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Abstract
Ever since quantum field theory was first applied to the derivation of nuclear forces in the mid-20th century, the renormalization of pion exchange with realistic couplings has presented a challenge. The implementation of effective field theories (EFTs) in the 1990s promised a solution to this problem but unexpected obstacles were encountered. The response of the nuclear community has been to focus on chiral potentials with regulators chosen to produce a good description of data. Meanwhile, a successful EFT without explicit pion exchange --- Pionless EFT --- has been formulated where renormalization is achieved order by order in a systematic expansion of low-energy nuclear observables. I describe how lessons from Pionless EFT are being applied to the construction of a properly renormalized Chiral EFT.
Highlights
In the aftermath of the solution of the “problem of infinities” in Quantum Electrodynamics (QED), an intense quest set in to renormalize nuclear forces, where pion exchange replaced the photon exchange responsible for atomic forces. (For an early example, see reference [1].) It was quickly understood that the only relativistic pion-nucleon coupling that is renormalizable is pseudoscalar [2]
The crucial point is that only the combination of the two effects matter, and physics enters through the fitting of as many observables as LECs—observables which are either calculated in the underlying theory or measured experimentally
The power counting of Chiral Perturbation Theory (ChPT) is based on naive dimensional analysis” (NDA), which comes from demanding that the effective field theories (EFTs) expansion be renormalized order by order so as to ensure model independence
Summary
In the aftermath of the solution of the “problem of infinities” in Quantum Electrodynamics (QED), an intense quest set in to renormalize nuclear forces, where pion exchange replaced the photon exchange responsible for atomic forces. (For an early example, see reference [1].) It was quickly understood that the only relativistic pion-nucleon coupling that is renormalizable is pseudoscalar [2]. The only way to eliminate it, at least with a momentum- or coordinate-space cutoff, is to include at LO a non-derivative, chirally breaking contact interaction, which according to NDA should appear two orders down the expansion, that is, at next-to-next-to-leading order (N2LO)1 It was later shown [20, 21] that oscillatory cutoff dependence appears at LO in waves where OPE is attractive, singular, and accounted for non-perturbatively. They differ in detail from the field-theoretical renormalization described below, renormalization-group analyses of the Schrödinger equation [22, 32,33,34] support this picture. I expand on the renormalization issues summarized in reference [35], but I refer the reader to the latter for a more complete review of ChEFT and its relation to other nuclear EFTs
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