Chiral extrapolations and the covariant small scale expansion
Abstract We calculate the nucleon and the delta mass to fourth order in a covariant formulation of the small scale expansion. We analyze lattice data from the MILC Collaboration and demonstrate that the available lattice data combined with our knowledge of the physical values for the nucleon and delta masses lead to consistent chiral extrapolation functions for both observables up to fairly large pion masses. This holds in particular for very recent data on the delta mass from the QCDSF Collaboration. The resulting pion–nucleon sigma term is σ π N = 48.9 MeV . This first quantitative analysis of the quark-mass dependence of the structure of the Δ ( 1232 ) in full QCD within chiral effective field theory suggests that (the real part of) the nucleon–delta mass-splitting in the chiral limit, Δ 0 = 0.33 GeV , is slightly larger than at the physical point. Further analysis of simultaneous fits to nucleon and delta lattice data are needed for a precision determination of the properties of the first excited state of the nucleon.