N* Spectroscopy from Lattice QCD: The Roper Explained

TL;DR

This review discusses recent lattice QCD studies of nucleon excitations, focusing on the Roper resonance, highlighting methodological advances, emerging consensus, and insights from wave functions and form factors.

Contribution

It synthesizes recent progress in lattice QCD calculations of nucleon excitations, clarifies the nature of the Roper resonance, and discusses effective field theory approaches in finite volume.

Findings

Consensus on low-lying spectrum among lattice groups

Wave functions and form factors shed light on state structures

Finite volume methods help interpret lattice results

Abstract

This brief review focuses on the low-lying even- and odd-parity excitations of the nucleon obtained in recent lattice QCD calculations. Commencing with a survey of the 2014-15 literature we'll see that results for the first even-parity excitation energy can differ by as much as 1 GeV, a rather unsatisfactory situation. Following a brief review of the methods used to isolate excitations of the nucleon in lattice QCD, and drawing on recent advances, we'll see how a consensus on the low-lying spectrum has emerged among many different lattice groups. To provide insight into the nature of these states we'll review the wave functions and electromagnetic form factors that are available for a few of these states. Consistent with the Luscher formalism for extracting phase shifts from finite volume spectra, the Hamiltonian approach to effective field theory in finite volume can provide guidance on the manner in which physical quantities manifest themselves in the finite volume of the lattice. With this insight, we will address the question; Have we seen the Roper in lattice QCD?