Abstract: We have analyzed the singularities of a triangle loop integral in detail and derived a formula for an easy evaluation of the triangle singularity on the physical boundary. It is applied to the Lambda(b) -> J/psi K(-)p process via Lambda*-charmonium-proton intermediate states. Although the evaluation of absolute rates is not possible, we identify the chi(c1) and the psi(2S)as the relatively most relevant states among all possible charmonia up to the psi(2S). The Lambda(1890)chi(c1)p loop is very special, as its normal threshold and triangle singularities merge at about 4.45 GeV, generating a narrow and prominent peak in the amplitude in the case that the chi(c1)p is in an S wave. We also see that loops with the same charmonium and other Lambda* hyperons produce less dramatic peaks from the threshold singularity alone. For the case of chi(c1)p -> J/psi p and quantum numbers 3/2(-) or 5/2(+), one needs P and D waves, respectively, in the chi(c1)p, which drastically reduce the strength of the contribution and smooth the threshold peak. In this case, we conclude that the singularities cannot account for the observed narrow peak. In the case of 1/2(+), 3/2(-) quantum numbers, where chi(c1)p -> J/psi p can proceed in an S wave, the Lambda(1890)chi(c1)p triangle diagram could play an important role, though neither can assert their strength without further input from experiments and lattice QCD calculations.

Abstract: 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(0)(b) -> I ) J/psi 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)*()) (D) over bar (()*()) molecules, by including the Lambda(c)(D) over bar (()*()) and eta(c)p as explicit inelastic channels in addition to the J/psi p, 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)*()) (D) over bar (()*()), and inelastic channels and without the Lambda(c)(D) over bar (()*()) interactions, (b) scheme II, where the one-pion exchange (OPE) is added to scheme I, and (c) scheme III, where the Lambda(c)(D) over bar (()*()) 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/psi p invariant mass distribution are consistent with the interpretation of the P-c(4312) and P-c(4440)/P-c(4457) as Sigma(c)(D) over bar and Sigma(c)(D) over bar* hadronic molecules, respectively, and that the data show clear evidence for a new narrow state, P-c(4380), identified as a Sigma(c)*(D) over bar 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)*())<(D)over ( )anf eta(c)p mass distributions from Lambda(0)(b) ->( )Sigma(()(c)*()) (D) over barK(-) and Lambda(0)(b) -> eta(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)(D) over bar (()*()) final states.