Abstract
We discuss the systematics of power counting in general effective field theories, focusing on those that are nonrenormalizable at leading order. As an illuminating example we consider chiral perturbation theory gauged under the electromagnetic U(1) symmetry. This theory describes the low-energy interactions of the octet of pseudo-Goldstone bosons in QCD with photons and has been discussed extensively in the literature. Peculiarities of the standard approach are pointed out and it is shown how these are resolved within our scheme. The presentation follows closely our recent discussion of power counting for the electroweak chiral Lagrangian. The systematics of the latter is reviewed and shown to be consistent with the concept of chiral dimensions. The results imply that naive dimensional analysis (NDA) is incomplete in general effective field theories, while still reproducing the correct counting in special cases.
Highlights
Effective field theories (EFTs) are the most efficient way of describing physics at a certain energy scale, provided there is a mass gap and the dynamical field content as well as the symmetries at that scale are known
What makes EFTs especially useful is that the operators one can build out of the fields can be organized according to their importance in a systematic expansion
In weakly-coupled scenarios the power counting reduces to a dimensional expansion, where fields have canonical dimensions and higher-dimension operators are weighted with inverse powers of a cutoff scale Λ, whose value indicates the scale of new physics
Summary
Effective field theories (EFTs) are the most efficient way of describing physics at a certain energy scale, provided there is a mass gap and the dynamical field content as well as the symmetries at that scale are known. It is constrained by the requirement that the terms in the leading-order Lagrangian must have the same chiral dimension Following this method, extensions of χ PT to include dynamical photons [6] and leptons [7] have been formulated. In this Letter we will clarify these issues by reassessing the χ DC and NDA prescriptions in the light of a general power-counting formula for strongly-coupled theories with fermions, gauge bosons and scalars, initially derived in [11,12]. We will specialize it to the strong and electroweak interactions and compare it with the predictions of χ DC and NDA.
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