We present spectra of highly excited D and Ds mesons up to around 3.8 GeV determined using dynamical lattice QCD. We employ novel computational techniques and the variational method with a large basis of carefully constructed operators in order to ex
tract and reliably identify the continuum spin of an extensive set of excited states. These include states with high spin and states identified as having an explicit gluonic contribution. Calculations were performed on two volumes, both with a pion mass of approximately 400 MeV, achieving a high statistical precision for both ground and excited states. We discuss our results in light of experimental observations, comment on the phenomenological implications and identify the lightest `supermultiplet of hybrid mesons in each sector.
We present a progress report on our study of the charmonium spectrum in full QCD on anisotropic lattices generated by the Hadron Spectrum Collaboration. We adopt a large basis of interpolating operators to extract the excited charmonium states using
the variational method. A detailed spectrum of excited charmonium mesons in many $J^{PC}$ channels is obtained. Hybrid states with exotic and non-exotic quantum numbers are determined and preliminary results from a study of disconnected contributions to the $eta_c$ are presented.
