Spin effects in heavy hybrid mesons on an anisotropic lattice

Abstract 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 −c 1 σ · B /2m b 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 c 1 for several values of c 1 . 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.