Nucleon Excited State Wave Functions from Lattice QCD

Abstract

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. We present a detailed examination of the quark-mass dependence of the probability distributions for these states, searching for a nontrivial role for the multi-particle components mixed in the finite-volume QCD eigenstates. Finally we examine the dependence of the d-quark probability distribution on the positions of the two u quarks. The results are fascinating, with the underlying S-wave orbitals governing the distributions even at rather large u-quark separations.

15 pages, 9 figures. arXiv admin note: text overlap with arXiv:1304.0325

References in corpus (4)

• Lattice QCD determination of patterns of excited baryon states
• A Study of Hadron Deformation in Lattice QCD
• Searching for low-lying multi-particle thresholds in lattice spectroscopy
• Wave Functions of the Proton Ground State in the Presence of a Uniform Background Magnetic Field in Lattice QCD

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