Properties of charmonium and bottomonium from lattice QCD with very fine lattices

Lattice methods are essential theoretical tools for performing calculations in quantum chromodynamics (QCD). To make theoretical predictions (or postdictions) of properties of hadrons, we must solve the theory of QCD which describes their constituent quarks — and conversely, to further our knowledge of quarks, which are fundamental constituents of matter, we must examine the properties of their hadronic bound states, since free quarks are not observed due to the phenomenon known as quark confinement. It is not possible to solve QCD analytically, and so we must turn to numerical methods such as lattice QCD. Despite being a well-established and mature formalism, lattice QCD has only really come into fruition over the last decade or so, developing in parallel with the advent of high-performance computing facilities. The available computing power is now sufficient to perform calculations on very fine lattices, with lattice spacings of about 0.06fm or less. These are beneficial for two reasons: firstly, they are closer to the continuum limit, meaning that continuum extrapolations are better controlled; and secondly, it is only on finer and finer lattices that we are able to accurately simulate heavier and heavier quarks, such as charm and bottom. We use very fine lattices from the MILC collaboration to determine multiple properties of heavyonium systems, in each case using the HISQ action for heavy valence quarks. Correlator fitting, and continuum and chiral extrapolations, are performed via Bayesian least-squares fitting methods. The first calculation simulates charmonium via charm quarks at their physical mass, as well as bottomonium, via multiple intermediate heavy quark masses and an extrapolation in this heavy mass. Notably, this is a fully relativistic method of calculating the bottom quark, and is complementary to effective-action methods such as NRQCD. We perform this calculation on gauge configurations with 2+1 flavours of quarks in the sea, and are able to accurately determine properties of the ground-state pseudoscalar and vector mesons in each system, including their decay constants, the hyperfine mass splitting, and the temporal moments of the vector correlators — which we also make use of to renormalise the vector current. To fully investigate some small anomalies in some of the vector results, we also repeat a subset of these calculations using a one-link instead of a local vector current. The second calculation represents an in-depth study of charmonium, including radial and orbital excitations as well as the ground states. We again simulate charm quarks at their physical mass, but this time on gauge configurations with 2+1+1 flavours of quarks in the sea, including those with light sea quarks at their physical masses. We also include a set of well-constructed smearing functions designed to increase the overlap of our correlators with the ground state, and therefore allow us to extract data on charmonium excited states more accurately. Specifically, we concentrate on conventional low-lying excited states in the charmonium system, and accurately extract various mass splittings in the spectrum (including the 1S hyperfine splitting, and the spin-averaged 2S − 1S splitting) as well as temporal moments of the vector correlator (which we again utilise in a renormalisation procedure), and decay constants of the ground-state pseudoscalar and vector. We also use the calculated mass splittings to accurately reconstruct a selected portion of the charmonium spectrum. This is the first time that we have used smeared operators with staggered quarks for this purpose, and so this calculation acts as a strong base upon which to build future work on excited states.