Open accessJournal Article

# Spin-parities of the $P_c(4440)$ and $P_c(4457)$ in the One-Boson-Exchange Model

02 Mar 2021-Physical Review D (American Physical Society)-Vol. 103, Iss: 5, pp 054004
Abstract: The LHCb collaboration has recently observed three pentaquark peaks, the ${P}_{c}(4312)$, ${P}_{c}(4440)$ and ${P}_{c}(4457)$. They are very close to a pair of heavy baryon-meson thresholds, with the ${P}_{c}(4312)$ located 8.9 MeV below the $\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}$ threshold, and the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ located 21.8 and 4.8 MeV below the ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ one. The spin-parities of these three states have not been measured yet. In this work we assume that the ${P}_{c}(4312)$ is a ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ $\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}$ bound state, while the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ are ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ bound states of unknown spin-parity, where we notice that the consistent description of the three pentaquarks in the one-boson-exchange model can indeed determine the spin and parities of the later, i.e., of the two ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ molecular candidates. For this determination we revisit first the one-boson-exchange model, which in its original formulation contains a short-range deltalike contribution in the spin-spin component of the potential. We argue that it is better to remove these deltalike contributions because, in this way, the one-boson-exchange potential will comply with the na\"{\i}ve expectation that the form factors should not have a significant impact in the long-range part of the potential (in particular the one-pion-exchange part). Once this is done, we find that it is possible to consistently describe the three pentaquarks, to the point that the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ can be predicted from the ${P}_{c}(4312)$ within a couple of MeV with respect to their experimental location. In addition the so-constructed one-boson-exchange model predicts the preferred quantum numbers of the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ molecular pentaquarks to be ${\frac{3}{2}}^{\ensuremath{-}}$ and ${\frac{1}{2}}^{\ensuremath{-}}$, respectively.

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Open accessJournal Article
J. Cheng1, Yan-Rui Liu1Institutions (1)
21 May 2019-Physical Review D
Abstract: In a chromomagnetic model, we analyze the properties of the newly observed ${P}_{c}(4457{)}^{+}$, ${P}_{c}(4440{)}^{+}$, and ${P}_{c}(4312{)}^{+}$ states. We estimate the masses of the $(uud{)}_{{8}_{c}}(c\overline{c}{)}_{{8}_{c}}$ and $(uds{)}_{{8}_{c}}(c\overline{c}{)}_{{8}_{c}}$ pentaquark states by considering the isospin breaking effects. Their values are determined by calculating mass distances from the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{++}{D}^{\ensuremath{-}}$ and ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}+}{D}^{\ensuremath{-}}$ thresholds, respectively. It is found that the isospin breaking effects on the spectrum are small. From the uncertainty consideration and the rearrangement decay properties in a simple model, we find that it is possible to assign the ${P}_{c}(4457{)}^{+}$, ${P}_{c}(4440{)}^{+}$, and ${P}_{c}(4312{)}^{+}$ as ${J}^{P}=3/{2}^{\ensuremath{-}}$, $1/{2}^{\ensuremath{-}}$, and $3/{2}^{\ensuremath{-}}$ pentaquark states, respectively. The assignment in the molecule picture can be different, in particular for the ${P}_{c}(4312{)}^{+}$. The information from open-charm channels, e.g., $\mathcal{B}[{P}_{c}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Sigma}}}_{c}^{++}{D}^{\ensuremath{-}}]/\mathcal{B}[{P}_{c}\ensuremath{\rightarrow}J/\ensuremath{\psi}p]$, will play an important role in distinguishing the inner structures of the ${P}_{c}$ states. Discussions and predictions based on the calculations are also given.

