP 117, 1077 (2007); EPJ A31, 701 (2007) ・・・ • new level-classification scheme ・ S. Ishida, M. Ishida, T. Komada, T. Maeda, M. Oda, K. Yamada and I.Yamauchi, AIP Conf. Proc. 717, 716 (2004) ・・・ • chiral models ・ M.A.Nowak, M.Rho and I.Zahed, PRD48, 4370 (1993) ・ W.A.Bardeen and C.T.Hill, PRD49, 409 (1994) ・ W.A.Bardeen, E.J.Eichten and C.T.Hill PRD 68, 054024 (2003) ・・・

6. heavy quark symmetry chiral symmetry ☆ “chiral doubling” M.A.Nowak, M.Rho and I.Zahed, PRD48, 4370 (1993) excited states ground states ◎ Analysis based on the NJL-like model

7. ☆ Our approach M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, 074002 (2004) An Effective Model of hadrons based on ・ the Heavy quark symmetry in the heavy sector ・ the chiral symmetry in the light quark sector (Hidden Local symmetry for p and r) chiral doubling + ⇒ Mass splitting ? Hadronic decay widths ?

8. Outline 1. Introduction 2. An Effective Model 3. Mass Splitting & HadronicDecay Processes 4. Chiral doubling in Heavy Baryons 5. Summary

9. 2. An Effective Model

10. ◎ Chiral Perturbation Theory with HLS H.Georgi, PRL 63, 1917 (1989); NPB 331, 311 (1990): M.H. and K.Yamawaki, PLB297, 151 (1992) M.Tanabashi, PLB 316, 534 (1993): M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) Systematic low-energy expansion including dynamical r loop expansion ⇔ derivative expansion ☆ Effective Lagrangian for the light quark sector ◎ Hidden Local Symmetry Theory ・・・ EFT for r and p M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, PRL 54 1215 (1985) M. Bando, T. Kugo and K. Yamawaki, Phys. Rept. 164, 217 (1988) M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) based on chiral symmetry of QCD ρ ・・・ gauge boson of the HLS

11. ◎ velocity super-selection rule gluon heavy quark The velocity of a heavy quark is not changed by the QCD interaction. ☆ Heavy quark symmetry ・・・ a symmetry of QCD at MQ → ∞ limit ◎ Heavy quark number conservation No pair production of heavy quarks by QCD interaction. ◎ SU(2) spin symmetry QCD interaction cannot flip the spin of heavy quarks.

12. Fluctuation mode around the On-shell Heavy Quark energy of fluctuation mode energy of heavy quark on-shell energy of heavy quark at rest ・・・ Expansion parameter

13. ☆ QCD Lagrangian (heavy quark sector) ◎ introducing the fluctuation mode

15. - “Light-quark cloud” (Brown Muck) ・・・ made of light quarks and gluons typical energy scale ～ ΛQCD Q angular momentum carried by “Brown muck” ◎ spin of meson spin of heavy quark ・ MQ → ∞ limit same Ｊｌ Q(↑) Q(↓) conservation of Jl ⇒ classification of hadrons by Jl Heavy Meson Multiplet ・・・ degenerate masses ☆ Heavy-Light Mesons (Qq type)

16. ・ Bi-spinor field Y・・・ light constiuent quark field ; annihilates heavy mesons (not generate) ☆ Ground states ・・・ Jl =1/2 ; JP = (0- , 1-) Pseudoscalar meson P ; Vector meson P* P = ( D0, D+, Ds ) P* = ( D*0, D*+, D*s )

17. ◎ Transformation property ◎ Kinetic Lagrangian

18. ☆ Excited states ・・・ Jl =1/2 ; JP = (0+ , 1+) ◎ Interaction terms are introduced in a similar way.

19. 3. Mass Splitting and Hadronic Decay Processes ΔM = M(0+,1+) – M(0-,1-)

20. integrate out matching Bare theory bare mass splitting ΔＭ（Λ） Quantum effects through RGE Quantum theory physical mass splitting ΔＭ ☆ Wilsonian matching M.H. and K.Yamawaki, PRD 64, 014023 (2001) high energy QCD quarks and gluons (perturbative treatment) Both (perturbative) QCD and EFT are applicable Λ EFT for hadrons low energy

21. ☆ Comparison with QCD sum rule Wilsonian matching QCD sum rule matching Borel transformation RGE in EFT matching at Borel mass scale Borel transformation Physical quantities at low energy Energy at the maching scale L OPE

22. ☆ Correlators matching at

23. ◎ Matching condition at Q2 = (MD + L)2 ◎ Relation valid at the matching scale L

24. neglect ◎ Numerical Estimation

25. What is the characteristic feature of the chiral doubling ? ⇒ Hadronic Decay processes ☆ RGE evolution Quantum Corrections through RGE r meson loop gives a dominant contribution Existence of the Heavy quark symmetry simplifies the calculation. Good agreement with experiment !

