The charmonium-molecule hybrid structure of the X(3872)

Makoto Takizawa (Showa Pharmaceutical Univ.)Sachiko Takeuchi (Japan College of Social Work)Kiyotaka Shimizu (Sophia University)

International conference on the structure of baryons,BARYONS’10, Osaka, Japan. Dec. 8, 2010

Ref: M. Takizawa and S. Takeuchi, EPJ web of conference 3, (2010) 03026; Prog. Theor. Phys. Suppl. 186 (2010) 160.

ContentsProblems of X(3872) as C C-bar stateProblems of X(3872) as D0 D*0-bar moleculeCoupling between C C-bar core state,

D0 D*0-bar state and D+D*- stateInteraction between D and D*Wavefunction and isospin symmetry

breaking Energy spectrumNumerical resultsDiscussionSummary

About X(3872)First observation: 2003, Belle, KEKB

cited more than 500 timesB- → K- π+ π- J/ψ decay

Sharp peak of the invariant mass distribution of π+ π- J/ψ

Mass: (3871.5 ± 0.19) MeV about 0.3 MeV below D0 D*0-bar thresold

Width: less than 3.0 MeV Quantum Number: JPC = 1++ ?Other decay mode:

X(3872) → γ J/ψ 、 γψ(2S) 　X(3872) → π+ π- π0 J/ψ

International Journal of Theoretical Physics International Journal of Theoretical Physics

B+ → K+ + J/ψ + ππ(π)

11 Sep 2010 jps fall meeting @ 九州工業大学

B+ → X(3872) ＋ K+ → J/ψ ＋ vector meson

→π’s

Problems of X(3872) as C C-bar State1. 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. If 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.

Is X(3872) isospin mixed state?

Isovector component is smaller than isoscalar component : 10~20%

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

D. Gamermann and E. Oset, Phys. Rev. D80:014003,2009.M. Kerliner and H. J. Lipkin, arXiv:1008.0203.K. Terasaki, Prog. Theor. Phys. 122:1205,2010.

X(3872) as D0 D*0-bar Molecule

mD0 + mD*0 = (3871.81 ± 0.36) MeV

mX(3872) = (3871.50 ± 0.19) MeV

X(3872) is a very shallow bound state of D0 D*0-bar: D0 D*0-bar Molecule

Problem of X(3872) as D0 D*0-bar Molecule

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

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

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

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

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

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

ccu-bar

u-bar

c-bar

c-bar

D0

D*0-bar

ccd-bar

c-bar

c-bar

D+

D*-

u u

d-bar

d d

Like the σ-meson exchangeNo isospin symmetry breaking

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

Interaction:

)()(

11)(*)(*

**

22220000

qDDUqDD

qqqDDUqDD

Diagram

c c-bar core

D*0-bar

D0 D+

D*-

+. . . . .

c c-bar core

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

Energy spectrumWe 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: Mass Mass of the cc-bar core: 3.95 GeV

from 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 3.871 GeV with coupling strength g = 0.0185 GeV3/2

Lambda = 0.3 GeV, Calculated bound state energy is 3.871 GeV with coupling strength g = 0.0094 GeV3/2

Numerical results: WavefunctionLambda = 0.5 GeV

Lambda = 0.3 GeV

Large isospin symmetry breakingCutoff dependence is small

Why so large isospin symmetry breaking?mD0 + mD*0 = (3871.81 ± 0.36) MeV

mD+ + mD*- = (3879.89 ± 0.37) MeV

mX = 3871.5 MeV

Binding EnergyNeutral D case: 0.81 MeVCharged D case: 8.89 MeV

Large difference

Numerical results: WavefunctionLambda = 0.5 GeV

D0 D*0-bar

D+ D*-

r [fm]

r psi(r) [GeV1/2]

Numerical results: Energy spectrum

Lambda = 0.3 GeV

GeVX(3872) bound state

CC-bar state

Numerical results: Energy spectrum

Lambda = 0.5 GeV

GeVX(3872) bound state

CC-bar state disappears

Numerical results:Mass of the cc-bar core: 3.95 GeV

from S. Godfrey, N. Isgur, Phys. Rev. D 32 (1985) 189.

Cutoff: 0.5 GeV & 1.0 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) componentsΛ=0.5 GeV

0 0.10.20.30.40.50.60.70.80.9 10

0.2

0.4

0.6

0.8

1

D+ D*-

D0 D*0

c c-bar core

g / g (lambda=0)

Numerical results: X(3872) componentsΛ=0.5 GeV

0 0.10.20.30.40.50.60.70.80.9 10

0.10.20.30.40.50.60.70.80.9

1

D D* I =0D D* I=1c c-bar core

g / g (lambda=0)

Numerical results: X(3872) componentsΛ=1.0 GeV

g / g (lambda=0)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0

0.2

0.4

0.6

0.8

1

D+ D*-D0 D*0c c-bar core

Numerical results: X(3872) componentsΛ=1.0 GeV

g / g (lambda=0)0 0.10.20.30.40.50.60.70.80.9 1

00.10.20.30.40.50.60.70.80.9

1

D D* I =0D D* I=1c c-bar core

DiscussionBound state of hadrons

Kinetic energy v.s. Potential energy

Bound state of two hadronsDeuteron

Heavier Hadron -> Smaller kinetic termAbout 1 GeV mass (proton, neutron)-> bound state exists

DiscussionCharm quark hadrons -> mass is

bigger than 1 GeVPossibility of forming the bound

statesBottom quark hadrons -> more

probablePossibility of the exotic hadrons

Discussion -X(3872)-Quarkonium-hadronic molecule

hybrid structure ー＞ new style of hadronsProperties of X(3872) can be

explained by the charmonium-hadronic molecule structure, naturally

Quark model result of the charmonium ismeaningful as the core state.

Discussion -X(3872)-Large Isospin symmetry breaking

can be explained by the present picture

No observation of isospin multiplet is clearly explained, since the intermediate isoscalar ccbar state causes the attractive force between D and D*

Discussion -X(3872)-Production rate

compact ccbar component

Radiative decay

Charmonium state is 2 3P1Easy to transit to ψ(2S) than J/ψ(need the calculation to confirm it)

B X (2S) B X J / 3.41.4

SummaryCharmonium-hadronic molecule

hybrid structure can explain the observed properties of the X(3872) naturally.

Backup

Numerical results: WavefunctionLambda = 0.5 GeV

D0 D*0-bar

D+ D*-

r [fm]

psi(r) [GeV3/2]

Numerical results: WavefunctionLambda = 0.3 GeV

D0 D*0-bar

D+ D*-

r [fm]

r psi(r) [GeV1/2]

Numerical results: WavefunctionLambda = 0.3 GeV

D0 D*0-bar

D+ D*-

r [fm]

psi(r) [GeV3/2]

Numerical results: cc-bar core in complex energy planeΛ=0.5 GeV