Excited nucleons with chirally improved fermions

Abstract

We study positive and negative parity nucleons on the lattice using the chirally improved lattice Dirac operator. Our analysis is based on a set of three operators chi_i with the nucleon quantum numbers but in different representations of the chiral group and with different diquark content. We use a variational method to separate ground state and excited states and determine the mixing coefficients for the optimal nucleon operators in terms of the chi_i. We clearly identify the negative parity resonances N(1535) and N(1650) and their masses agree well with experimental data. The mass of the observed excited positive parity state is too high to be interpreted as the Roper state. Our results for the mixing coefficients indicate that chiral symmetry is important for N(1535) and N(1650) states. We confront our data for the mixing coefficients with quark models and provide insights into the physics of the nucleon system and the nature of strong decays.Comment: Tables added, small modifications in the tex

Spatially improved operators for excited hadrons on the lattice

“…Certainly it is easy to construct a profile function which is a color singlet, but since we are interested in visualizing the sources s (α,a) individually for all a = 1, 2, 3, we use the form Eq. (4).…”

“…While the coupling of the operator χ 1 to both the nucleon and the lowest negative parity state has been reliably established, the operator χ 2 couples neither to the nucleon, nor to the Roper state. For a detailed study of this issue and for an interpretation of this fact see [4]. Hence a remaining possibility to see the Roper state is to use χ 1 and try to separate the strong signal of the ground state (the nucleon) from the weak signal of the radial excited state (the Roper state, if indeed the Roper state is a 3-quark state) at small Euclidean time.…”

“…Previous attempts to study these issues on the lattice [1] - [4] have mainly used the two interpolating fields, χ 1 and χ 2 ,…”

“…Therefore it is advantageous to optimize the spatial properties of the interpolating operators. An example for this fact is the mentioned Roper state where the variational method based on nucleon operators that differ only in their diquark content but have the same spatial wave function did not lead to success [4]. It can be argued that a node in the radial wave function is necessary to capture reliably the Roper state or other radially excited hadrons.…”

“…A prominent example for such a system is the nucleon and its excited states. In particular the first excited positive parity nucleon, the so-called Roper state, has seen a lot of attention from the lattice community during the last two years [1] - [4]. Revealing the true nature of the Roper state with non-perturbative methods is an important task.…”