Searching for the first radial excitation of the Δ(1232) in lattice QCD

We present a lattice QCD analysis of the Δ-baryon spectrum, with the goal of finding the position of the 2 s radial excitation of the Δ(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 π 2 . We identify the lowest lying state as being a 1 s state, consistent with the well known Δ(1232). The first excitation is identified as a 2 s state, but is found to have a mass of approximately 2.15 GeV on our ∼3 fm lattice, which does not appear to be associated with the Δ(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.