Effective field theory for doubly heavy baryons and lattice QCD

In this thesis, we study effective field theories for doubly heavy baryons and lattice QCD. We construct a chiral Lagrangian for doubly heavy baryons and heavy mesons that is invariant under heavy quark-diquark symmetry at leading order and includes the leading O(1/mQ) symmetry violating operators. The theory is used to predict the electromagnetic decay width of the J = 32 member of the ground state doubly heavy baryon doublet. Numerical estimates are provided for doubly charm baryons. We also calculate chiral corrections to doubly heavy baryon masses and strong decay widths of low lying excited doubly heavy baryons. We derive the couplings of heavy diquarks to weak currents in the limit of heavy quark-diquark symmetry, and construct the chiral Lagrangian for doubly heavy baryons coupled to weak currents. Chiral corrections to doubly heavy baryon zero-recoil semileptonic decay for both unquenched and partially quenched QCD are calculated. This theory is used to derive chiral extrapolation formulae for measurements of the doubly heavy baryon zero-recoil semileptonic decay form factors in lattice QCD simulations. Additionally, we study the pion physics on lattice using chiral perturbation theory. For finite volume field theories with discrete translational invariance, conserved currents can obtain additional corrections from infrared effects. We demonstrate this for pions using chiral perturbation theory coupled to electromagnetism in a periodic box. Gauge invariant single particle effective theories are constructed to explain these results. We use chiral perturbation theory to study the extraction of pion electromagnetic polarizabilities from lattice QCD. Chiral extrapolation formulae are derived for partially quenched and quenched QCD simulations. We determine finite volume corrections to the Compton scattering tensor of pions.