72 Citations

Open accessJournal Article
Bo Wang1, Lu Meng1, Shi-Lin Zhu1Institutions (1)
Abstract: The newly observed Pc(4312), Pc(4440) and Pc(4457) at the LHCb experiment are very close to the $${\varSigma}_c\overline{D}$$ and $${\varSigma}_c{\overline{D}}^{\ast }$$ thresholds. In this work, we perform a systematic study and give a complete picture on the interactions between the $${\varSigma}_c^{\left(\ast \right)}$$ and $${\overline{D}}^{\left(\ast \right)}$$ systems in the framework of heavy hadron chiral effective field theory, where the short-range contact interaction, long-range one-pion-exchange contribution, and intermediate-range two-pion-exchange loop diagrams are all considered. We first investigate the three Pc states without and with considering the Λc contribution in the loop diagrams. It is difficult to simultaneously reproduce the three Pcs unless the Λc is included. The coupling between the $${\varSigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)}$$ and $${\Lambda}_c{\overline{D}}^{\left(\ast \right)}$$ channels is crucial for the formation of these Pcs. Our calculation supports the Pc(4312), Pc(4440) and Pc(4457) to be the S-wave hidden-charm $${\left[{\varSigma}_c\overline{D}\right]}_{J=1/2}^{I=1/2},{\left[{\varSigma}_c{\overline{D}}^{\ast}\right]}_{J=1/2}^{I=1/2}$$ and $${\left[{\varSigma}_c{\overline{D}}^{\ast}\right]}_{J=3/2}^{I=1/2}$$ molecular pentaquarks, respectively. Our calculation disfavors the spin assignment $${J}^P=\frac{1^{-}}{2}$$ for Pc(4457) and $${J}^P=\frac{3^{-}}{2}$$ for Pc(4440), because the excessively enhanced spin-spin interaction is unreasonable in the present case. We obtain the complete mass spectra of the $${\left[{\varSigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)}\right]}_J$$ systems with the fixed low energy constants. Our result indicates the existence of the $${\left[{\varSigma}_c^{\ast }{\overline{D}}^{\ast}\right]}_J\left(J=\frac{1}{2},\frac{3}{2},\frac{5}{2}\right)$$ hadronic molecules. The previously reported Pc(4380) might be a deeper bound one. Additionally, we also study the hidden-bottom $${\varSigma}_b^{\left(\ast \right)}{B}^{\left(\ast \right)}$$ systems, and predict seven bound molecular states, which could serve as a guidance for future experiments. Furthermore, we also examine the heavy quark symmetry breaking effect in the hidden-charm and hidden-bottom systems by taking into account the mass splittings in the propagators of the intermediate states. As expected, the heavy quark symmetry in the bottom cases is better than that in the charmed sectors. We notice that the heavy quark symmetry in the $${\varSigma}_c\overline{D}$$ and $${\varSigma}_c^{\ast}\overline{D}$$ systems is much worse for some fortuitous reasons. The heavy quark symmetry breaking effect is nonnegligible in predicting the effective potentials between the charmed hadrons.

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43 Citations

Open accessJournal Article
Bo Wang1, Lu Meng1, Shi-Lin Zhu1Institutions (1)
Abstract: The newly observed $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ at the LHCb experiment are very close to the $\Sigma_c\bar{D}$ and $\Sigma_c\bar{D}^\ast$ thresholds. In this work, we perform a systematic study and give a complete picture on the interactions between $\Sigma_c^{(\ast)}$ and $\bar{D}^{(\ast)}$ systems in the framework of heavy hadron chiral perturbation theory, where the short-range contact interaction, long-range one-pion-exchange contribution, and intermediate-range two-pion-exchange loop diagrams are all considered. We first investigate the three $P_c$ states without and with considering the $\Lambda_c$ contribution in the loop diagrams. It is difficult to simultaneously reproduce the three $P_c$s unless the effect of $\Lambda_c$ is included. The coupling between $\Sigma_c^{(\ast)}\bar{D}^{(\ast)}$ and $\Lambda_c\bar{D}^{(\ast)}$ channels is crucial for the formation of these $P_c$s. Our calculation supports the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ to be the $S$-wave hidden-charm $[\Sigma_c\bar{D}]_{J=1/2}^{I=1/2}$, $[\Sigma_c\bar{D}^\ast]_{J=1/2}^{I=1/2}$ and $[\Sigma_c\bar{D}^\ast]_{J=3/2}^{I=1/2}$ molecular pentaquarks, respectively. Our calculation disfavors the spin assignment $J^P=\frac{1}{2}^-$ for $P_c(4457)$ and $J^P=\frac{3}{2}^-$ for $P_c(4440)$, because the excessively enhanced spin-spin interaction is unreasonable in the present case. We obtain the complete mass spectra of the $[\Sigma_c^{(\ast)}\bar{D}^{(\ast)}]_J$ systems with the fixed low energy constants. Our result indicates the existence of $[\Sigma_c^{\ast}\bar{D}^{\ast}]_J~(J=\frac{1}{2},\frac{3}{2},\frac{5}{2})$ hadronic molecules. The previously reported $P_c(4380)$ might be a deeper bound one. Additionally, we also study the hidden-bottom $\Sigma_b^{(\ast)}B^{(\ast)}$ systems, and predict seven bound molecular states, which could serve as a guidance for future experiments....

