Study Of Spin-dependent Masses And Configuration Mixings In Heavy Quarkonia And Hybrids Using Lattice Nonrelativistic Quantum Chromodynamics

While we may know the overall quantum numbers of a given meson state and that such a state is necessarily a color singlet, we do not know a priori the relative spin and color alignments of the constituents: the quarks, antiquarks, and gluons. The overall meson wavefunction may have contributions from different spin- color configurations: one where the quark and antiquark alone account for the spin of the meson; or another where a gluon excitation also contributes to the total spin (a hybrid state), while helping to form the color singlet. The determination of the relative contributions of each these configurations to the overall meson state is the focus of this work. We use the lattice formulation of quantum chromodynamics (QCD) and we restrict our analysis to the limit of heavy quark masses. We are therefore able to use a non- relativistic approximation for the quark and antiquark Hamiltonians (NRQCD). This provides the additional separation of the spin- and orbital-angular-momentum degrees of freedom of the quarks. We therefore have a clear separation of basis states where the meson spin is carried by only the quark and antiquark spins, their relative orbital motion, or a combination of the two; and also the state where a gluon excitation is needed, along with the quark and antiquark, to form the correct quantum numbers. Using only the static and kinetic terms of the heavy-quark Hamiltonian we create meson-like correlators with the same quantum numbers, but with different color- spin configurations. From these correlators we extract the masses and amplitudes which form the basis of a two- state system. We then apply the lowest-order spin- dependent interaction at various intermediate time slices to form correlators between different configurations. From these “mixed” correlators we extract the off-diagonal matrix elements of our two-state Hamiltonian. Diagonalizing this Hamiltonian, we find the relative contribution of each spin-color configuration to the true heavy-meson ground state