Chiral Extrapolations and the Covariant Small Scale Expansion

TL;DR

This paper uses covariant chiral effective field theory to analyze lattice QCD data, providing insights into nucleon and delta masses, their quark-mass dependence, and the sigma term, with implications for understanding baryon structure.

Contribution

It presents the first quantitative covariant chiral extrapolation of nucleon and delta masses using lattice data, including the delta mass from recent collaborations.

Findings

Consistent chiral extrapolation functions up to large pion masses.

Pion-nucleon sigma term estimated at 48.9 MeV.

Delta mass in the chiral limit slightly larger than at physical point.

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 sigma_{piN} = 48.9 MeV. This first quantitative analysis of the quark-mass dependence of the structure of the Delta(1232) in full QCD within chiral effective field theory suggests that (the real part of) the nucleon-delta mass-splitting in the chiral limit, Delta_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.