格點量子色動力學: Domain-Wall 夸克之探討

Abstract

Quantum Chromodynamics (QCD) is the fundamental theory for the interaction between quarks and gluons. It manifests as the short-range strong interaction inside the nucleus, and plays an important role in the evolution of the early universe, from the quark-gluon phase to the hadron phase. To solve QCD is a grand challenge, since it requires very large-scale numerical simulations of the discretized action of QCD on the 4-dimensional space-time lattice. Moreover, since quarks are relativistic fermions, the 5-th dimension is introduced such that massless quarks with exact chiral symmetry can be realized at finite lattice spacing, on the boundaries of the 5-th dimension, the so-called domain-wall fermion (DWF). In this thesis, we discuss the formulation of lattice QCD with exact chiral symmetry, and the algorithms to perform Monte Carlo simulation of QCD with dynamical u, d, s, and c quarks. We also derive the axial Ward identity for lattice QCD with domain-wall fermion, and from which we obtain a formula for the residual mass, that can be used to measure the chiral symmetry breaking due to the finite extension $ N_s $ in the fifth dimension. Furthermore, we obtain an upper bound for the residual mass in lattice QCD with the optimal domain-wall fermion.