Abstract
First principles calculations of the form factors of baryon excitations are now becoming accessible through advances in Lattice QCD techniques. In this paper, we explore the utility of the parity-expanded variational analysis (PEVA) technique in calculating the Sachs electromagnetic form factors for excitations of the proton and neutron. We study the two lowest-lying odd-parity excitations and demonstrate that at heavier quark masses, these states are dominated by behaviour consistent with constituent quark models for the $N^*(1535)$ and $N^*(1650)$, respectively. We also study the lowest-lying localised even-parity excitation, and find that its form factors are consistent with a radial excitation of the ground state nucleon. A comparison of the results from the PEVA technique with those from a conventional variational analysis exposes the necessity of the PEVA approach in baryon excited-state studies.
Highlights
Investigating the structure of hadronic excited states is recognized as an important frontier in the field of nonperturbative QCD
The intriguing question is, how does the quantum field theory of QCD construct these states and how does this composition compare with the expectations of current models? Can something as simple as a constituent quark model capture the essence of these states? What role do meson-baryon dressings play in describing these states? Our aim is to address these most fundamental questions by examining the electromagnetic structure of nucleon excited states as observed in lattice QCD
In this paper we presented the first calculations of the elastic form factors of lattice nucleon excitations from the first principles of QCD
Summary
Our aim is to address these most fundamental questions by examining the electromagnetic structure of nucleon excited states as observed in lattice QCD. The results are fascinating, validating quark-model predictions in some cases and demanding a more important role for meson-baryon interactions in others. While experimental measurements of resonance transition amplitudes have been made, it is much harder to measure elastic form factors in the resonance regime. We can probe a stable target such as a ground-state proton and measure how it is excited into the unstable resonance of interest through an examination of its decay products. The difficulty of measuring such quantities experimentally provides the opportunity for lattice QCD to lead experiment and create new knowledge
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