Masayasu Harada (Nagoya Univ.)

1. D Meson Mass Splitting in the Hidden Local Symmetry (with the Vector Manifestation) Masayasu Harada(Nagoya Univ.) at “Challenge to New Exotic Hadrons with Heavy Quarks” (RCNP, July 7, 2007) based on M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, 074002 (2004)

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, arXiv:0704.1345 ・・・ ◎ 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 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 4. Hadronic Decay Processes 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. - “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)

14. ・ 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 )

15. ◎ Transformation property ◎ Kinetic Lagrangian

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

17. 3. Mass Splitting ΔM = M(0+,1+) – M(0-,1-)

18. 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

19. ☆ 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

20. ☆ Correlators matching at

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

22. neglect ◎ Numerical Estimation

23. r g g DM What is the characteristic feature of the chiral doubling ? ⇒ Hadronic Decay processes ☆ RGE evolution Good agreement with experiment !

24. 4. Hadronic Decay Processes

25. ◎ One pion mode Test of the chiral doubling ! ・ input ・ predictions

26. ～ ・ 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

27. ⇒ Chiral symmetry restoration in hot and/or dense QCD will be detected through D mesons B.Friman, talk at QM04 0