Light-by-light forward scattering sum rules for charmonium states

Abstract

We apply three forward light-by-light scattering sum rules to charmonium states. We show that these sum rules imply a cancellation between charmonium bound state contributions, which are mostly known from the $\gamma \gamma$ decay widths of these states, and continuum contributions above $D\bar{D}$ threshold, for which we provide a duality estimate. We also show that two of these sum rules allow to predict the yet unmeasured ${\gamma }^{\ast }\gamma$ coupling of the ${\chi }_{c1}(1P)$ state, which can be tested at present high-luminosity $e^{+}{e}^{-}$ colliders.

Comments: 9 pages, 2 figures