Power counting of the pion-dilaton effective field theory
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912306126913536 |
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| author | Golterman, Maarten Shamir, Yigal |
| author_facet | Golterman, Maarten Shamir, Yigal |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15606 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Power counting of the pion-dilaton effective field theory Golterman, Maarten Shamir, Yigal High Energy Physics - Phenomenology High Energy Physics - Lattice 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. |
| title | Power counting of the pion-dilaton effective field theory |
| topic | High Energy Physics - Phenomenology High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2407.15606 |