Formal Developments for Lattice QCD with Applications to Hadronic Systems

TL;DR

This paper presents formal developments and proposals to improve lattice QCD calculations for hadronic systems, focusing on discretization effects, finite-volume methods, boundary conditions, and electromagnetic interactions.

Contribution

It introduces new formal techniques and extensions for lattice QCD, including symmetry recovery, finite-volume methods for complex systems, and boundary condition improvements.

Findings

Enhanced understanding of rotational symmetry recovery with smeared operators.

Extended Luscher method to complex two-nucleon systems.

Proposed boundary condition strategies to optimize deuteron binding energy calculations.

Abstract

Lattice quantum chromodynamics (QCD) will soon become the primary theoretical tool in rigorous studies of single- and multi-hadron sectors of QCD. It is truly ab initio meaning that its only parameters are those of standard model. The result of a lattice QCD calculation corresponds to that of nature only in the limit when the volume of spacetime is taken to infinity and the spacing between discretized points on the lattice is taken to zero. A better understanding of these discretization and volume effects not only provides the connection to the infinite-volume continuum observables, but also leads to optimized calculations that can be performed with available computational resources. This thesis includes various formal developments in this direction, along with proposals for improvements, to be applied to the upcoming lattice QCD studies of nuclear and hadronic systems. Among these developments are i) an analytical investigation of the recovery of rotational symmetry with the use of suitably-formed smeared operators toward the continuum limit, ii) an extension of the Luscher finite-volume method to two-nucleon systems with arbitrary angular momentum, spin, parity and center of mass momentum, iii) the application of such formalism in extracting the scattering parameters of the 3S1-3D1 coupled channels, iv) an investigation of twisted boundary conditions in the single- and two-hadron sectors, with proposals for improving the volume-dependence of the deuteron binding energy upon proper choices of boundary conditions, and v) exploring the volume dependence of the masses of hadrons and light-nuclei due to quantum electrodynamic interactions, including the effects arising from particles' compositeness. The required background as well as a brief status report of the field pertinent to the discussions in this thesis are presented.