Abstract
AbstractThis study investigates the nature of the $$X_0(2900)$$
X
0
(
2900
)
and $$\chi _{c0}(3930)$$
χ
c
0
(
3930
)
based on experimental results of the process $$B^+$$
B
+
$$\rightarrow $$
→
$$D^+ D^- K^+$$
D
+
D
-
K
+
. We focus on the S-wave $$D^{*-}K^{*+}$$
D
∗
-
K
∗
+
and $$D_s^+D_s^-$$
D
s
+
D
s
-
molecular states, which can be related to the $$X_0(2900)$$
X
0
(
2900
)
and $$\chi _{c0}(3930)$$
χ
c
0
(
3930
)
, respectively. Using effective Lagrangians, we construct the potential kernel of the $$D^{*-}K^{*+}$$
D
∗
-
K
∗
+
–$$D^{-}K^{+}$$
D
-
K
+
and $$D_s^+D_s^-$$
D
s
+
D
s
-
–$$D^+D^-$$
D
+
D
-
interactions with a one-boson-exchange model, and determine the scattering amplitudes and their poles through a quasipotential Bethe–Salpeter equation approach. By incorporating the potential kernel into the three-body decay process $$B^+$$
B
+
$$\rightarrow $$
→
$$D^+ D^- K^+$$
D
+
D
-
K
+
, we evaluate the $$D^-K^+$$
D
-
K
+
and $$D^+D^-$$
D
+
D
-
invariant mass spectra, as well as the Dalitz plot, using Monte Carlo simulation. A satisfactory fit to the $$D^-K^+$$
D
-
K
+
and $$D^+D^-$$
D
+
D
-
invariant mass spectra is achieved after introducing additional Breit–Wigner resonances, $$X_1(2900)$$
X
1
(
2900
)
, $$\psi (3770)$$
ψ
(
3770
)
, and $$\chi _{c2}(3930)$$
χ
c
2
(
3930
)
. Prominent signals of the $$X_0(2900)$$
X
0
(
2900
)
and $$\chi _{c0}(3930)$$
χ
c
0
(
3930
)
states appear as peaks in the $$D^-K^+$$
D
-
K
+
and $$D^+D^-$$
D
+
D
-
invariant mass spectra near 2900 and 3930 MeV, respectively. Clear event concentration from the $$X_0(2900)$$
X
0
(
2900
)
and $$\chi _0(3930)$$
χ
0
(
3930
)
is evident as strips in the Dalitz plot. The results suggest that both $$X_0(2900)$$
X
0
(
2900
)
and $$\chi _{c0}(3930)$$
χ
c
0
(
3930
)
can be interpreted as molecular states, with the inclusion of $$X_1(2900)$$
X
1
(
2900
)
and $$\chi _2(3930)$$
χ
2
(
3930
)
necessary to describe structures in the $$D^-K^+$$
D
-
K
+
and $$D^+D^-$$
D
+
D
-
invariant mass spectra, respectively.
Publisher
Springer Science and Business Media LLC
Reference44 articles.
1. R. Aaij et al. [LHCb], A model-independent study of resonant structure in $$B^+\rightarrow D^+D^-K^+$$ decays. Phys. Rev. Lett. 125, 242001 (2020)
2. R. Aaij et al. [LHCb], Amplitude analysis of the $$B^+\rightarrow D^+D^-K^+$$ decay. Phys. Rev. D 102, 112003 (2020)
3. R. Aaij et al. [LHCb], Observation of new charmonium(-like) states in $$B^+ \rightarrow D^{*\pm } D^{\mp } K^+$$ decays. arXiv:2406.03156 [hep-ex]
4. J.R. Zhang, Open-charm tetraquark candidate: note on $$X_0$$(2900). Phys. Rev. D 103(5), 054019 (2021)
5. Z.G. Wang, Analysis of the $$X_0(2900)$$ as the scalar tetraquark state via the QCD sum rules. Int. J. Mod. Phys. A 35(30), 2050187 (2020)