Measurement of the hybrid content of heavy quarkonia using lattice nonrelativistic QCD

Abstract

Using lowest-order lattice nonrelativistic QCD to create heavy meson propagators and applying the spin-dependent interaction, ${c}_{B}(\ensuremath{-}{g/2m}_{q})\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ensuremath{\cdot}\stackrel{\ensuremath{\rightarrow}}{B},$ at varying intermediate time slices, we compute the off-diagonal matrix element of the Hamiltonian for the quarkonium-hybrid two-state system. Thus far, we have results for one set of quenched lattices with an interpolation in quark mass to match the bottomonium spectrum. After diagonalization of the two-state Hamiltonian, we find the ground state of the $\ensuremath{\Upsilon}$ to show a ${0.0035(1)c}_{B}^{2}$ (with ${c}_{B}^{2}\ensuremath{\sim}1.5--3.1)$ probability admixture of hybrid, $|b\overline{b}g〉.$