Structure of the exotic heavy mesons

Makoto Takizawa (Showa Pharmaceutical Univ.)

CollaboratorsSachiko Takeuchi (Japan College of Social Work)Kiyotaka Shimizu (Sophia University)

Heavy Quark Hadrons at J-PARC, Tokyo Institute of Technology, June 22, 2012

arXiv:1206.4877

Contents

• X(3872): experimental status -> Prof. Olsen’s talk

• X(3872): How exotic X(3872) is? • Structure of the X(3872):

Charmonium- hadronic molecule hybrid• Zb1 and Zb2

• Consistency between X(3872) and Zb

X(3872): experimental status• First observation: 2003, Belle, KEKB

Mass: (3871.57 ± 0.25) MeV (PDG 2011) 0.16 MeV below D0 D*0-bar thresold 3871.73MeV PDG2012 (3871.68 ± 0.17) MeVCharged B decays: (3871.4 ± 0.6 ± 0.1 ) MeV (BABAR)Neutral B decays: : (3868.7 ± 1.5 ± 0.4 ) MeV (BABAR)B decays: (3871.85 ± 0.27 ± 0.19 ) MeV (Belle)p pbar collisions: (3871.61 ± 0.16 ± 0.19 ) MeV (CDF)p p collisions: (3871.95 ± 0.48 ± 0.12 ) MeV (LHCB)

• Width: less than 1.2 MeV • Quantum Number: JPC = 1++ , 2-+ ?

B+ → K+ + J/ψ + ππ(π)

• B+ → X(3872) ＋ K+ → J/ψ ＋ vector meson →π’s

11 Sep 2010 jps fall meeting @ 九州工業大学

X(3872) : How exotic X(3872) is?

1. Not CCbar

Estimated energy of 2 3P1 c c-bar state by the potential model is 3950 MeV, which is about 80 MeV higher than the observed mass of X(3872).

2. Large isospin symmetry breakingIf X(3872) is c c-bar state, it is isoscalar.X(3872) → ρ0 J/ψ → π+ π- J/ψ : isovectorThis decay means large isospin breaking.

• (0.8 ± 0.3) by BABAR• Isovector component is smaller than

isoscalar component : 10~30%

• Estimation of isospin component from this value is an issue of the discussion

3. Not D0 D*0-bar Molecule

• D0 D*0-bar is 50% isovector and 50% isoscalar: Too big the isovector component

• Why are there no charged X(3872)?D+ D*0-bar, D0 D*- molecules

• The production rate of such molecular-like state may be too small.

Charmonium D0 D*0-bar, D+ D*- molecule hybrid

• Structure of X(3872): c c-bar core state (charmonium) is coupling to D0 D*0-bar and D+ D*- states

• Effect of the isospin symmetry breaking is introduced by the mass differences between neutral and charged D, D* mesons

Coupling between C C-bar core and D0 D*0-bar, D+ D*-

c c-bar core D*0-bar

D0 D+

D*-

+ . . . . .

Coupling between C C-bar core, D0 D*0-bar and D+ D*-

• cc-bar core state:• D0 D*0-bar state :

• D+ D*- state : in the center of mass frameq is the conjugate momentum of the relative coordinate

Coupling between C C-bar core, D0 D*0-bar and D+ D*-

• Charge conjugation + state is assumed• Interaction: Isospin symmetric

Coupling between C C-bar core, D0 D*0-bar and D+ D*-

• X(3872) is a mixed state:

• Isospin base:

Isospin symmetric case: c2 = c3 No isovector component

Coupling between C C-bar core, D0 D*0-bar and D+ D*-

• Schroedinger Equation

Numerical results: Mass

• Mass of the cc-bar core: 3.95 GeVfrom S. Godfrey, N. Isgur, Phys. Rev. D 32 (1985) 189.

• Cutoff: 0.3GeV and 0.5 GeV

Lambda = 0.5 GeV, Calculated bound state energy is 3.87157 GeV with coupling strength g = 0.05115 Lambda = 0.3 GeV, Calculated bound state energy is 3.87157 GeV with coupling strength g = 0.05440

Numerical results: Wavefunction• Lambda = 0.5 GeV, B.E. = 0.16 MeV

• Lambda = 0.3 GeV

• Large isospin symmetry breaking• Cutoff dependence is small

Why so large isospin symmetry breaking?• mD0 + mD*0 = 3871.73 MeV

• mD+ + mD*- = 3879.79 ± 0.37 MeV

• mX = 3871.57 MeV

• Binding EnergyNeutral D case: 0.16 MeVCharged D case: 8.22 MeV

Large difference

Numerical results: Wavefunction• Lambda = 0.5 GeV, B.E. = 0.16 MeV

Case of mx = 3868.7 MeV from Neutral B decay data

• Lambda = 0.5 GeV, B.E. = 3.03 MeV

Lambda = 0.5 GeV, B.E. = 3.03 MeV

Energy spectrum• We consider c c-bar core state is

produced in the production process• Transition strength S(E):

B

K

E=Energy transfer

X(3872)

Numerical results: Energy spectrum• Lambda = 0.3 GeV, B.E. = 0.16 MeV

X(3872) bound state

CC-bar state

Numerical results: Energy spectrum• Lambda = 0.5 GeV, B.E. = 0.16 MeV

X(3872) bound state

CC-bar state disappears

Interaction between D and D*

c c-bar core D*0-bar

D0 D+

D*-

+ . . . . .

c c-bar core

Interaction between D0 and D*0bar, D+ and D*-

• Interaction:

Numerical results:

• Mass of the cc-bar core: 3.95 GeVfrom S. Godfrey, N. Isgur, Phys. Rev. D 32 (1985) 189.

• Cutoff: 0.5 GeV

• Determination of the interaction strengthsFirst, we set λ=0, then g is fixed so as to reproduce mass of X(3872) to be 3.8715 GeV

Then, we change the value of g from 0.9g, 0.8g, 0.7g, … and determine the value of λ so as to reproduce mass of X(3872) to be 3.8715 GeV

Numerical results: X(3872) components

Λ=0.5 GeV, mX = 3.87157 GeV

Numerical results: X(3872) componentsΛ=0.5 GeV, mX = 3.87157 GeV

Numerical results: X(3872) components

Λ=0.5 GeV, mX = 3.8687 GeV

Summary of X(3872)

• Charmonium- hadronic molecule haybridΛ=0.5 GeV, B.E. = 3.03 MeV, g/g0 = 0.5

• 7% cc-bar core: good for production rate• size of the isospin symmetry breaking is OK• no charged partnar of X(3872) because ccbar cannot

couple to the charged state• cc-bar core state: decay width is large -> not observed

Zb

• M(Zb1) = 10607.2 ± 2.0 MeV/c2 Γ1 = 18.4 ± 2.4 MeVBB*bar threshold: 10604 MeV/c2

BB*bar molecule• M(Zb2) = 10652.2 ± 1.5 MeV/c2

Γ2 = 11.5 ± 2.2 MeVB*B*bar threshold: 10650 MeV/c2

B*B*bar molecule• IG (JP) = 1+ (1+)

• Interaction between B and B* is similar to that between D and D* because of the heavy quark symmetry

In the case of X (3872), about 60% of the attraction is coming from coupling to ccbar core state and rest (40%) is interaction between D and D* -> JUST FOR Zb interaction-> Ohkoda-san’s talk yesterday

• Charmonium above the open charm threshold exprimentally observed states are L >=1 decay modes

• Charmonium with L =0 open cham decay mode have not been observed