We discuss a scenario in which the $P_c(4450{)}^{+}$ heavy pentaquark is a ${\mathrm{\Sigma }}_c{\overline{D}}^{*}\text{−}{\mathrm{\Lambda }}_c(2595)\overline{D}$ molecule. The ${\mathrm{\Lambda }}_{c1}\overline{D}\to {\mathrm{\Sigma }}_c{\overline{D}}^{*}$ transition is mediated by the exchange of a pion almost on the mass shell that generates a long-range $1/r^2$ potential. This is analogous to the effective force that is responsible for the Efimov spectrum in three-boson systems interacting through short-range forces. The equations describing this molecule exhibit approximate scale invariance, which is anomalous and broken by the solutions. If the $1/r^2$ potential is strong enough this symmetry survives in the form of discrete scale invariance, opening the prospect of an Efimov-like geometrical spectrum in two-hadron systems. For a molecular pentaquark with quantum numbers ${\frac{3}{2}}^{-}$ the attraction is not enough to exhibit discrete scale invariance, but this prospect might very well be realized in a ${\frac{1}{2}}^{+}$ pentaquark or in other hadron molecules involving transitions between particle channels with opposite intrinsic parity and a pion near the mass shell. A very good candidate is the ${\mathrm{\Lambda }}_c(2595){\overline{\mathrm{\Xi }}}_b-{\mathrm{\Sigma }}_c{{\overline{\mathrm{\Xi }}}_b}^{\prime }$ molecule. Independently of this, the $1/r^2$ force is expected to play a very important role in the formation of this type of hadron molecule, which points to the existence of ${\frac{1}{2}}^{+}$ ${\mathrm{\Sigma }}_c{D}^{*}\text{−}{\mathrm{\Lambda }}_c(2595)D$ and $1^{+}$ ${\mathrm{\Lambda }}_c(2595){\mathrm{\Xi }}_b-{\mathrm{\Sigma }}_c{\mathrm{\Xi }}_b^{\prime }$ molecules and $0^{+}/1^{-}$ ${\mathrm{\Lambda }}_c(2595){\overline{\mathrm{\Xi }}}_b-{\mathrm{\Sigma }}_c{{\overline{\mathrm{\Xi }}}_b}^{\prime }$ baryonia.

• Received 22 April 2017

DOI:https://doi.org/10.1103/PhysRevD.97.094036

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society