Strong Isospin Breaking in the Nucleon and Delta Masses on the Lattice

Abstract

Strong isospin breaking in the spectrum of the nucleons and deltas can be studied in lattice QCD with the help of chiral perturbation theory. At leading order in the chiral expansion, the mass splittings between the proton and neutron and between the deltas are linear in the quark mass difference. The next-to-leading order contributions to these splittings vanish even away from the strong-isospin limit. Therefore, any non-linear quark mass dependence of these mass splittings is a signal of the next-to-next-to-leading order mass contributions, thus providing access to LECs at this order. We determine the mass splittings of the nucleons and deltas in two-flavor, heavy baryon chiral perturbation theory to next-to-next-to-leading order. We also derive expressions for the nucleon and delta masses in partially quenched chiral perturbation theory to the same order. The resulting mass expressions will be useful both for the extrapolation of lattice data on baryon masses, and for the study of strong isospin breaking.

24 pages, revised version with slight modifications to text and formulae

References in corpus (13)

• Light hadrons with improved staggered quarks: approaching the continuum limit
• Chiral extrapolations of baryon masses for unquenched three-flavor lattice simulations
• Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass
• Hadronic physics with domain-wall valence and improved staggered sea quarks
• Octet Baryon Masses in Partially Quenched Chiral Perturbation Theory
• Decuplet Baryon Masses in Partially Quenched Chiral Perturbation Theory
• Baryon masses and nucleon sigma terms in manifestly Lorentz-invariant baryon chiral perturbation theory
• In Search of the Chiral Regime
• Baryon Masses in Partially Quenched Heavy Hadron Chiral Perturbation Theory
• Computing Electromagnetic Effects in Fully Unquenched QCD
• The Omega- and the strange quark mass
• The chiral limit of QCD and above
• Light hadrons in 2+1 flavor lattice QCD

Cited by in corpus (36)

• Modern Theory of Nuclear Forces
• FLAG Review 2021
• Roy-Steiner-equation analysis of pion-nucleon scattering
• Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea
• Baryon spectrum with $N_f=2+1+1$ twisted mass fermions
• Strangeness and charmness content of nucleon from overlap fermions on 2+1-flavor domain-wall fermion configurations
• Strong-Isospin Violation in the Neutron-Proton Mass Difference from Fully-Dynamical Lattice QCD and PQQCD
• The low-lying baryon spectrum with two dynamical twisted mass fermions
• Delta-excitations and the three-nucleon force
• Towards grounding nuclear physics in QCD
• Isospin breaking effects due to the up-down mass difference in Lattice QCD
• Nucleon Scalar and Tensor Charges from Lattice QCD with Light Wilson Quarks
• Electromagnetic and spin polarisabilities in lattice QCD
• Baryon mass splittings and strong CP violation in SU(3) Chiral Perturbation Theory
• Two Meson Systems with Ginsparg-Wilson Valence Quarks
• Chiral Extrapolations and the Covariant Small Scale Expansion
• Light stops, blind spots, and isospin violation in the MSSM
• Strange and charm baryon masses with two flavors of dynamical twisted mass fermions
• Hyperons in Two Flavor Chiral Perturbation Theory
• Universality of Mixed Action Extrapolation Formulae
• Scale setting and the light baryon spectrum in $N_f=2+1$ QCD with Wilson fermions
• Taming the Pion Cloud of the Nucleon
• Nucleon resonance parameters from Roy-Steiner equations
• Möbius domain-wall fermions on gradient-flowed dynamical HISQ ensembles
• Hyperon Axial Charges in Two-Flavor Chiral Perturbation Theory
• Flavor Twisted Boundary Conditions and the Nucleon Vector Current
• The mass of the Delta resonance in a finite volume: fourth-order calculation
• Axial couplings in heavy hadron chiral perturbation theory at the next-to-leading order
• Connected Parts of Decuplet Electromagnetic Properties
• Nucleon form factors and parton distributions in nonlocal chiral effective theory
• Effective Field Theory for the Anisotropic Wilson Lattice Action
• New lessons from the nucleon mass, lattice QCD and heavy baryon chiral perturbation theory
• Topics in Effective Field Theory for Lattice QCD
• Topics in Lattice QCD and Effective Field Theory
• Reducing Baryon Noise in Lattice QCD Through Partial Quenching
• Matrix elements of $\Delta B=0$ operators in heavy hadron chiral perturbation theory