On the Determination of Elastic and Inelastic Nuclear Observables from Lattice QCD

Abstract

One of the overarching goals of nuclear physics is to rigorously compute properties of hadronic systems directly from the fundamental theory of the strong interaction, Quantum Chromodynamics (QCD). Currently, lattice QCD (LQCD) provides the only reliable option for performing calculations of low-energy hadronic observables. LQCD calculations are necessarily performed in a finite Euclidean spacetime. As a result, it is necessary to construct formalism that maps the finite-volume observables determined via LQCD to the infinite-volume quantities of interest. This methodology is commonly referred to as the Luscher method, as it was Martin Luscher who first developed such formalism for scalar bosons with zero total momentum below inelastic thresholds. In this work, we review recent progress on the generalization of this formalism. We present a detailed derivation of the extension of Luscher's seminal work for multi-channel two-body scalar systems, two-nucleon non-relativistic systems, and three-body non-relativistic scalar systems. For all of these scenarios we allow for the total momenta of the systems of interest to be nonzero. We also present steps towards being able to study weak processes involving two-nucleon systems, in particular we show how to determine the transition amplitude for proton-proton fusion (pp->e^+ + nu_e) directly from LQCD.