Searching for the first radial excitation of the $\Delta (1232)$ in lattice QCD

Abstract

We present a lattice QCD analysis of the $\Delta$-baryon spectrum, with the goal of finding the position of the $2s$ radial excitation of the $\Delta (1232)$ ground state. Using smeared three-quark operators in a correlation matrix analysis, we report masses for the ground, first and second excited states of the $J^P=3/2^{+}$ spectrum across a broad range of $m_{\pi }^2$. We identify the lowest lying state as being a $1s$ state, consistent with the well known $\Delta (1232)$. The first excitation is identified as a $2s$ state, but is found to have a mass of approximately 2.15~GeV on our $\sim 3$ fm lattice, which does not appear to be associated with the $\Delta (1600)$ resonance in a significant manner. We also report on the spin-$1/2$ and odd-parity states accessible via our methods. The large excitation energies of the radial excitations provide a potential resolution to the long-standing missing baryon resonances problem.

Comments: 16 pages, 9 figures