Strong decays of $P_{\psi }^N(4312{)}^{+}$ to $J/\psi ({\eta }_c)p$ and ${\bar{D}}^{(\ast )}{\Lambda }_c$ within the Bethe-Salpeter framework

Abstract

Based on the effective Lagrangian in the heavy quark limit, we calculate the one-boson-exchange interaction kernel of $P_{\psi }^N(4312{)}^{+}$ as the $\bar{D}{\Sigma }_c$ molecular state in isospin-$\frac{1}{2}$. We present the Bethe-Salpeter equation and wave function for the constituent particles to be a (pseudo)scalar meson and a $\frac{1}{2}$ baryon. By solving the Bethe-Salpeter equation, we obtain $P_{\psi }^N(4312{)}^{+}$ as the $\bar{D}{\Sigma }_c$ molecular state with $J^P=(\frac{1}{2}{)}^{-}$. Combining the effective Lagrangian and the obtained BS wave function, the partial decay widths of $P_{\psi }^N(4312{)}^{+}$ to $J/\psi p$, ${\eta }_{c}p$, ${\bar{D}}^{\ast 0}{\Lambda }_c^{+}$ and ${\bar{D}}^0{\Lambda }_c^{+}$ are calculated to be $0.17$, $0.085$, $8.8$, and $0.026$ MeV, respectively, which are roughly consistent with the LHCb experimental measurements and some other theoretical researches. The obtain results indicate the fraction of ${\bar{D}}^{\ast 0}{\Lambda }_c^{+}$ channel amounts to $\sim 90\%$ of $P_{\psi }^N(4312{)}^{+}$, and is a highly promising channel to be discovered in the near future experiments. Our results favor the interpretation of $P_{\psi }^N(4312{)}^{+}$ as the $\bar{D}{\Sigma }_c$ molecular state with $J^P=(\frac{1}{2}{)}^{-}$ and isospin $I=\frac{1}{2}$.

28 pages, 7 figures

References in corpus (15)

• FeynCalc 9.3: New features and improvements
• Study of $P_c(4457)$, $P_c(4440)$, and $P_c(4312)$ in a quasipotential Bethe-Salpeter equation approach
• Heavy quark spin symmetric molecular states from ${\bar{D}}^{(\ast )}{\Sigma }_c^{(\ast )}$ and other coupled channels in the light of the recent LHCb pentaquarks
• Strong Decays of Charmed Baryons in Heavy Hadron Chiral Perturbation Theory
• Interpretation of the Narrow $J/\psi p$ Peaks in ${\Lambda }_b\to J/\psi p{K}^{-}$ Decay in the Compact Diquark Model
• Magnetic dipole moments of the hidden-charm pentaquark states: $P_c(4440)$, $P_c(4457)$ and $P_{cs}(4459)$
• A possible global group structure for exotic states
• The magnetic moment of $P_c(4312)$ as a $\bar{D}{\Sigma }_c$ molecular state
• Selected strong decays of pentaquark State $P_c(4312)$ in a chiral constituent quark model
• Experimental constraints on the properties of $P_c$ states
• Decay properties of $P_c$ states through the Fierz rearrangement
• $P_c$ Resonances in the Compact Pentaquark Picture
• Dynamical Analysis of Screening in Scalar-Tensor Theory
• Relations between strong decay widths of the $P_c$ pentaquarks in the SU(4) flavor-spin model
• Mass spectra, wave functions and mixing effects of the $(bcq)$ baryon

Cited by in corpus (6)

• Hidden-charm pentaquark states in a mass splitting model
• The electromagnetic form factors of heavy-light pseudo-scalar and vector mesons
• Probing the hidden-bottom pentaquark resonances in photonuclear bottomonium production near threshold: differential observables
• Strong decays of $P_{\psi }^N(4440{)}^{+}$ and $P_{\psi }^N(4457{)}^{+}$ within the Bethe-Salpeter framework
• Distribution amplitudes of heavy-light pseudo-scalar and vector mesons from Dyson-Schwinger equations framework
• $D^{\ast }D\pi$ and $B^{\ast }B\pi$ couplings from Dyson-Schwinger equations framework