Spin-parities of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4440</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4457</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> in the one-boson-exchange model

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.

Topics & Concepts