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38 Citations

Open accessJournal Article
Fu-Lai Wang1, Rui Chen, Zhan-Wei Liu1, Xiang Liu1Institutions (1)
06 Feb 2020-Physical Review C
Abstract: Inspired by the observations of three ${P}_{c}$ states, we systematically investigate interactions between an $S$-wave charmed baryon ${\mathcal{B}}_{c}^{(*)}={\mathrm{\ensuremath{\Lambda}}}_{c}/{\mathrm{\ensuremath{\Sigma}}}_{c}/{\mathrm{\ensuremath{\Sigma}}}_{c}^{*}$ and an anticharmed meson $\overline{T}={\overline{D}}_{1}/{\overline{D}}_{2}^{*}$ with the one-pion-exchange potential model and the one-boson-exchange potential model, and search for possible new types of ${P}_{c}$ states with the structures of ${\mathcal{B}}_{c}^{(*)}\overline{T}$. Both $S\ensuremath{-}D$ wave mixing and coupled channel effects are considered. Our results suggest that in some ${\mathcal{B}}_{c}^{(*)}\overline{T}$ systems there are ideal candidates of new types of ${P}_{c}$ states---i.e., the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}_{1}$ state with $I({J}^{P})=1/2(1/{2}^{+})$, the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}_{2}^{*}$ state with $I({J}^{P})=1/2(3/{2}^{+})$, the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}{\overline{D}}_{1}$ state with $I({J}^{P})=1/2(1/{2}^{+})$, and the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{*}{\overline{D}}_{2}^{*}$ states with $I({J}^{P})=1/2(1/{2}^{+},3/{2}^{+})$---and we suggest that these predicted new types of ${P}_{c}$ states can be detected in the process ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}\ensuremath{\psi}(2S)p{\ensuremath{\pi}}^{\ensuremath{-}}$. Meanwhile, we also extend our study to the interactions between an $S$-wave charmed baryon and a charmed meson in a $T$ doublet, and we predict a series of double-charm molecular pentaquarks.

28 Citations

Open accessJournal Article
Jun He1, Dian-Yong ChenInstitutions (1)
Abstract: In this work, we systemically investigate the molecular states from the $\Sigma^{(*)}_c\bar{D}^{(*)}-\Lambda_c\bar{D}^{(*)}$ interaction with the help of the Lagrangians with heavy quark and chiral symmetries in a quasipotential Bethe-Salpeter equation (qBSE) approach. The molecular states are produced from isodoublet (I=1/2) $\Sigma_c\bar{D}$ interaction with spin parity $J^P=1/2^-$ and $\Sigma_c\bar{D}^*$ interaction with $1/2^-$ and $3/2^-$. Their masses and widths are consistent with the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ observed at LHCb. The states, $\Sigma_c^*\bar{D}^*(1/2^-)$, $\Sigma_c^*\bar{D}^*(3/2^-)$ and $\Sigma^*_c\bar{D}(3/2^-)$, are also produced with the same parameters. The isodoublet $\Sigma_c^*\bar{D}^*$ interaction with $5/2^-$, as well as the isoquartet (I=3/2) $\Sigma_c\bar{D}^*$ interactions with $1/2^-$ and $3/2^-$, $\Sigma_c^*\bar{D}^*$ interaction with $3/2^-$ and $5/2^-$, are also attractive while very large cutoff is required to produce a molecular state. We also investigate the origin of the widths of these molecular states in the same qBSE frame. The $\Lambda\bar{D}^*$ channel is dominant in the decays of the states, $\Sigma_c\bar{D}^*(1/2^-)$, $\Sigma_c\bar{D}^*(3/2^-)$, $\Sigma_c^*\bar{D}(3/2^-)$, and $\Sigma_c\bar{D}(1/2^-)$. The $\Sigma^*_c\bar{D}^*(1/2^-)$ state has large coupling to $\Sigma_c\bar{D}$ channel while the $\Sigma_c\bar{D}^*$, $\Sigma^*_c\bar{D}$ and $\Lambda_c\bar{D}^*$ channels provide similar contributions to the width of the $\Sigma^*_c\bar{D}^*(3/2^-)$ state. These results will be helpful to understand the current LHCb experimental results, and the three predicted states and the decay pattern of these hidden-charmed molecular pentaquarks can be checked in future experiments.

23 Citations

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Open accessJournal Article
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Topics: Particle Data Group (59%), ,

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Murray Gell-Mann1, M. M. Lévy1Institutions (1)
01 May 1960-Il Nuovo Cimento
Abstract: In order to derive in a convincing manner the formula of Goldberger and Treiman for the rate of charged pion decay, we consider the possibility that the divergence of the axial vector current in β-decay may be proportional to the pion field. Three models of the pion-nucleon interaction (and the weak current) are presented that have the required property. The first, using gradient coupling, has the advantage that it is easily generalized to strange particles, but the disadvantages of being unrenormalizable and of bringing in the vector and axial vector currents in an unsymmetrical way. The second model, using a strong interaction proposed bySchwinger and a weak current proposed byPolkinghorne, is renormalizable and symmetrical betweenV andA, but it involves postulating a new particle and is hard to extend to strange particles. The third model resembles the second one except that it is not necessary to introduce a new particle. (Renormalizability in the usual sense is then lost, however). Further research along these lines is suggested, including consideration of the possibility that the pion decay rate may be plausibly obtained under less stringent conditions.

Topics: Pion (55%), Particle decay (54%), Pseudovector (53%) ... read more

1,712 Citations

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1,445 Citations

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