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.

arXiv comment11 pp, 2 figs, version accepted for publication in Phys. Lett. B

References in corpus (25)

• Chiral Dynamics in Nucleons and Nuclei
• The QCD spectrum with three quark flavors
• The 1/N Expansion for Baryons
• Renormalization of relativistic baryon chiral perturbation theory and power counting
• Heavy Baryon Chiral Perturbation Theory with Light Deltas
• Aspects of chiral pion-nucleon physics
• Light Hadron Spectroscopy with Two Flavors of Dynamical Quarks on the Lattice
• The chiral effective pion-nucleon Lagrangian of order p^4
• Effective theory of the Delta(1232) in Compton scattering off the nucleon
• The form factors of the nucleon at small momentum transfer
• Pion-nucleon scattering inside the Mandelstam triangle
• The nucleon mass in N_f=2 lattice QCD: finite size effects from chiral perturbation theory
• Chiral Analysis of Quenched Baryon Masses
• Light hadron spectroscopy with two flavors of $O(a)$-improved dynamical quarks
• Nucleon mass, sigma term and lattice QCD
• Pion-nucleon scattering in an effective chiral field theory with explicit spin-3/2 fields
• Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass
• Infrared regularization of baryon chiral perturbation theory reformulated
• Infrared regularization with spin-3/2 fields
• Strong Isospin Breaking in the Nucleon and Delta Masses on the Lattice
• Baryon masses, chiral extrapolations, and all that
• Chiral QCD: Baryon dynamics
• The chiral limit of QCD and above
• Baryon Mass Extrapolation
• Chiral Effective Field Theories with explicit Spin 3/2 Degrees of Freedom---A Status Report

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• Baryon spectrum with $N_f=2+1+1$ twisted mass fermions
• 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
• Including the $\Delta (1232)$ resonance in baryon chiral perturbation theory
• Nucleon mass: from lattice QCD to the chiral limit
• The low-lying baryon spectrum with two dynamical twisted mass fermions
• Delta-excitations and the three-nucleon force
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• Schwinger functions and light-quark bound states, and sigma terms
• Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions
• Three-nucleon force in chiral EFT with explicit $\Delta (1232)$ degrees of freedom: Longest-range contributions at fourth order
• Consistency of the $\pi \Delta$ interaction in chiral perturbation theory
• Chiral corrections to the Roper mass
• Hyperon decay form factors in chiral perturbation theory
• Finite-volume effects on octet-baryon masses in covariant baryon chiral perturbation theory
• Baryon Masses and Axial Couplings in the Combined 1/Nc and Chiral Expansions
• Decuplet baryon masses in covariant baryon chiral perturbation theory
• Virtual decuplet effects on octet baryon masses in covariant baryon chiral perturbation theory
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• Baryon transition form factors at the pole
• The $\Delta (1232)$ axial charge and form factors from lattice QCD
• Chiral Lagrangians with $\Delta (1232)$ to one loop
• Baryon Chiral Perturbation Theory combined with the $1/{\mathbf{N}}_{\mathbf{c}}$ Expansion in SU(3) I: Framework
• Meson-baryon sigma terms in QCD Sum Rules
• Quark mass dependence of nucleon mass and axial-vector coupling constant
• Chiral Analysis of the Nucleon Mass and Sigma Commutator
• Mass and width of the $\Delta (1232)$ resonance using complex-mass renormalization
• Quark Masses: An Environmental Impact Statement
• Lowest-lying octet baryon masses in covariant baryon chiral perturbation theory