AbstractIn a molecular scenario, we investigate the isospin-breaking hidden charm decay processes of X(3872), i.e., $$X(3872) \rightarrow \pi ^+ \pi ^- J/\psi $$
X
(
3872
)
→
π
+
π
-
J
/
ψ
, $$X(3872) \rightarrow \pi ^+ \pi ^- \pi ^0 J/\psi $$
X
(
3872
)
→
π
+
π
-
π
0
J
/
ψ
, and $$X(3872)\rightarrow \pi ^0\chi _{cJ}$$
X
(
3872
)
→
π
0
χ
cJ
. We assume that the source of the strong isospin violation comes from the different coupling strengths of X(3872) to its charged components $$D^{*+} D^-$$
D
∗
+
D
-
and neutral components $$D^{*0 } {\bar{D}}^0$$
D
∗
0
D
¯
0
as well as the interference between the charged meson loops and neutral meson loops. The former effect could fix our parameters by using the measurement of the ratio $$\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- \pi ^0 J/\psi ]/\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- J/\psi ]$$
Γ
[
X
(
3872
)
→
π
+
π
-
π
0
J
/
ψ
]
/
Γ
[
X
(
3872
)
→
π
+
π
-
J
/
ψ
]
. With the determined parameter range, we find that the estimated ratio $$\Gamma [X(3872) \rightarrow \pi ^0 \chi _{c1}/\Gamma [X(3872) \rightarrow \pi ^+ \pi ^- J/\psi ]$$
Γ
[
X
(
3872
)
→
π
0
χ
c
1
/
Γ
[
X
(
3872
)
→
π
+
π
-
J
/
ψ
]
is well consistent with the experimental measurement from the BESIII collaboration. Moreover, the partial width ratio of $$\pi ^0 \chi _{cJ}$$
π
0
χ
cJ
for $$J=0,1,2$$
J
=
0
,
1
,
2
is estimated to be $$1.77{-}1.65:1:1.09{-}1.43$$
1.77
-
1.65
:
1
:
1.09
-
1.43
, which could be tested by further precise measurements of BESIII and Belle II.
Observation of the isospin breaking decay
ϒ(10860)→ϒ(1S)f0(980)→ϒ(1S)ηπ0
with the Belle II detector