Date Awarded


Document Type


Degree Name

Doctor of Philosophy (Ph.D.)




David Richards


The work presented here is devoted to the calculations of the decay constants of the pion and its excited states. All calculations were carried out in the framework of lattice quantum chromodynamics, a well-established formalism of strong interactions enabling the ab initio solution of the theory. After a short introduction and review of the fundamental approaches and methods commonly used in lattice QCD, I provide a detail description of the numerical simulations which were performed at three values of the pion mass between 400 and 700 MeV, using an anisotropic clover fermion action with three flavors of quarks. The results obtained indicate that the decay constant of the first excitation, and more notably of the second, is suppressed with respect to that of the ground-state pion, but that the suppression shows little dependence on the quark mass. The second part of this thesis is focused on applications of the methods of perturbation theory to lattice QCD. Here, I give some motivation, and describe the main techniques of perturbative calculations on the lattice, emphasizing its distinctions from the continuum counterpart. I then employ the same anisotropic clover action that was used in numerical study for derivation of lattice Feynman rules which might be used for the calculations of the renormalization parameters helping to connect bare lattice results with real physics.



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