Cutoff schemes in chiral perturbation theory and the quark mass expansion of the nucleon mass

Abstract

We discuss the use of cutoff methods in chiral perturbation theory. We develop a cutoff scheme based on the operator structure of the effective field theory that allows to suppress high momentum contributions in Goldstone boson loop integrals and by construction is free of the problems traditional cutoff schemes have with gauge invariance or chiral symmetries. As an example, we discuss the chiral expansion of the nucleon mass. Contrary to other claims in the literature we show that the mass of a nucleon in heavy baryon chiral perturbation theory has a well behaved chiral expansion up to effective Goldstone boson masses of 400 MeV when one utilizes standard dimensional regularization techniques. With the help of the here developed cutoff scheme we can demonstrate a well-behaved chiral expansion for the nucleon mass up to 600 MeV of effective Goldstone Boson masses. We also discuss in detail the prize, in numbers of additional short distance operators involved, that has to be paid for this extended range of applicability of chiral perturbation theory with cutoff regularization, which is usually not paid attention to. We also compare the fourth order result for the chiral expansion of the nucleon mass with lattice results and draw some conclusions about chiral extrapolations based on such type of representation.

19 pp, 8 figs

Cited by in corpus (7)

• Chiral extrapolations of baryon masses for unquenched three-flavor lattice simulations
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• Baryon masses, chiral extrapolations, and all that
• Extraction of the pion-nucleon sigma-term from the spectrum of exotic baryons
• Pion mass dependence of the nucleon mass in the chiral quark soliton model
• The chiral limit of QCD and above
• Unification of the physics of nucleons and nuclei