The nucleon and Delta-resonance masses in relativistic chiral effective-field theory

Abstract

We study the chiral behavior of the nucleon and $\Delta$-isobar masses within a manifestly covariant chiral effective-field theory, consistent with the analyticity principle. We compute the $\pi N$ and $\pi \Delta$ one-loop contributions to the mass and field-renormalization constant, and find that they can be described in terms of universal relativistic loop functions, multiplied by appropriate spin, isospin and coupling constants. We show that these relativistic one-loop corrections, when properly renormalized, obey the chiral power-counting and vanish in the chiral limit. The results including only the $\pi N$-loop corrections compare favorably with the lattice QCD data for the pion-mass dependence of the nucleon and $\Delta$ masses, while inclusion of the $\pi \Delta$ loops tends to spoil this agreement.

13 pages, 3 figs, 2 tables

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• Light baryon masses with dynamical twisted mass fermions
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• Spin 3/2 Beyond the Rarita-Schwinger Framework
• On the quark-mass dependence of the baryon ground-state masses
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• Delta-baryon mass in a covariant Faddeev approach
• Consistency of the $\pi \Delta$ interaction in chiral perturbation theory
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• Large-N_c operator analysis of 2-body meson-baryon counterterms in the chiral Lagrangian
• The electromagnetic form factors of the transition from the spin-3/2 Sigma to the Lambda hyperon
• The mass of the Delta resonance in a finite volume: fourth-order calculation
• Isospin splittings in the decuplet baryon spectrum from dynamical QCD+QED
• New low-$Q^2$ measurements of the ${\gamma }^{\ast }N\to \Delta (1232)$ Coulomb quadrupole form factor, pion cloud parametrizations and Siegert's theorem
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• Mass and width of the $\Delta (1232)$ resonance using complex-mass renormalization
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• Quartet of spin-3/2 baryons in chiral multiplet $(1,1/2)\oplus (1/2,1)$ with mirror assignment
• Chiral perturbation theory study of the axial $N\to \Delta (1232)$ transition
• Background field approach to electromagnetic properties of baryons
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