Abstract
Abstract
In the present work, we propose to investigate the productions of
$$P_{c}(4312)$$
P
c
(
4312
)
,
$$P_{c}(4440)$$
P
c
(
4440
)
, and
$$P_{c}(4457)$$
P
c
(
4457
)
in the
$$e^{+} e^{-} \rightarrow p \bar{p} J/\psi $$
e
+
e
-
→
p
p
¯
J
/
ψ
process by utilizing an effective Lagrangian approach, where
$$P_{c}(4312)$$
P
c
(
4312
)
is considered as
$$\Sigma _{c} \bar{D}$$
Σ
c
D
¯
molecular state with
$$J^{P}=1/2^{-}$$
J
P
=
1
/
2
-
, while
$$P_{c}(4440)$$
P
c
(
4440
)
and
$$P_{c}(4457)$$
P
c
(
4457
)
are considered as
$$\Sigma _{c} \bar{D}^{*}$$
Σ
c
D
¯
∗
molecular states with
$$J^{P}=1/2^{-}$$
J
P
=
1
/
2
-
and
$$J^{P}=3/2^{-}$$
J
P
=
3
/
2
-
, respectively. For the
$$e^{+} e^{-} \rightarrow \bar{p} P_{c}(4312)$$
e
+
e
-
→
p
¯
P
c
(
4312
)
,
$$e^{+} e^{-} \rightarrow \bar{p} P_{c}(4440)$$
e
+
e
-
→
p
¯
P
c
(
4440
)
, and
$$e^{+} e^{-} \rightarrow \bar{p} P_{c}(4457)$$
e
+
e
-
→
p
¯
P
c
(
4457
)
processes, the cross sections are evaluated to be (
$$27.8^{+42.2}_{-17.9}$$
27
.
8
-
17.9
+
42.2
) fb, (
$$38.7^{+58.6}_{-25.1}$$
38
.
7
-
25.1
+
58.6
) fb, and (
$$1.44^{+2.18}_{-0.93}$$
1
.
44
-
0.93
+
2.18
) fb at
$$\sqrt{s}=6$$
s
=
6
GeV, respectively, where the central values are estimated with
$$\Lambda _{r}=2.5$$
Λ
r
=
2.5
GeV, and the uncertainties are resulted from the variations of
$$\Lambda _{r}$$
Λ
r
from 2.0 to 3.0 GeV. Considering that the
$$P_{c}$$
P
c
states can decay into
$$J/\psi p$$
J
/
ψ
p
, we estimate the cross sections for
$$e^{+} e^{-} \rightarrow p \bar{p} J/\psi $$
e
+
e
-
→
p
p
¯
J
/
ψ
and the differential cross sections depending on the
$$J/\psi p$$
J
/
ψ
p
invariant mass. At
$$\sqrt{s}=6$$
s
=
6
GeV, the cross sections for
$$e^{+} e^{-} \rightarrow p \bar{p} J/\psi $$
e
+
e
-
→
p
p
¯
J
/
ψ
are estimated to be (
$$14.7^{+22.2}_{-9.50}$$
14
.
7
-
9.50
+
22.2
) fb. Moreover, our estimations indicate that the cross section resulted from the
$$P_{c}(4440)$$
P
c
(
4440
)
and
$$\bar{P}_{c}(4440)$$
P
¯
c
(
4440
)
intermediate states is dominant. In the
$$J/\psi p$$
J
/
ψ
p
invariant mass spectrum, our estimations reveal that the peak structure between 4.42 and 4.46 GeV primarily originates from
$$P_{c}(4440)$$
P
c
(
4440
)
.