Zero-locus diagnostic of the direct contact term in ϕ→π+π-π0
Abstract
We formulate, within a fixed FSI-improved amplitude convention, a zero-locus diagnostic for the direct contact term in ϕ→π+π-π0. The resonant ρπ contribution is dressed channel by channel with the complex Omnès function, the direct term is multiplied by the averaged Omnès factor, and a real constant background is retained as a smooth residual amplitude. In this convention, FFSI=R+c eiδdirD with c=gϕ3πeff, and the difference of two constrained invariant-mass gradients of the reduced Dalitz density gives a local quadratic identity for c on the zero-contour. The construction provides a closure and stability diagnostic complementary to a global Dalitz-plot fit. For the benchmark input gϕ3πeff=−24.0 GeV−3, we identify a numerically stable zero-contour branch around M+0=0.460±0.025 GeV and M+−≤0.560 GeV, where the tight-contour median estimator reproduces gϕ3πest≃ −24.0 GeV−3, a closure recovery of the injected coupling within the chosen FSI-improved convention rather than an independent extraction. We further vary the mass-window selection of the branch. The median remains close to the injected value under shifts of the M+0 window and moderate changes of its width, while the mean and standard deviation are more sensitive to outlier points near unstable quadratic branches. The method therefore identifies Dalitz-plane regions where the direct-term interference is locally well-conditioned and provides useful guidance for control-region choices and systematic variations in future global fits.
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BibTeX
@misc{nam2026zerolocus,
title = {{Zero-locus diagnostic of the direct contact term in $ϕ\toπ^+π^-π^0$}},
author = {Seung-il Nam and Jung Keun Ahn},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10094},
eprint = {2609.10094},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10094},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Zero-locus diagnostic of the direct contact term in ϕ→π^+π^-π^0
AU - Seung-il Nam
AU - Jung Keun Ahn
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10094
UR - https://arxiv.org/abs/2609.10094
AB - We formulate, within a fixed FSI-improved amplitude convention, a zero-locus diagnostic for the direct contact term in ϕ→π^+π^-π^0. The resonant ρπ contribution is dressed channel by channel with the complex Omnès function, the direct term is multiplied by the averaged Omnès factor, and a real constant background is retained as a smooth residual amplitude. In this convention, F^FSI=R+c e^iδ_dirD with c=g_ϕ3π^eff, and the difference of two constrained invariant-mass gradients of the reduced Dalitz density gives a local quadratic identity for c on the zero-contour. The construction provides a closure and stability diagnostic complementary to a global Dalitz-plot fit. For the benchmark input g_ϕ3π^eff=−24.0 GeV^−3, we identify a numerically stable zero-contour branch around M_+0=0.460±0.025 GeV and M_+−≤0.560 GeV, where the tight-contour median estimator reproduces g_ϕ3π^est≃ −24.0 GeV^−3, a closure recovery of the injected coupling within the chosen FSI-improved convention rather than an independent extraction. We further vary the mass-window selection of the branch. The median remains close to the injected value under shifts of the M_+0 window and moderate changes of its width, while the mean and standard deviation are more sensitive to outlier points near unstable quadratic branches. The method therefore identifies Dalitz-plane regions where the direct-term interference is locally well-conditioned and provides useful guidance for control-region choices and systematic variations in future global fits.
ER -