Spin effects in heavy hybrid mesons on an anisotropic lattice

We present a quenched calculation of lowest bottomonium hybrid states on an anisotropic lattice with Landau mean-link tadpole improvement, using the improved NRQCD Hamiltonian. We investigate the quark-spin s=0,1 sectors which contain both the non-exotic 1−− and the exotic 1−+, and demonstrate their degeneracy in the case of the lowest order Hamiltonian. Both states are found at around 1.6 GeV above the ϒ ground state. We examine the spin-splitting for several hybrid states (1−−, 1−+, 0−+, 2−+) which is due to the −c1 σ·B/2mb term in the NRQCD Hamiltonian, all other terms having negligible effect. The spin splittings are well resolved outside errors and are surprisingly large. We investigate their dependence on c1 for several values of c1. We calculate one contribution to these splittings using the Born-Oppenheimer picture for hybrids and show that the observed size of the effect is plausibly explained by mixing with hybrid states with more than one constituent gluon.