Hybrid static potentials and properties of heavy hybrid mesons from lattice QCD

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Hybrid mesons have quantum numbers different from quark model quantum numbers. They are states predicted by QCD, where gluons contribute in a non-trivial way. Investigating such exotic mesons is currently a hot topic in experimental and theoretical particle physics. In particular on the theoretical side non-perturbative predictions are necessary, to conclusively interpret the wealth of currently existing and future experimental data.One approach to study hybrid mesons using lattice QCD is to compute hybrid static potentials. Such potentials are defined as the energy of the ground state in a sector with an infinitely heavy quark and an infinitely heavy antiquark, spatially separated and connected by a gluonic flux tube, which realizes the non-trivial quantum numbers. Such systems are quite close to hybrid mesons with heavy valence quarks. We plan to perform modern fully dynamical precision lattice QCD computations of these hybrid static potentials using rather fine lattice spacings, in particular to better resolve the short range part of these potentials.In a second step we will use the obtained hybrid static potentials as non-perturbative input for non-relativistic Schrödinger equations, whose solutions yield predictions for masses and other properties of hybrid mesons. We also plan to explore conceptual improvements regarding these calculations, in particular taking into account the effects of the heavy quark spins, which have always been neglected in the past, even though their contribution is expected to be a significant fraction of the binding energy.