Power Counting Regime of Chiral Effective Field Theory and Beyond

Abstract

Chiral effective field theory complements numerical simulations of quantum chromodynamics (QCD) on a space-time lattice. It provides a model-independent formalism for connecting lattice simulation results at finite volume and a variety of quark masses to the physical world. The asymptotic nature of the chiral expansion places the focus on the first few terms of the expansion. Thus, knowledge of the power-counting regime (PCR) of chiral effective field theory, where higher-order terms of the expansion may be regarded as negligible, is as important as knowledge of the expansion itself. Through the consideration of a variety of renormalization schemes and associated parameters, techniques to identify the PCR where results are independent of the renormalization scheme are established. The nucleon mass is considered as a benchmark for illustrating this general approach. Because the PCR is small, the numerical simulation results are also examined to search for the possible presence of an intrinsic scale which may be used in a nonperturbative manner to describe lattice simulation results outside of the PCR. Positive results that improve on the current optimistic application of chiral perturbation theory beyond the PCR are reported.

18 pages, 55 figures

References in corpus (7)

• 2+1 Flavor Lattice QCD toward the Physical Point
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• Nucleon sigma term and strange quark content from lattice QCD with exact chiral symmetry
• Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass
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• Parton distributions from nonlocal chiral SU(3) effective theory. I. Splitting functions
• Nucleon resonance structure in the finite volume of lattice QCD
• Regularisation in Nonperturbative Extensions of Effective Field Theory
• Chiral Effective Theory Methods and their Application to the Structure of Hadrons from Lattice QCD
• Finite-volume corrections to charge radii
• Chiral extrapolation beyond the power-counting regime
• Limitations of the heavy-baryon expansion as revealed by a pion-mass dispersion relation
• Chiral Analysis of the Nucleon Mass and Sigma Commutator
• Magnetic Polarisability of Octet Baryons via Lattice QCD
• Flavor symmetry breaking in the $\Delta$ sea
• From QCD phenomenology to nuclear physics phenomenology: the chiral confining model