All About the Neutron from Lattice QCD

TL;DR

Lattice QCD simulations using the path integral approach reveal fundamental quantum properties of QCD, providing insights into nucleon structure and related phenomenological quantities despite their stochastic nature.

Contribution

This paper explains how lattice QCD simulations extract quantum properties and observables of nucleons, illustrating the methods with specific examples.

Findings

Determination of nucleon isovector charges.

Quantification of quark intrinsic spin contribution.

Calculation of the pion-nucleon sigma term.

Abstract

I describe how simulations of lattice QCD using the path integral formulation provide the two basic quantum mechanical properties of QCD, its ground state in which correlation functions are calculated, and Fock state wavefunctions between which matrix elements of operators are calculated. Both constructs are stochastic, so unfortunately one gets no intuitive picture or even a qualitative understanding of what they look like, nevertheless they contain and display all the subtleties of the quantum field theory. Today, these simulations provide many quantities that are impacting phenomenology and experiments. I illustrate the methods and the steps in the analysis using, as examples, three observables: the isovector charges of the nucleon, the contribution of the quark's intrinsic spin to the nucleon spin, and the pion-nucleon sigma term.