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.