Masayasu Harada (Nagoya Univ.) based on M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, (2004) M.H., Work in progress at “Heavy Quark Physics in QCD” (KEK, September 7, 2009)

☆ Discovery of New D Mesons (2003 ～ )

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

☆ several proposal ◎ 4-quark picture ◎ 2-quark picture chiral models ・ K. Terasaki, PRD 68, (2003) ・ S. Yasui and M. Oka, PRD76, (2007) ・・・ 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) ・・・ ・ 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, (2003) ・・・

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

☆ Our approach chiral doubling + ⇒ Mass splitting ? Hadronic decay widths ? 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  and  ) M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, (2004)

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

based on chiral symmetry of QCD ρ ・・・ gauge boson of the HLS ◎ Hidden Local Symmetry Theory ・・・ EFT for  and  M. Bando, T. Kugo, S. Uehara, K. Yamawaki and T. Yanagida, PRL (1985) M. Bando, T. Kugo and K. Yamawaki, Phys. Rept. 164, 217 (1988) M.H. and K.Yamawaki, Physics Reports 381, 1 (2003) 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  loop expansion ⇔ derivative expansion ◎ Chiral Perturbation Theory with HLS ☆ Effective Lagrangian for the light quark sector

☆ Heavy quark symmetry ・・・ a symmetry of QCD at M Q → ∞ limit ◎ velocity super-selection rule gluon heavy quark The velocity of a heavy quark is not changed by the QCD interaction. ◎ 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.

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

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

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

☆ Ground states ・・・ J l =1/2 ; J P = (0 -, 1 - ) Pseudoscalar meson P ; Vector meson P* P = ( D 0, D +, D s ) P* = ( D* 0, D* +, D* s ) ・ Bi-spinor field ;  ・・・ light constiuent quark field annihilates heavy mesons (not generate)

◎ Transformation property ◎ Kinetic Lagrangian

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

ΔM = M(0 +,1 + ) – M(0 -,1 - )

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

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

☆ Correlators at matching

◎ Matching condition at Q 2 = (M D +  ) 2 ◎ Relation valid at the matching scale 

◎ Numerical Estimation neglect

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

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

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

☆ ground state heavy baryon Binding energy isospin and anglular momentum of light cloud of heavy meson are locked with each other k : D(1 - ) – D(0 - ) –  D(1 + ) – D(1 + ) –  coupling k ~ 0.6 from D(1 - ) → D(0 - ) +  decay k  : D(0 - ) – D(0 - ) – , D(1 - ) – D(1 - ) –  coupling k  = 1 if we assume the vector meson dominance. Hear I take k  = O(1)  1 : force mediated by pion :  1 ~ 0.40 GeV  2 : force mediated by omega meson :  2 ~ 0.26 GeV : K = 0, 1 values of  1 and  1 are given in K.S.Gupta, M.A.Momen, J.Schechter and A. Subbaraman, PRD47, R4835 (1993) V H < 0 for K = 0 : bound V H > 0 for K = 1 : unbound

☆ Determination of k  M(  (1/2+)) = M N + M D(0-,1-) – 1.2 k k  (GeV) M D(0-,1-) = ( M D(0-) + 3 M D(1-) )/4 ~ 1.97 (GeV) k ~ 0.6 from D(1 - ) → D(0 - ) +  decay M(  (1/2+)) ~ (GeV) k  ~ 0.37 ・・・ reasonable value ⇒ Boundstate approach seems to work ! M N ~ 0.94 (GeV) Note : This is very rough estimation in M Q → ∞ limit. We should include 1/M Q corrections.

☆ An excited Heavy baryon : K = 0, 1 k G : D(1 + ) – D(0 + ) –  D(1 + ) – D(1 + ) –  coupling k G  : D(0 + ) – D(0 + ) – , D(1 + ) – D(1 + ) –  coupling ・ chiral doubling of {D(0 -,1 - ), D(0 +,1 + ) } ⇒ k G = k ~ 0.6 ; k G  = k  ・ Binding energy is same as the ground state (K = 0) : V G = V H ・ M(  (1/2-)) – M(  (1/2+)) = M D(0+,1+) – M D(0-,1-) ~ 0.43 GeV ⇒ M(  (1/2-)) ~ 2.72 (GeV) ・  c (1/2-;2595) is unlikely the chiral partner to  c (1/2+;2286) ・  c (1/2-;2595),  c (3/2-;2625) } ・・・ r = 1 boundstate of D(0-,1-) and nucleon  1,  2 : same for ground state in the M Q → ∞ limit.

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

・ 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  ・ RG evolution to determine the physical mass splitting ～ ◎ Hadronic decay processes ・ D → D π mode ～ Test of the chiral doubling ! D = chiral partner of D ～

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