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 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.

11 pp, 2 figs, version accepted for publication in Phys. Lett. B

References in corpus (3)

• Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass
• Baryon masses, chiral extrapolations, and all that
• The chiral limit of QCD and above

Cited by in corpus (25)

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• Towards a theory of hadron resonances
• Light baryon masses with dynamical twisted mass fermions
• Axial coupling constant of the nucleon for two flavours of dynamical quarks in finite and infinite volume
• Nucleon mass: from lattice QCD to the chiral limit
• Delta-excitations and the three-nucleon force
• The lowest-lying baryon masses in covariant SU(3)-flavor chiral perturbation theory
• Chiral Perturbation Theory and the first moments of the Generalized Parton Distriputions in a Nucleon
• The pion mass dependence of the nucleon form-factors of the energy momentum tensor in the chiral quark-soliton model
• The Delta-resonance in a finite volume
• Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions
• Consistency of the $\pi \Delta$ interaction in chiral perturbation theory
• Chiral corrections to the Roper mass
• Hyperon decay form factors in chiral perturbation theory
• Pion mass dependence of the nucleon mass in the chiral quark soliton model
• Four-quark condensates and chiral symmetry restoration in a resonance gas model
• Chiral symmetry and the axial nucleon to Delta(1232) transition form factors
• The mass of the Delta resonance in a finite volume: fourth-order calculation
• Chiral Lagrangians with $\Delta (1232)$ to one loop
• Meson-baryon sigma terms in QCD Sum Rules
• Chiral Analysis of the Nucleon Mass and Sigma Commutator
• Quark Masses: An Environmental Impact Statement