Scale Invariance in Heavy Hadron Molecules

Understand

We discuss a scenario in which the $P_c(4450)^{+}$ heavy pentaquark is a $\Sigma_c \bar{D}^*$-$\Lambda_{c}(2595) \bar{D}$ molecule.

• The $\Lambda_{c1} \bar{D} \to \Sigma_c \bar{D}^*$ 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.