Spin-3/2 nucleon andΔbaryons in lattice QCD

We present the first results for masses of spin-$\frac{3}{2}$ N and $\Delta$ baryons in lattice QCD using fat-link irrelevant clover fermions. Spin-$\frac{3}{2}$ interpolating fields, providing overlap with both spin-$\frac{3}{2}$ and spin-$\frac{1}{2}$ states, are considered. In the isospin-$\frac{1}{2}$ sector we observe, after appropriate spin and parity projection, a strong signal for the $J^P={\frac{3}{2}}^{-}$ state together with a weak but discernible signal for the ${\frac{3}{2}}^{+}$ state with a mass splitting near that observed experimentally. We also find good agreement between the ${\frac{1}{2}}^{\pm }$ masses and earlier nucleon mass simulations with the standard spin-$\frac{1}{2}$ interpolating field. For the isospin-$\frac{3}{2}$ $\Delta$ states, clear mass splittings are observed between the various ${\frac{1}{2}}^{\pm }$ and ${\frac{3}{2}}^{\pm }$ channels, with the calculated level orderings in good agreement with those observed empirically.