Quarkonium chromo-polarizability from the decays $J/\psi(\Upsilon) \to \pi \pi \ell^+ \ell^-$

Abstract

It is pointed out that the diagonal amplitude of the $E1-E1$ chromo-electric interaction with soft gluon fields (chromo-polarizability) can be measured directly for the $J/\psi$ and $\Upsilon$ resonances in the decays $J/\psi \to \pi \pi \ell^+ \ell^-$ and $\Upsilon \to \pi \pi \ell^+ \ell^-$ with soft pions. For the $J/\psi$ this amplitude is often discussed in connection with the $J/\psi$ interaction with nuclear matter, while for the $\Upsilon$ the chromo-polarizability enters the estimates of the non-perturbative mass shift of the resonance relevant to precision determination of the $b$ quark mass from the $\Upsilon$ mass.