Structure of the exotic heavy mesons
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Transcript of Structure of the exotic heavy mesons
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