Masayasu Harada (Nagoya Univ.)

based on M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, 074002 (2004) M.H., Work in progress

at “Heavy Quark Physics in QCD” (KEK, September 7, 2009)

☆ Discovery of New D Mesons (2003 ～ )

◎ Masses of DsJ (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, 011501 (2003)・ S. Yasui and M. Oka, PRD76, 034009 (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, 054024 (2003)・・・

☆ “chiral doubling” M.A.Nowak, M.Rho and I.Zahed, PRD48, 4370 (1993)

excited states

ground states

heavy quarksymmetry

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 p and r)

M.H., M.Rho and C.Sasaki, Phys. Rev. D 70, 074002 (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 r and pM. 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)

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

◎ Chiral Perturbation Theory with HLS

☆ Effective Lagrangian for the light quark sector

☆ Heavy quark symmetry ・・・ a symmetry of QCD at MQ → ∞ limit

◎ velocity super-selection rule

gluon

heavy quark

The velocity of a heavy quark isnot 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 ofheavy 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 ～ ΛQCD

spin of heavy quark

◎ spin of mesonangular momentum carried by “Brown muck”

・ MQ → ∞ limit

conservation of Jl ⇒ classification of hadrons by Jl

Q(↑) Q(↓)

same Ｊｌ

Heavy Meson Multiplet ・・・ degenerate masses

-

☆ Ground states ・・・ Jl =1/2 ; JP = (0- , 1-)

Pseudoscalar meson P ; Vector meson P*

P = ( D0, D+, Ds ) P* = ( D*0, D*+, D*s )

・ Bi-spinor field

; Y ・・・ light constiuent quark field

annihilates heavy mesons (not generate)

◎ Transformation property

◎ Kinetic Lagrangian

☆ Excited states ・・・ Jl =1/2 ; JP = (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, 014023 (2001)

matching

(perturbative treatment)

Both (perturbative) QCD and EFT are applicable

integrateout

☆ Comparison with QCD sum rule

OPE

Energy

Physical quantities at low energy

QCD sum rule

matching

at Borel mass scale

Borel transformation

Borel transformation

matching

Wilsonian matching

RGE in EFT

at the maching scale L

☆ Correlators

atmatching

◎ Matching condition at Q2 = (MD + L)2

◎ Relation valid at the matching scale L

◎ Numerical Estimationneglect

☆ RGE evolution

Good agreement with experiment !

What is the characteristic feature of the chiral doubling ?

⇒ Hadronic Decay processes

Quantum Corrections through RGE

r meson loop givesa 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 (qbarQ) 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-) – , p D(1+) – D(1+) – p coupling k ~ 0.6 from D(1-) → D(0-) + p decaykw : D(0-) – D(0-) – w , D(1-) – D(1-) – w coupling kw = 1 if we assume the vector meson dominance. Hear I take k w = O(1)

D1 : force mediated by pion : D1 ~ 0.40 GeVD2 : force mediated by omega meson : D2 ~ 0.26 GeV

: K = 0 , 1

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 : boundVH > 0 for K = 1 : unbound

☆ Determination of kw

M(L(1/2+)) = MN + MD(0-,1-) – 1.2 k + 0.26 k w (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)

kw ~ 0.37 ・・・ reasonable value ⇒ Boundstate approach seems to work !

MN ~ 0.94 (GeV)

Note : This is very rough estimation in MQ → ∞ limit. We should include 1/MQ corrections.

☆ An excited Heavy baryon

: K = 0 , 1kG : D(1+) – D(0+) – , p D(1+) – D(1+) – p coupling

kGw : D(0+) – D(0+) – w , D(1+) – D(1+) – w coupling

・ 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

D1 , D2 : same for ground state in the MQ → ∞ limit.

☆ Application to heavy Pentaquark

M(Qc(1/2-)) = MN + MD(0-,1-) – 0.4 k – 0.26 k w ~ 2.57 (GeV)

D1 ~ 0.40 GeV , D2 ~ 0.26 GeV

k ~ 0.6 , kw ~ 0.37

K = 1 gives a bound state.

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

・ 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

～

◎ 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(L(1/2-)) ~ 2.7 (GeV) : chiral partner to Lc(1/2+;2286)

・ 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

may be very broad since D(0+,1+) are very broad

M(Qc(1/2-)) ~ 2.57 (GeV)

☆ Application to Pentaquark