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The nature of the three narrow hidden-charm pentaquark Pc states, i.e., Pc(4312), Pc(4440) and Pc(4457), is under intense discussion since their discovery from the updated analysis of the process $$ {\Lambda}_b^0\to J/\psi {pK}^{-} $$ Λ b 0 → J / ψ pK − by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124, 072001 (2020)], in which the Pc states are treated as $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ Σ c ∗ D ¯ ∗ molecules, by including the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ Λ c D ¯ ∗ and ηcp as explicit inelastic channels in addition to the J/ψp, as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ Σ c ∗ D ¯ ∗ , and inelastic channels and without the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ Λ c D ¯ ∗ interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ Λ c D ¯ ∗ interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S-wave-to-D-wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/ψp invariant mass distribution are consistent with the interpretation of the Pc(4312) and Pc(4440)/Pc(4457) as $$ {\Lambda}_c\overline{D} $$ Λ c D ¯ and $$ {\Sigma}_c{\overline{D}}^{\ast } $$ Σ c D ¯ ∗ hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, Pc(4380), identified as a $$ {\Sigma}_c^{\ast}\overline{D} $$ Σ c ∗ D ¯ molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the Pc(4440) and Pc(4457) being JP = 3/2− and 1/2−, respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the Pc(4440) and the Pc(4457) in the $$ {\Sigma}_c^{\left(\ast \right)}\overline{D} $$ Σ c ∗ D ¯ and ηcp mass distributions from $$ {\Lambda}_b^0\to {\Sigma}_c^{\left(\ast \right)}\overline{D}{K}^{-} $$ Λ b 0 → Σ c ∗ D ¯ K − and $$ {\Lambda}_b^0\to {\eta}_c{pK}^{-} $$ Λ b 0 → η c pK − will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ Λ c D ¯ ∗ final states.
The nature of the three narrow hidden-charm pentaquark Pc states, i.e., Pc(4312), Pc(4440) and Pc(4457), is under intense discussion since their discovery from the updated analysis of the process $$ {\Lambda}_b^0\to J/\psi {pK}^{-} $$ Λ b 0 → J / ψ pK − by LHCb. In this work we extend our previous coupled-channel approach [Phys. Rev. Lett. 124, 072001 (2020)], in which the Pc states are treated as $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ Σ c ∗ D ¯ ∗ molecules, by including the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ Λ c D ¯ ∗ and ηcp as explicit inelastic channels in addition to the J/ψp, as required by unitarity and heavy quark spin symmetry (HQSS), respectively. Since inelastic parameters are very badly constrained by the current data, three calculation schemes are considered: (a) scheme I with pure contact interactions between the elastic, i.e., $$ {\Sigma}_c^{\left(\ast \right)}{\overline{D}}^{\left(\ast \right)} $$ Σ c ∗ D ¯ ∗ , and inelastic channels and without the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ Λ c D ¯ ∗ interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ Λ c D ¯ ∗ interactions are included in addition. It is shown that to obtain cutoff independent results, OPE in the multichannel system is to be supplemented with S-wave-to-D-wave mixing contact terms. As a result, in line with our previous analysis, we demonstrate that the experimental data for the J/ψp invariant mass distribution are consistent with the interpretation of the Pc(4312) and Pc(4440)/Pc(4457) as $$ {\Lambda}_c\overline{D} $$ Λ c D ¯ and $$ {\Sigma}_c{\overline{D}}^{\ast } $$ Σ c D ¯ ∗ hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, Pc(4380), identified as a $$ {\Sigma}_c^{\ast}\overline{D} $$ Σ c ∗ D ¯ molecule, which should exist as a consequence of HQSS. While two statistically equally good solutions are found in scheme I, only one of these solutions with the quantum numbers of the Pc(4440) and Pc(4457) being JP = 3/2− and 1/2−, respectively, survives the requirement of regulator independence once the OPE is included. Moreover, we predict the line shapes in the elastic and inelastic channels and demonstrate that those related to the Pc(4440) and the Pc(4457) in the $$ {\Sigma}_c^{\left(\ast \right)}\overline{D} $$ Σ c ∗ D ¯ and ηcp mass distributions from $$ {\Lambda}_b^0\to {\Sigma}_c^{\left(\ast \right)}\overline{D}{K}^{-} $$ Λ b 0 → Σ c ∗ D ¯ K − and $$ {\Lambda}_b^0\to {\eta}_c{pK}^{-} $$ Λ b 0 → η c pK − will shed light on the quantum numbers of those states, once the data are available. We also investigate possible pentaquark signals in the $$ {\Lambda}_c{\overline{D}}^{\left(\ast \right)} $$ Λ c D ¯ ∗ final states.
The infinite chain of transitions of one pair of mesons (channel I) into another pair of mesons (channel II) can produce bound states and resonances in both channels even if no interactions inside channels exist. These resonances which can occur also in meson-baryon channels are called channel-coupling (CC) resonances. A new mechanism of CC resonances is proposed where transitions occur due to a rearrangement of confining strings inside each channel — the recoupling mechanism. The amplitude of this recoupling mechanism is expressed via overlap integrals of the wave functions of participating mesons (baryons). The explicit calculation with the known wave functions yields the peak at E = 4.12 GeV for the transitions $$ J/\psi +\phi \leftrightarrow {D}_s^{\ast }+{\overline{D}}_s^{\ast } $$ J / ψ + ϕ ↔ D s ∗ + D ¯ s ∗ , which can be associated with χc1 (4140), and a narrow peak at 3.98 GeV with the width 10 MeV for the transitions $$ {D}_s^{-}+{D}_0^{\ast}\leftrightarrow J/\psi +{K}^{\ast -} $$ D s − + D 0 ∗ ↔ J / ψ + K ∗ − , which can be associated with th recently discovered Zcs (3985).
Motivated by the observation of the first hidden charm pentaquarks by the LHCb collaboration in 2015 and the updated analysis with an order-of-magnitude larger data set in 2019, we estimate their cross sections for the prompt production as well as their heavy quark spin partners, in the $$\Sigma _c^{(*)}\bar{D}^{(*)}$$ Σ c ( ∗ ) D ¯ ( ∗ ) hadronic molecular picture, at the center-of-mass energy $$7~\text {TeV}$$ 7 TeV in the pp collision. Their cross sections are several $${\mathrm {nb}}$$ nb and we would expect several tens hidden charm pentaquark events in the LHC based on its current integrated luminosity. The cross sections show a sizable deviation of the cross sections for hidden charm pentaquarks with the third isospin component $$I_z=+\frac{1}{2}$$ I z = + 1 2 ($$P_c^+$$ P c + ) from those with $$I_z=-\frac{1}{2}$$ I z = - 1 2 ($$P_c^0$$ P c 0 ). The cross sections decrease dramatically with the increasing transverse momentum. Our study can also tell where to search for the missing hidden charm pentaquarks. The confirmation of the complete hidden charm pentaquarks in the heavy quark symmetry would further verify their $$\Sigma _c^{(*)}\bar{D}^{(*)}$$ Σ c ( ∗ ) D ¯ ( ∗ ) molecular interpretation. In addition, the relative strength among these cross sections for pentaquarks can help us to identify the quantum numbers of the $$P_c(4440)$$ P c ( 4440 ) and $$P_c(4457)$$ P c ( 4457 ) .
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