Strong decays of $P_{\psi }^N(4440{)}^{+}$ and $P_{\psi }^N(4457{)}^{+}$ within the Bethe-Salpeter framework

Abstract

By combining the effective Lagrangian and Bethe-Salpeter framework, we studied the mass spectra, wave functions, and strong decay widths of the two pentaquark states $P_{\psi }^N(4440{)}^{+}$ and $P_{\psi }^N(4457{)}^{+}$ reported by LHCb in 2019. Taking into account both the mass ordering and the decay widths, our results favor the interpretation of $P_{\psi }^N(4440{)}^{+}$ and $P_{\psi }^N(4457{)}^{+}$ as the isospin-$\frac{1}{2}$ $[{\bar{D}}^{\ast }{\Sigma }_c]$ molecular states with $J^P$ configuration $(\frac{3}{2}{)}^{-}$ and $(\frac{1}{2}{)}^{-}$, respectively. We first calculate the one-boson-exchange interaction kernel of $[{\bar{D}}^{\ast }{\Sigma }_c]$ in the isospin-$\frac{1}{2}$ configuration. Then we present the Bethe-Salpeter equation (BSE) and wave functions for the bound states of a vector meson and a $\frac{1}{2}$ baryon with $J^P={\frac{1}{2}}^{-}$ and ${\frac{3}{2}}^{-}$. The obtained mass results for the $(\frac{3}{2}{)}^{-}$ and $(\frac{1}{2}{)}^{-}$ are $4.442$ and $4.457$ GeV, respectively. Combining the effective Lagrangians and the BS wave functions, we further calculate the strong decay channels ${\bar{D}}^{(\ast )0}{\Lambda }_c^{+}$, $J/\psi ({\eta }_c)p$, and $\bar{D}{\Sigma }_c^{(\ast )}$ for the two $P_{\psi }^N$ states. In the favored ${\frac{3}{2}}^{-}$ and ${\frac{1}{2}}^{-}$ configuration, the obtained total widths are $21.8$ MeV and $13.0$ MeV, respectively, which are substantially consistent with the LHCb data. Our results suggest that ${\bar{D}}^0{\Lambda }_c^{+}$ and ${\bar{D}}^{(\ast )0}{\Lambda }_c^{+}$ are the dominant decay channels to detect $P_{\psi }^N(4440{)}^{+}$ and $P_{\psi }^N(4457{)}^{+}$, respectively.

arXiv comment54 pages, 6 figures, 8 tables. Accepted by JHEP

References in corpus (57)

• New Developments in FeynCalc 9.0
• Phenomenology of Heavy Meson Chiral Lagrangians
• FeynCalc 9.3: New features and improvements
• Prediction of narrow $N^{\ast }$ and ${\Lambda }^{\ast }$ resonances with hidden charm above 4 GeV
• New Exotic Meson and Baryon Resonances from Doubly-Heavy Hadronic Molecules
• Threshold cusps and triangle singularities in hadronic reactions
• Identifying exotic hidden-charm pentaquarks
• Emergence of a complete heavy-quark spin symmetry multiplet: seven molecular pentaquarks in light of the latest LHCb analysis
• The possible hidden-charm molecular baryons composed of anti-charmed meson and charmed baryon
• Strong LHCb evidence supporting the existence of the hidden-charm molecular pentaquarks
• Sigma_c Dbar and Lambda_c Dbar states in a chiral quark model
• 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
• Interpretation of the LHCb $P_c$ States as Hadronic Molecules and Hints of a Narrow $P_c(4380)$
• Strong Decays of Charmed Baryons in Heavy Hadron Chiral Perturbation Theory
• Nonfactorizable contributions in B decays to charmonium: the case of $B^{-}\to K^{-}{h}_c$
• Possible interpretations of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$
• Exploring the molecular scenario of $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$
• Nucleon Resonances with Hidden Charm in Coupled-Channel Models
• Coupled-channel approach to $T_{cc}^{+}$ including three-body effects
• Effect of charmed meson loops on charmonium transitions
• ${\Lambda }_{c}N$ bound states revisited
• The hidden charm pentaquark states and ${\Sigma }_c{\bar{D}}^{(\ast )}$ interaction in 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
• Semileptonic $B_c$ Decay and Heavy Quark Spin Symmetry
• Strong decays of the latest LHCb pentaquark candidates in hadronic molecule pictures
• Molecular Interpretation of the $P_c(4440)$ and $P_c(4457)$ States
• $P_c$ pentaquarks with chiral tensor and quark dynamics
• Decays of $P_c$ into $J/\psi N$ and ${\eta }_{c}N$ with heavy quark spin symmetry
• Some decay properties of hidden-charm pentaquarks as baryon-meson molecules
• Tetraquark candidates in the LHCb's di-$J/\psi$ mass spectrum
• Probing hidden-charm decay properties of $P_c$ states in a molecular scenario
• Coupled-channel effects of the ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$-${\Lambda }_c(2595)\bar{D}$ system and molecular nature of the $P_c$ pentaquark states from one-boson exchange model
• A possible global group structure for exotic states
• $P_c(4312{)}^{+}$, $P_c(4380{)}^{+}$, and $P_c(4457{)}^{+}$ as double triangle cusps
• Analysis of the strong decays of the $P_c(4312)$ as a pentaquark molecular state with QCD sum rules
• Mass spectra and wave functions of $T_{QQ\bar{Q}\bar{Q}}$ tetraquarks
• Recently observed $P_c$ as molecular states and possible mixture of $P_c(4457)$
• Effects of a $N^{\ast }$ resonance with hidden charm in the ${\pi }^{-}p\to D^{-}{\Sigma }_c^{+}$ reaction near threshold
• The $B_c$ Decays to $P$-wave Charmonium by Improved Bethe-Salpeter Approach
• Is $D_{sJ}^{+}(2632)$ the first radial excitation of $D_s^{\ast }(2112)$?
• The mass spectra and wave functions for the doubly heavy baryons with $J^P=1^{+}$ heavy diquark core
• Two-Body Strong Decay of Z(3930) as the ${\chi }_{c2}(2P)$ State
• Selected strong decays of pentaquark State $P_c(4312)$ in a chiral constituent quark model
• Partial decay widths of $P_c(4312)$ as a $\bar{D}{\Sigma }_c$ molecular state
• Experimental constraints on the properties of $P_c$ states
• Study of isospin eigenstates of the pentaquark molecular states with strangeness
• Decay properties of $P_c$ states through the Fierz rearrangement
• Isospin eigenstates of the color singlet-singlet type pentaquark states
• $P_c$ Resonances in the Compact Pentaquark Picture
• $D$-Wave Charmonia ${\eta }_{c2}$($1{}^1{D}_2$), ${\psi }_2$($1{}^3{D}_2$), and ${\psi }_3$($1{}^3{D}_3$) in $B_c$ Decays
• Study on possible molecular states composed of ${\Lambda }_c\bar{D}$ (${\Lambda }_{b}B$) and ${\Sigma }_c\bar{D}$ (${\Sigma }_{b}B$) within the Bethe-Salpeter framework
• Study of the excited $1^{-}$ charm and charm-strange mesons
• Mixing angle and decay constants of $J^P=1^{+}$ heavy-light mesons
• Strong decays of $P_{\psi }^N(4312{)}^{+}$ to $J/\psi ({\eta }_c)p$ and ${\bar{D}}^{(\ast )}{\Lambda }_c$ within the Bethe-Salpeter framework
• 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 (1)

• Unravelling Pentaquarks with Born--Oppenheimer effective theory