Nucleon Excited State Wave Functions from Lattice QCD

Understand

We apply the eigenvectors from a variational analysis to successfully extract the wave functions of even-parity excited states of the nucleon, including the Roper.

• We explore the first four states in the spectrum excited by the standard nucleon interpolating field.
• We find that the states exhibit a structure qualitatively consistent with a constituent quark model, where the ground, first-, second- and third-excited states have 0, 1, 2, and 3 nodes in the radial wave function of the d-quark about two $u$ quarks at the origin.
• Moreover the radial amplitude of the probability distribution is similar to that predicted by constituent quark models.