Three hidden-charm pentaquark $P_c$ states, $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ were revealed in the ${\mathrm{\Lambda }}_b^0\to J/\psi p{K}^{-}$ process measured by LHCb using both run I and run II data. Their nature is under lively discussion, and their quantum numbers have not been determined. We analyze the $J/\psi p$ invariant mass distributions under the assumption that the crossed-channel effects provide a smooth background. For the first time, such an analysis is performed employing a coupled-channel formalism with the scattering potential involving both one-pion exchange as well as short-range operators constrained by heavy quark spin symmetry. We find that the data can be well described in the hadronic molecular picture, which predicts seven ${\mathrm{\Sigma }}_c^{(*)}{\overline{D}}^{(*)}$ molecular states in two spin multiplets, such that the $P_c(4312)$ is mainly a ${\mathrm{\Sigma }}_c\overline{D}$ bound state with $J^P=1/2^{-}$, while $P_c(4440)$ and $P_c(4457)$ are ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ bound states with quantum numbers $3/2^{-}$ and $1/2^{-}$, respectively. We also show that there is evidence for a narrow ${\mathrm{\Sigma }}_c^{*}\overline{D}$ bound state in the data which we call $P_c(4380)$, different from the broad one reported by LHCb in 2015. With this state included, all predicted ${\mathrm{\Sigma }}_c\overline{D}$, ${\mathrm{\Sigma }}_c^{*}\overline{D}$, and ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ hadronic molecules are seen in the data, while the missing three ${\mathrm{\Sigma }}_c^{*}{\overline{D}}^{*}$ states are expected to be found in future runs of the LHC or in photoproduction experiments.

We study meson-baryon scattering with strangeness \char21{}1 in unitary chiral perturbation theory. Ten coupled channels are considered in our work, namely, ${$\pi${}}^{0}$\Lambda${}$, ${$\pi${}}^{0}{$\Sigma${}}^{0}$, ${$\pi${}}^{$-${}}{$\Sigma${}}^{+}$, ${$\pi${}}^{+}{$\Sigma${}}^{$-${}}$, ${K}^{$-${}}p$, ${\overline{K}}^{0}n$, $$\eta${}$\Lambda${}$, $$\eta${}{$\Sigma${}}^{0}$, ${K}^{0}{$\Xi${}}^{0}$, and ${K}^{+}{$\Xi${}}^{$-${}}$. A large amount of experimental data are analyzed, including the recent precise measurement by the SIDDHARTA Collaboration of the energy shift and width of the $1s$ state of kaonic hydrogen. This leads to a strong constraint on the free parameters in our theory and of the resulting meson-baryon scattering amplitudes. We also analyze the uncertainty that stems by using several different strategies to perform the fits to data. It is found that large uncertainties in the subthreshold extrapolation of the ${K}^{$-${}}p$ scattering amplitude arise by either employing only one common weak pseudoscalar decay constant or distinguishing between ${f}_{$\pi${}}$, ${f}_{K}$, and ${f}_{$\eta${}}$. However, in both cases a good reproduction of experimental data is obtained. We also discuss the pole content of the resulting $S$-wave amplitudes, particularly in connection with the two-pole structure of the $$\Lambda${}(1405)$ resonance.

In this work, the complete one-loop calculation of meson-meson scattering amplitudes within U(3)$\bigotimes${}U(3) chiral perturbation theory with explicit resonance states is carried out for the first time. Partial waves are unitarized from the perturbative calculation employing a nonperturbative approach based on the N/D method. Once experimental data are reproduced in a satisfactory way we then study the resonance properties, such as the pole positions, corresponding residues and their NC behaviors. The resulting NC dependence is the first one in the literature that takes into account the fact that the $\eta${}1 becomes the ninth Goldstone boson in the chiral limit for large NC. Within this scheme the vector resonances studied, $\rho${}(770), K*(892) and $\phi${}(1020), follow an NC trajectory in agreement with their standard q\ifmmode\bar\else\textasciimacron\fi{}q interpretation. The scalars f0(1370), a0(1450) and K*(1430) also have for large NC a q\ifmmode\bar\else\textasciimacron\fi{}q pole position trajectory and all of them tend to a bare octet of scalar resonances around 1.4~GeV. The f0(980) tends asymptotically to the bare pole position of a singlet scalar resonance around 1~GeV. The $\sigma${}, $\kappa${} and a0(980) scalar resonances have a very different NC behavior. The case of the $\sigma${} resonance is analyzed with special detail.

The nature of the three narrow hidden-charm pentaquark P_c states, i.e., P_c(4312), P_c(4440) and P_c(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 P_c 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 η_cp 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 P_c(4312) and P_c(4440)/P_c(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, P_c(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 P_c(4440) and P_c(4457) being J^P = 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 P_c(4440) and the P_c(4457) in the $$ {\Sigma}_c^{\left(\ast \right)}\overline{D} $$Σ c ∗ D ¯ and η_cp 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.