Nucleon excited state wave functions from lattice QCD

Abstract

We apply the eigenvectors from a variational analysis to successfully extract the three-quark color-singlet wave functions of even-parity excited states of the nucleon. 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 multiparticle 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.