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.
Highlights
The success of the quark model, following the realization of the importance of SU(3) flavor symmetry in the context of the eightfold way, led to understanding the properties of a large number of mesons and baryons
We are interested in heavy hybrid mesons, i.e., in mesons composed of heavy c or b quarks, where gluons contribute to the quantum numbers JPC in a nontrivial way
We find that the optimum is Ez 1⁄4 r=a independent of r and Ex, i.e., the z extent of operator SI;1 should be identical to the quark-antiquark separation, when used to compute the ground state hybrid static potential in the Πu sector
Summary
The success of the quark model, following the realization of the importance of SU(3) flavor symmetry in the context of the eightfold way, led to understanding the properties of a large number of mesons and baryons. It is very challenging to understand the internal structure of exotic hadrons, and even though there is little doubt that hybrid mesons and baryons exist, not much else is known about them It is a notable feature of hybrid mesons that, due to their excited gluonic degrees of freedom, part of them have JPC quantum numbers, which are forbidden in the quark model.. This is expected to be a good approximation, because the time scales of the gluons and of the heavy charm or bottom quarks are significantly different and, their dynamics decouples almost completely In this context effective theory approaches like potential nonrelativistic QCD (pNRQCD) are extremely useful, e.g., when parametrizing discrete lattice field theory results for hybrid static potentials by continuous functions (for recent pNRQCD articles on hybrid mesons cf e.g., [7,35,36]) Effective theory approaches like potential nonrelativistic QCD (pNRQCD) are extremely useful, e.g., when parametrizing discrete lattice field theory results for hybrid static potentials by continuous functions (for recent pNRQCD articles on hybrid mesons cf. e.g., [7,35,36])
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