Hadron-Hadron Interactions from <em>N_f = 2+1+1</em> Lattice QCD

Abstract

In this work the calculation of the <em>ρ</em> resonance's decay parameters with <em>N_f = 2+1+1</em> flavour lattice QCD is presented. The calculation is performed based on gauge configuration ensembles produced by the ETM collaboration which were generated with three different lattice spacing values and pion masses ranging from <em>230</em> MeV to <em>500</em> MeV. The calculation of resonance parameters with Lattice QCD requires correlation functions of all relevant decay channels in multiple moving reference frames. In this work operators resembling a <em>ρ</em> meson as well as a p⁺p system are used. The boost to moving frames breaks rotational symmetry and thereby causes a level splitting. Operators which transform like basis states of the reduced symmetry groups' irreducible representations are constructed to determine each energy level individually. Aided by the stochastic Laplacian Heaviside method correlation functions are calculated for all lattice momenta up to <em>(0, 0, 2)</em> and all irreducible representations that emerge. <br /> From these correlation functions energy levels are determined under consideration of systematic error sources. Most notably the effect of thermal pollutions and bias from fit range selection are taken into account. By applying the Lüscher method the energy spectra are translated into phase shift curves on each ensemble separately. From a Breit-Wigner fit to the phase shift curves the <em>ρ</em> meson mass and width on all ensembles are determined. The results are fed into a combined fit of mass and width and extrapolated to the chiral and continuum limit. <br /> The main result of this thesis are the continuum extrapolated values of <em>M_ρ</em> and <em>Γ_ρ</em> at the physical point which were determined to <center> <em>M_ρ = 769(19)</em> MeV and <em>Γ_ρ = 129(7)</em> MeV. </center> <br /> Lattice artefacts could not be resolved within the statistical uncertainties of this work. While the <em>ρ</em> meson mass is in very good agreement with experiment the corresponding decay width differs by about two standard deviations from its experimental counterpart.