Precision computation of hybrid static potentials in SU(3) lattice gauge theory

Abstract

We perform a precision computation of hybrid static potentials with quantum numbers ${\Lambda }_{\eta }^{\epsilon }={\Sigma }_g^{-},{\Sigma }_u^{+},{\Sigma }_u^{-},{\Pi }_g,{\Pi }_u,{\Delta }_g,{\Delta }_u$ using SU(3) lattice gauge theory. The resulting potentials are used to estimate masses of heavy $\bar{c}c$ and $\bar{b}b$ hybrid mesons in the Born-Oppenheimer approximation. Part of the lattice gauge theory computation, which we discuss in detail, is an extensive optimization of hybrid static potential creation operators. The resulting optimized operators are expected to be essential for future projects concerning the computation of 3-point functions as e.g. needed to study spin corrections, decays or the gluon distribution of heavy hybrid mesons.

41 pages, 10 figures, 9 tables, corrected a typo, corrected spelling, reorganized introduction, added minor clarifications in sections 2.1, 3, 4.1, 4.3 and 5, corrected formulas in tables 1-7 ($S=\cdots \to USU=\dots$)

References in corpus (16)

• Non-Standard Heavy Mesons and Baryons, an Experimental Review
• On the generalized eigenvalue method for energies and matrix elements in lattice field theory
• Hybrid Mesons
• Nonperturbative determination of the QCD potential at O(1/m)
• Spin-dependent potentials from lattice QCD
• The Born-Oppenheimer approximation in an effective field theory language
• Spin structure of heavy-quark hybrids
• The static-light meson spectrum from twisted mass lattice QCD
• Colour field densities of the quark-antiquark excited flux tubes in SU(3) lattice QCD
• Determination of ${\Lambda }_{\overline{\text{MS}}}^{(n_f=2)}$ and analytic parameterization of the static quark-antiquark potential
• Relativistic corrections to the static potential at O(1/m) and O(1/m^2)
• Lattice study of hybrid static potentials
• Hybrid Mesons from the Lattice
• Colour fields of the quark-antiquark excited flux tube
• Computation of hybrid static potentials in SU(3) lattice gauge theory
• Structure of hybrid static potential flux tubes in SU(2) lattice Yang-Mills theory

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