Hadronic and electromagnetic interactions of quarkonia

We examine the hadronic interactions of quarkonia, focusing on the decays $\psi \mathrm{}\left(2S\right)\mathrm{}\to J/\psi \pi \pi$ and ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}\to {\rm Y}\mathrm{}\left(1S\right)\mathrm{}\pi \pi$. The leading gluonic operators in the multipole expansion are matched onto the chiral Lagrangian with the coefficients fit to available data, both at tree level and loop level in the chiral expansion. A comparison is made with naive expectations loosely based on the large-$N_c$ limit of QCD in an effort to determine the reliability of this limit for other observables, such as the binding of $J/\psi$ to nuclei. Crossing symmetry is used to estimate the cross section for inelastic $\pi J/\overrightarrow{\psi }\pi \psi \mathrm{}\left(2S\right)\mathrm{}$ scattering, potentially relevant for heavy ion collisions. The radiative decays $\psi \mathrm{}\left(2S\right)\mathrm{}\to J/\psi {\pi }^{+}{\pi }^{-}\gamma$ and ${\rm Y}\mathrm{}\left(2S\right)\mathrm{}\to {\rm Y}\mathrm{}\left(1S\right)\mathrm{}{\pi }^{+}{\pi }^{-}\gamma$ are determined at tree level in the chiral Lagrangian. Measurement of such decays will provide a test of the multipole and chiral expansions. We briefly discuss decays from the ${\rm Y}\mathrm{}\left(3S\right)\mathrm{}$ and also the contribution from $\pi$’s to the electromagnetic polarizability of quarkonia.