| Description |
The purpose of this dissertation is to provide high-precision lattice quantum chromodynamics (QCD) simulation results for the mass splittings of low-lying charmonium states as the test of the Standard Model, and, further, to study the nature of a higher mass charmonium-like state called X(3872). Since the discovery of charmonium, it has played an important role in the study of QCD. However, it had been impossible to study charmonium energy levels at a low energy regime in QCD perturbative theory due to color connement, which is the consequence of the SU(3) nonabelian gauge theory in QCD. From this point of view, numerical simulation with lattice QCD is a unique method that provides a nonperturbative, ab initio approach for studying hadronic states governed by the strong interactions. In this dissertation, I describe a high-precision study of the splittings of the low-lying charmonium states, particularly the 1S and 1P states, including a chiral-continuum extrapolation. The highly excited charmonium states, discovered in the past decade, are much more challenging to study because their energy levels lie near or above the D^0 D^0 threshold, so they cannot be explained within the conventional quark model. Among those, we are interested in the narrow charmonium-like state, X(3872), due to its closeness to the DD* threshold and its possible four-quark nature. Since the X(3872) mass is within 1 MeV of the DD* threshold, it is a strong candidate for a DD* molecular state. Therefore, we use interpolating operators including both the conventional, excited P-wave charmonium state, Xc1, and the DD* open charm state for the isospin 0 channel. I provide the theoretical background for the lattice calculation and the corresponding methodologies, report on our high-precision results for the mass splittings of low-lying charmonium states, I introduce a new methodology called the \staggered variational method"", which is a variational method applied to the staggered fermion formalism, and nally, I present the simulation results for the X(3872) with quantum numbers J^{PC} = 1^{++} and isospin 0, using lattice QCD, as well as the detailed analysis and our interpretation to reveal the physical nature of X(3872). |
