Towards a high-precision description of resonances through lattice simulations

Abstract

Resonances play a significant role in the phenomenology of the Standard Model. For example, many hadronic resonances are found in flavour-physics processes, which can be central to New Physics searches. The realistic determination of resonance parameters is an important step in the direction of understanding such phenomena. First-principles quantum chromodynamics (QCD) computations using lattice approaches have developed in the last two decades to the point where physical quark masses can now be directly employed. In this context, studying the dynamical properties of QCD, such as scattering amplitudes and resonances, has been challenging, but the development of nite-volume and computational techniques has made it feasible.

In this work, we perform the first calculation of K*(892) and p(770) resonance parameters at physical quark masses with a reliable estimate of systematic uncertainties. This is done on a single domain-wall Nf = 2 + 1 RBC-UKQCD ensemble at the physical point. We begin by describing the phenomenological aspects of the strong interaction and the underlying quantum field theory. The algorithmic aspect of lattice QCD using the Monte Carlo method and the description of angular momentum on a cubic spatial lattice are reviewed. Next, we cover the formal groundwork of finitevolume quantum field theory that allows the extraction of scattering amplitudes from lattice observables.

Determining the low-energy spectra is a key goal of lattice QCD. Using the developed open-source distillation library based on Grid and Hadrons, we compute finite-volume correlators on the physical-point ensemble. We construct a basis of operators to study ππ and Kπ scattering in the relevant channels. This involves using a generalised eigenvalue problem to compute optimised hadronic interpolators and obtain finite-volume energy levels. Finally, the optimised correlator data is used to extract scattering phase shifts and model-averaged p(770) and K*(892) resonance parameters via finite-volume effects.