Power counting of the pion-dilaton effective field theory

Golterman, Maarten; Shamir, Yigal

doi:10.1103/PhysRevD.111.074505

Power counting of the pion-dilaton effective field theory

Journal Article · Thu Apr 10 00:00:00 EDT 2025 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.111.074505· OSTI ID:2554048

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Confining QCD-like theories close to the conformal window have a “walking” coupling. This is believed to lead to a light singlet scalar meson in the low-energy spectrum, a dilaton, which is the pseudo-Nambu-Goldstone boson for the approximate scale symmetry. Extending chiral perturbation theory to include the dilaton requires a new small parameter to control the dilaton mass and its interactions. In our previous work we derived a systematic power counting for the dilaton couplings by matching the effective low-energy theory to the underlying theory using mild assumptions. In this paper we examine two alternative power countings which were proposed in the literature based on a phenomenological picture for the conformal transition. We find that one of these power countings fails, in fact, to generate a systematic expansion; the other coincides with the power counting we derived. We also point out that the so-called $Δ$ -potential coincides with the tree-level potential of the former, invalid, power counting.

Published by the American Physical Society 2025

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Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0013682

OSTI ID:: 2554048

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 7 Vol. 111; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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