Applications of chiral perturbation theory to lattice QCD.

摘要

Quantum chromodynamics (QCD) is the fundamental theory that describes the interaction of quarks and gluons. Thus, in principle, one should be able to calculate all properties of hadrons from the QCD Lagrangian. It turns out, however, that such calculations can only be performed numerically on a computer using the nonperturbative method of lattice QCD, in which QCD is simulated on a discrete spacetime grid. Because lattice simulations use unphysically heavy quark masses (for computational reasons), lattice results must be connected to the real world using expressions calculated in chiral perturbation theory (chiPT), the low-energy effective theory of QCD. Moreover, because real spacetime is continuous, they must be extrapolated to the continuum using an extension of chiPT that includes lattice discretization effects, such as staggered chiPT.; This thesis is organized as follows. We motivate the need for lattice QCD and present the basic methodology in Chapter 1. We describe a common approximation made in lattice simulations---partial quenching---and a successful method of discretizing the quarks used in simulations---staggering. We discuss the principles of effective field theory at the beginning of Chapter 2, and use them to derive the Lagrangian of chiPT. We then show how chiPT can be used, together with lattice data, to calculate quantities such as meson masses and decay constants from QCD first principles.; The body of this thesis focuses on the formulation of chiPT necessary for both partially quenched and staggered lattice simulations. In Chapter 3 we prove the existence of new operators in the partially quenched chiral Lagrangian. We derive their form, and explicitly show how they affect meson masses and decay constants. In Chapter 4 we derive the next-to-leading order staggered chiral Lagrangian. We use it to make predictions that test the validity of the staggered " Det4 trick". In Chapter 5, we calculate the kaon B-parameter, BK, to next-to-leading order in staggered chiPT. The value of BK places an important constraint on the apex of the CKM unitarity triangle, and thus on physics beyond the Standard Model. Finally, we summarize our results and their potential impact for current lattice simulations in Chapter 6.