We present our final results for the excited charmonium spectrum from a quenched calculation using a fully relativistic anisotropic lattice QCD action. A detailed excited charmonium spectrum is obtained, including both the exotic hybrids (with $J^{ PC} = 1^{ -+}, 0^{ +-}, 2^{ +-}$) and orbitally excited mesons (with orbital angular momentum up to 3). Using three different lattice spacings (0.197, 0.131, and 0.092 fm), we perform a continuum extrapolation of the spectrum. We convert our results in lattice units to physical values using lattice scales set by the $^1P_1-1S$ splitting. The lowest lying exotic hybrid $1^{ -+}$ lies at 4.428(41) GeV, slightly above the $D^{ **}D$ (S+P wave) threshold of 4.287 GeV. Another two exotic hybrids $0^{ +-}$ and $2^{ +-}$ are determined to be 4.70(17) GeV and 4.895(88) GeV, respectively. Our finite volume analysis confirms that our lattices are large enough to accommodate all the excited states reported here.
Categories: hep-lat