Exotic hadrons with heavy quark and antiquark in lattice QCDŠadl, Mitja (Avtor) Prelovšek, Saša (Mentor) quantum chromodynamics on the latticehadron spectroscopyhadronexotic mesontetraquarkmeson moleculeheavy quarksresonancescatteringIn the past two decades, experiments have revealed a rich hadronic spectrum, including exotic states that cannot be easily explained by the quark model. Studying these states requires non-perturbative methods. In this thesis, we employ lattice QCD, the only reliable first-principles approach for examining the non-perturbative aspects of QCD. We perform two lattice studies of exotic hadrons with a heavy $\bar{Q}Q$ pair, specifically charmonium-like ($\bar cc \bar qq$) and bottomonium-like ($\bar bb \bar qq$) tetraquarks with $I=1$, where numerous decay channels pose the biggest challenge. The most notable examples of these tetraquarks observed in experiments are the $Z_c$ ($\bar cc \bar qq$) and $Z_b$ ($\bar bb \bar qq$) states. In the study of charmonium-like states, we extract finite-volume spectra for states with $J^{PC}=1^{+\pm}$. This is the first simulation of these channels employing more than one volume and frames with nonzero total momentum. The resulting eigenenergies are compatible or just slightly shifted down with respect to non-interacting meson-meson energies. We extract the scattering amplitudes for $1^{+\pm}$, where both channels contain a virtual pole slightly below the threshold if $D\bar D^*$ is assumed to be decoupled from other channels. We also perform a coupled channel analysis of $J/\psi \pi$ and $D\bar D^*$ scattering with $1^{+-}$ within an effective field theory framework. The $J/\psi \pi$ and $D\bar D^*$ line shapes and eigenenergies from several lattice QCD simulations, including ours, are fitted simultaneously. Our findings suggest that the employed effective field theory can reasonably reconcile the peaks in the experimental line shapes and the lattice energies, although those lie close to non-interacting energies. The lattice study of the $\bar bb\bar qq$ systems employs static bottom quarks. Previous studies reveal that the potential between $B$ and $\bar{B}^*$ in the channel that couples to $\Upsilon\pi$ is very attractive. Our simulation considers three complementary channels for the first time. Spectra of the $\bar bb \bar qq$ system are extracted as a function of separation between $b$ and $\bar b$. The eigenenergies do not show sizable deviation from the $\bar bb+\bar qq$ and $\bar bq+\bar qb$ non-interacting energies. The resulting $B\bar{B}^*$ potential related to the channel coupled to $\eta_b\rho$ is not attractive, except slightly at small separation. The two mentioned potentials suggest that the linear combination of both may cause the existence of $Z_b$.20242024-09-28 08:15:12Doktorsko delo/naloga162860sl