Chiral perturbation theory on the lattice and its applications

Abstract

Chiral perturbation theory (chiPT), the low-energy effective theory of QCD, can be used to describe QCD observables in the low-energy region in a model-independent way. At any given order in the chiral expansion, chiPT introduces a finite number of parameters that encode the short-distance physics and that must be determined from experiment or numerical lattice QCD simulations. In this thesis, we calculate a number of hadronic observables in the quenched and partially quenched versions of chiPT:Chiral corrections to B(*) → D(*) at zero recoil are investigated in quenched chiPT. We study in detail the charge radii of the meson and baryon octets, electromagnetic properties of the baryon decuplet, and the baryon decuplet to octet electromagnetic transitions in both, quenched and partially quenched chiPT. We further show how effects due to the finite size of the lattice can be accounted for in heavy meson PT and calculate, as explicit examples, neutral B meson mixing and the heavy-light meson decay constants. We also demonstrate how one can account for effects due to finite lattice spacing in the low-energy theories, considering as an example electromagnetic meson and baryon properties.The results of our calculations are crucial to extrapolate quenched and partially quenched lattice data from the heavier light quark masses used on the lattice to the physical values.