We consider the contribution of charmed quarks to vacuum polarization and to $\gamma \gamma$ scattering. In quantum chromodynamics the calculation is reliable for small photon momenta provided that the quark mass $m_c$ is large compared with the scale of the hadronic mass $\mu$, $4{m_c}^2\gg {\mu }^2$. By the use of dispersion relations, the calculation is converted into a set of sum rules which impose model-independent upper bounds on the charmonium leptonic and photonic decay rates and enables one to estimate the hadronic widths as well. Weak leptonic decays of the charmed mesons are also estimated.

• Received 11 January 1977

DOI:https://doi.org/10.1103/PhysRevLett.38.626