Sachiko Takeuchi (Japan College of Social Work)

Makoto Takizawa (Showa Pharmaceutical Univ.)

Workshop “New Hadrons with Various Flavors”

Department of Physics, Nagoya Univ., Dec. 6, 2008

About X(3872)

Coupling between C C-bar core state and D0 D*0-bar state

D0 D*0-bar molecule

Coupling between D0 D*0-bar state and J/

Summary

First observation: 2003, Belle, KEKB

B- K- + - J/ decaySharp peak of the invariant mass distribution of + - J/

Mass: (3871.4 ± 0.6) MeV

Width: less than 2.3 MeV

Quantum Number: JPC = 1++

Other decay mode:X(3872) J/ X(3872) + - 0 J/

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

If X(3872) is c c-bar state, it is isoscalar.X(3872) 0 J/ + - J/ : isovectorThis decay means large isospin breaking.

Is X(3872) isospin mixed state?

mD + mD* = (3871.81 ± 0.36) MeVX(3872) is a very shallow bound state of D0 D*0-bar D0 D*0-bar Molecule

How about the production rate of such molecular-like state by the B-decay?

How about cusp

m + mJ/ = 775 + 3097 = 3872 MeV

m + mJ/ = 783 + 3097 = 3880 MeV

Color triplet scalar Diquark + vector antidiqaurk structure

Compact object: easy to create.

Isospin multiplets with electric charge statesshould exist, but not observed.

To study the hadron loop effects:intermediate state of D0 D*0-bar

Intermediate states of D0 D*0-bar + J/ :difference of the threshold

Calculate the energy spectrum using theGreen’s function method with simple separable interaction. We study only the qualitative feature.

c c-bar core D*0-bar

D0

cc-bar core state: X

S(E) =1

Im X G(E) X

G(E) =1

E ˆ H i

G(E) =GX0 (E) +GX

0 (E)VXDD*GDD*0 (E)VXDD*GX

0 (E) +

D0 D*0(

q ) VXDD* X =g

q 2 + 2

= 500MeV g = 0.03 cc-bar core mass = 3950 MeV Bound state 3863 MeV

3.90 3.95 4.00 4.05 4.10

2

4

6

8

10

= 200MeV g = 0.01 cc-bar core mass = 3950 MeV Bound state 3862 MeV

3.90 3.95 4.00 4.05 4.10

2

4

6

8

10

D0

D*0-bar

Separable interaction

D0D*0 = d3

q 1

q 2 +

2 D0D*0(

q )

S(E) =1

D0D*0 G(E) D0D*0

G(E) = GDD*0 (E) + GDD*

0 (E)V GDD*0 (E) +

D0D*0( q ) V D0D*0(

q ) = g

1 q 2 +

2

1

q 2 +2

= 200MeV g = -0.001Bound state 3865 MeV

4.0 4.2 4.4 4.6 4.8 5.0

5

10

15

20

= 500MeV g = -0.01Bound state 3864 MeV

4.0 4.2 4.4 4.6 4.8 5.0

0.5

1.0

1.5

2.0

2.5

3.0

D*0-bar

D0

J/

D0D*0 = d3

q 1

q 2 +

2 D0D*0(

q )

S(E) =1

D0D*0 G(E) D0D*0

G(E) = GDD*0 (E) + GDD*

0 (E)VDD* J / G J /0 (E)VDD* J / GDD*

0 (E) +

J / ( q ) VDD* J / D0D*0(

q ) = g

1 q 2 +

2

1

q 2 +2

= 200MeV g = 0.02Bound state 3865 MeV

4.0 4.2 4.4 4.6 4.8 5.0

0.05

0.10

0.15

0.20

If there exists 3950 MeV C C-bar state, the effect of coupling to D0D*0-bar state gives rise to the 3872 MeV bound state easily.

3950 MeV C C-bar state pushes up by the coupling effect and the resonance state above 3950 MeV should exist. However, such state is not observed. It means the coupling to D0D*0-bar state should strong.

In the case of D0 D*0-bar molecule picture, introduction of the weak attractive force gives rise to the shallow bound state. However the shape of the continuum spectrum seems to be different from the observation.