Spin-parities of the $P_c(4440)$ and $P_c(4457)$ in the one-boson-exchange model
Résumé
The LHCb collaboration has recently observed three pentaquark peaks, the Pc(4312), Pc(4440) and Pc(4457). They are very close to a pair of heavy baryon-meson thresholds, with the Pc(4312) located 8.9 MeV below the D¯Σc threshold, and the Pc(4440) and Pc(4457) located 21.8 and 4.8 MeV below the D¯*Σc one. The spin-parities of these three states have not been measured yet. In this work we assume that the Pc(4312) is a JP=12- D¯Σc bound state, while the Pc(4440) and Pc(4457) are D¯*Σc 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 D¯*Σc 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 naïve 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 Pc(4440) and Pc(4457) can be predicted from the Pc(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 Pc(4440) and Pc(4457) molecular pentaquarks to be 32- and 12-, respectively.