Power counting of the pion-dilaton effective field theory

Maarten Golterman; Yigal Shamir

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arXiv · 2407.15606

Power counting of the pion-dilaton effective field theory

Maarten Golterman·Yigal Shamir

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Abstract

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 $\Delta$-potential coincides with the tree-level potential of the former, invalid, power counting.

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Maarten Golterman, Yigal Shamir. 2024-07-22. Power counting of the pion-dilaton effective field theory. https://arxiv.org/abs/2407.15606

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