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Lattice Quantum Chromodynamics close to the light cone
We use near light cone coordinates in order to establish a Wilsonian lattice formulation of Yang-Mills theories which can be extrapolated onto the light cone. Such a formulation is predestinated for the description of non-perturbative high energy physics like structure functions on the lattice. The numerical standard approach of lattice gauge theory namely the Monte Carlo sampling of the Euclidean path integral fails because of a sign problem similar to Quantum Chromodynamics (QCD) at finite baryonic density. However, we can circumvent the sign problem by switching to a Hamiltonian formulation. We develop an effective lattice Hamiltonian describing the dynamics of the pure gauge sector of QCD which is in principle capable of determining ground state expectation values by means of Quantum-Diffusion-Monte Carlo methods. We analytically compute the ground state in the weak and strong coupling limit. These two analytical limits motivate a single plaquette ground state ansatz valid over the whole coupling range which is optimized with respect to the energy by the Ritz variational principle and which can be extrapolated onto the light cone. In addition, we compute the continuum ground state wave functional of the near light cone Hamiltonian in the light cone limit. We develop a method to determine gluon distribution functions of mesons modeled by their valence quark distribution applying the optimized near light cone ground state wave functional in the light cone limit.
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530 Physik
530 Physics