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Abstract

In this work, the authors use the effective Lagrangian method to investigate the production of singly charm pentaquark state with spin parity $J ^ P={1/2}^{-} $ . Based on the possible molecular state images of hadrons, the author discusses the production of singly charm pentaquark state ${c\bar suud}$ and decuplet baryon $\bar \varDelta$ by $B_{\mathrm{s}}$ meson with different molecular state configurations of $ND_{\mathrm{s}} $ or $ND ^ * _{\mathrm{s}} $ . To determine the coupling between pentaquark and their constituents in the molecular scheme, the authors follow the Weinberg compositeness condition to estimate the self-energy diagram of the singly charmed pentaquark. Further study on the production of pentaquark from $B_{\mathrm{s}}$ meson can be propeled by computing the transition matrix elements, or the triangle diagrams, which can be careful divided into two part subprocess, one associated with weak transition can be represented into form factor and decay constant, another one related to strong coupling of hadrons can be described by effective Lagrangian. Selecting the scale parameter α(10–200 MeV) and binding energy ε(5, 20, 50 MeV), the authors can find the branching ratio of the production $\bar B_{\mathrm{s}} \to P_ {{\mathrm{c}}\bar {{\mathrm{s}}}}\bar \varDelta $ . Under the configuration of $ND_{\mathrm{s}}$ molecule, the branching ratio of the Cabibbo allowed process $\bar B_{\mathrm{s}} \rightarrow P_{{{\mathrm{c}} \bar{{\mathrm{s}}}}} \bar \varDelta$ can reach to order of $10^{-5}$ . Moreover, the production branching ratio of $ND^*_{\mathrm{s}}$ molecule is only at the order of $10^{-8}$ . A increasing scale parameter αcan significantly improve the production branching ratio of the singly charm pentaquark. In addition, the binding energy and the coupling constants will also affect the magnitude of production. Therefore, considering the above factors, the production branching ratio of singly charm pentaquark in $B_{\mathrm{s}}$ decays have considerable results, which is worth experimental and theoretical research in the future. The findings of our work can provide a reference for the experimental search and study of singly charm pentaquark, and it is hoped that they will be verified in future experimental detections at Bfactories such as LHCb, Belle, and BaBar.

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Authors and contacts

Corresponding author:Li Na,TS22180005A31@cumt.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 12005294).

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References

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参数	$ {\bar B_{\mathrm{s}}\to D} $		$ {\bar B_{\mathrm{s}}\to D^*} $
参数	$ F_1(k_1) $	$ F_2(k_1) $	$ A_{0}(k_1) $	$ A_{1}(k_1) $	$ A_{2}(k_1) $	$ A_{3}(k_1) $
$ a_{0} $	$ 0.666 $	$ 0.666 $	$ 0.100 $	$ 0.105 $	$ 0.055 $	$ 0.059 $
$ a_{1} $	$ -0.206 $	$ -3.236 $	$ -0.180 $	$ -0.430 $	$ -0.010 $	$ -0.110 $
$ a_{2} $	$ -0.106 $	$ -0.075 $	$ -0.006 $	$ -0.100 $	$ -0.030 $	$ -0.250 $
$ a_{3} $	$ 0.00 $	$ -0.00 $	$ 0.00 $	$ -0.030 $	$ 0.060 $	$ -0.050 $
$ m_{{\mathrm{pole}}} $/GeV	$ — $	$ — $	$ 6.335 $	$ 6.275 $	$ 6.745 $	$ 6.745 $

DownLoad: CSV

分子态	产生道	分支比($ \times 10^{-6} $)
		$ \varepsilon $/MeV
		5	20	50
$ ND_{\mathrm{s}} $	$ \bar B_{\mathrm{s}} \xrightarrow[]{N} P_{{\mathrm{c}} \bar{{\mathrm{s}}}} \bar \varDelta $	29.40	31.37	24.51
$ ND_{\mathrm{s}} $	$ \bar B_{\mathrm{s}}\xrightarrow[]{N} P_{{\mathrm{c}} \bar{{\mathrm{s}}}}(\to \varLambda_{\mathrm{c}} K) \bar \varDelta $	0.223	0.194	0.137
$ ND^*_{\mathrm{s}} $	$ \bar B_{\mathrm{s}}\xrightarrow[]{N} P_{{\mathrm{c}} \bar{{\mathrm{s}}}} \bar \varDelta $	0.055	0.408	1.570
	$ \bar B_{\mathrm{s}}\xrightarrow[]{N} P_{{\mathrm{c}} \bar{{\mathrm{s}}}}(\to \varLambda_{\mathrm{c}} K) \bar \varDelta $	0.0006	0.0041	0.0157
	$ \bar B_{\mathrm{s}}\xrightarrow[]{N} P_{{\mathrm{c}} \bar{{\mathrm{s}}}}(\to \Sigma_{\mathrm{c}} K) \bar \varDelta $	0.0004	0.0024	0.0072
	$ \bar B_{\mathrm{s}}\xrightarrow[]{N} P_{{\mathrm{c}} \bar{{\mathrm{s}}}}(\to p D_{\mathrm{s}}) \bar \varDelta $	0.0002	0.0015	0.0050

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Vol. 73, Issue 13 - 2024-07-05

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