A mechanism of the power-counting breaking in chiral perturbation theory
Abstract
Chiral perturbation theory is a power tool for studying the low-energy strong interactions. In the conventional chiral expansion, according to the power counting rule, the higher-order corrections for physical observables are expected to decrease order by order as the chiral dimension increases. However, most previous study of πK scattering lengths by different references showed that the 𝒪(p6) correction to the scattering lengths is anomalously large and even exceeds the 𝒪(p4) one. It poses a serious challenge to the convergence of chiral expansion. In order to explore the underlying origin of this phenomenon, the contributions of two-loop diagrams, one-loop diagrams and tree diagrams for the πK scattering amplitude are detailed analyzed. The reducible two-loop integrals, sunset integrals and vertex integrals from the 𝒪(p6) order all violate the power counting rule. The sunset and vertex integrals can be largely canceled numerically, but not enough. Furthermore, πK scattering is compared with ππ scattering, which seems not violate the power counting rule. The analysis indicates that ππ scattering contains a higher symmetry, although each 𝒪(p6)-order part also violates the power counting rule, but the violation is much smaller than the one from πK scattering. Large kaon mass also makes a contribution to the power-counting breaking, but it is not a major origin. Hence, it needs to pay more attention to the many-loop low-symmetry diagrams in future work. These diagrams may give large contribution and cannot be ignored.
Related
- Minimal superfluid vortices in chiral perturbation theory
- Soft-Collinear Chiral Perturbation Theory for B → π form factors at large recoil
- Peripheral nucleon-nucleon scattering with explicit vector mesons in chiral perturbation theory
- How Fluctuations Control Chiral Symmetry Breaking in Reacting Mixtures of Chiral Molecules
- Quark orbital angular momentum from chiral symmetry breaking in QCD
BibTeX
@misc{ma2026mechanism,
title = {{A mechanism of the power-counting breaking in chiral perturbation theory}},
author = {Ming-Ze Ma and Shao-Zhou Jiang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17721},
eprint = {2610.17721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17721},
}
RIS
TY - UNPB
TI - A mechanism of the power-counting breaking in chiral perturbation theory
AU - Ming-Ze Ma
AU - Shao-Zhou Jiang
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17721
UR - https://arxiv.org/abs/2610.17721
AB - Chiral perturbation theory is a power tool for studying the low-energy strong interactions. In the conventional chiral expansion, according to the power counting rule, the higher-order corrections for physical observables are expected to decrease order by order as the chiral dimension increases. However, most previous study of πK scattering lengths by different references showed that the 𝒪(p^6) correction to the scattering lengths is anomalously large and even exceeds the 𝒪(p^4) one. It poses a serious challenge to the convergence of chiral expansion. In order to explore the underlying origin of this phenomenon, the contributions of two-loop diagrams, one-loop diagrams and tree diagrams for the πK scattering amplitude are detailed analyzed. The reducible two-loop integrals, sunset integrals and vertex integrals from the 𝒪(p^6) order all violate the power counting rule. The sunset and vertex integrals can be largely canceled numerically, but not enough. Furthermore, πK scattering is compared with ππ scattering, which seems not violate the power counting rule. The analysis indicates that ππ scattering contains a higher symmetry, although each 𝒪(p^6)-order part also violates the power counting rule, but the violation is much smaller than the one from πK scattering. Large kaon mass also makes a contribution to the power-counting breaking, but it is not a major origin. Hence, it needs to pay more attention to the many-loop low-symmetry diagrams in future work. These diagrams may give large contribution and cannot be ignored.
ER -