26. ☆ Hadronic Decay Processes ・ input ・ predictions ◎ One pion mode Test of the chiral doubling !

27. 4. Chiral doubling in heavy baryons ・・・ based on the boundstate approach to heavy baryons ☆ Boundstate approach heavy baryons (qqQ type) = heavy meson(qbarQ) bound to nculeon (qqq) as a soliton heavy meson r = 0 r = 1 Q q l=0 D(0-,1-) l=1 D(0+,1+) D(1+,2+) ・kinematical structure is same as the constituent quark model M.H., F.Sannino, J.Schechterand H.Weigel, PRD56, 4098 (1997)

28. ☆ ground state heavy baryon Binding energy : K = 0 , 1 isospin and anglular momentum of light cloud of heavy meson are locked with each other k : D(1-) – D(0-) – p , D(1+) – D(1+) – p coupling k ~ 0.6 from D(1-) → D(0-) + p decay kw : D(0-) – D(0-) – w , D(1-) – D(1-) – w coupling kw = 1 if we assume the vector meson dominance. Hear I take kw = O(1) D1 : force mediated by pion : D1 ~ 0.40 GeV D2 : force mediated by omega meson : D2 ~ 0.26 GeV values of D1 and D1 are given in K.S.Gupta, M.A.Momen, J.Schechter and A. Subbaraman, PRD47, R4835 (1993) VH < 0 for K = 0 : bound VH > 0 for K = 1 : unbound

29. ☆ Determination of kw M(L(1/2+)) = MN + MD(0-,1-) – 1.2 k + 0.26 kw (GeV) MD(0-,1-) = ( MD(0-) + 3 MD(1-) )/4 ~ 1.97 (GeV) k ~0.6 from D(1-) → D(0-) + p decay M(L(1/2+)) ~ 2.286 (GeV) MN ~ 0.94 (GeV) kw~ 0.37・・・ reasonable value ⇒ Boundstate approach seems to work ! Note : This is very rough estimation in MQ→ ∞ limit. We should include 1/MQ corrections.

30. ☆ An excited Heavy baryon : K = 0 , 1 kG : D(1+) – D(0+) – p , D(1+) – D(1+) – p coupling kGw : D(0+) – D(0+) – w , D(1+) – D(1+) – w coupling D1 , D2 : same for ground state in the MQ→ ∞ limit. ・ chiral doubling of {D(0-,1-) , D(0+,1+) } ⇒ kG = k ~ 0.6 ; kGw = kw ・Binding energy is same as the ground state (K = 0) :VG = VH ・ M(L(1/2-)) – M(L(1/2+)) = MD(0+,1+) – MD(0-,1-)~ 0.43 GeV ⇒ M(L(1/2-)) ~ 2.72 (GeV) ・Lc(1/2-;2595) is unlikely the chiral partner to Lc(1/2+;2286) ・{Lc(1/2-;2595) , Lc(3/2-;2625) } ・・・ r = 1 boundstate of D(0-,1-) and nucleon

31. ☆ Application to heavy Pentaquark D1 ~ 0.40 GeV , D2 ~ 0.26 GeV k~ 0.6 ,kw ~ 0.37 K = 1 gives a bound state. M(Qc(1/2-)) = MN + MD(0-,1-) – 0.4 k– 0.26 kw ~ 2.57 (GeV) cf : M(Qc(1/2-)) ~ 2.7 GeV without w contribution. Y.Oh, B.-Y.Park, and D.P.Min, PLB331, 362 (1994) note : CHORUS exp. did not observe Qc(2710). Nuclear Physics B 763 (2007) 268–282

32. ～ ・ D → D πmode ～ D = chiral partner of D ◎ Hadronic decay processes Test of the chiral doubling ! 5. Summary ～ ・ Effective Lagrangian for D, D, π, ρ based on the heavy quark symmetry and the chiral symmetry ・ matching with the OPE to determine the bare mass splitting at the matching scale L ・ RG evolution to determine the physical mass splitting

33. ☆ Chiral doubling in heavy baryons ・・・based on the boundstate approach ・Lc(1/2-;2595) is unlikely the chiral partner to Lc(1/2+;2286) ・{Lc(1/2-;2595) , Lc(3/2-;2625) } ・・・ r = 1 boundstate of D(0-,1-) and nucleon M(L(1/2-)) ~ 2.7 (GeV) : chiral partner to Lc(1/2+;2286) may be very broad since D(0+,1+) are very broad ☆ Application to Pentaquark M(Qc(1/2-)) ~ 2.57 (GeV)

34. The End