Scattering of particles with spin in lattice QCDSkerbiš, Urša (Avtor) Prelovšek, Saša (Mentor) LQCDhadronsspectroscopyscattering with spinelastic scatteringoperatorspentaquarkQuantum chromodynamics (QCD) is an area of particle physics investigating strong interaction and its phenomena. Perturbative QCD works very well at energies above 1 GeV. At energies below 1 GeV $\alpha_s$ is not much smaller than one and one cannot use perturbative treatment. In this energy region, a nonperturbative approach, including Lattice quantum chromodynamics (Lattice QCD), should be used. Most of the hadrons are hadronic resonances, and they can decay under strong interaction. Strong decays of the resonances can be studied through the scattering of hadrons on the lattice. Recent experiments have discovered multiple hadronic resonances with exotic quark structures - tetraquarks and pentaquarks. The scattering of hadrons and hadron spectroscopy is an area of Lattice QCD that we explore in this thesis. Hadronic resonances can decay into pairs of hadrons with or without spin. In order to study a scattering of two hadrons with spin one needs operators that create/annihilate two particles with spin in the desired quantum channel. Two hadron operators are used to extract the eigenenergies of the lattice. We construct operators for simulating the scattering of two hadrons with spin on the lattice. Three methods are shown to give consistent operators. Explicit expressions for operators are given for all irreducible representations. The total momentum of two hadrons is restricted to zero, since parity is a good quantum number in this case. We review the derivation of the relation between the scattering amplitude for twohadron scattering and eigenenergies from the lattice simulation originally proposed by Lüscher. The Lüscher relation is derived for the scattering of particles without spin from the point of view of QFT. Relation is later generalized for the system with nonzero spin. We predict eigenenergies for the scattering of the nucleon and $J/\psi$ meson if experimental $P_c$ resonance is coupled only to this channel. We perform the Lattice QCD simulation of $NJ/\psi$ and $N\eta_c$ scattering at $m_{\pi} \approx$266MeV in channels with all possible $J^P$. This presents the frst simulation at 4,1 - 4,5 GeV energies where pentaquarks reside. We explore the fate of $P_c$ in the one-channel approximation. The energies of eigenstates are extracted for the nucleon-charmonium system at zero total momentum for all quantum numbers, i.e. six lattice irreducible representations. No significant energy shifts are observed. The number of observed lattice eigenstates agrees with the number of states expected for noninteracting charmonium and nucleon. Our lattice data suggest that the hidden charm pentaquark $P_c$ is not coupled only to one channel (the $J/\psi$N or $\eta_cN$), but is probably a consequence of coupled channels effects or significant interaction in other channels (i.e. charmed meson and charmed baryon).20212021-05-11 11:48:17Doktorsko delo/naloga126934sl