Regge bounds and eikonal scaling in a four-dimensional scalar EFT
Abstract
Positivity bounds rest on twice-subtracted dispersion relations, which assume that the amplitude grows more slowly than s2. For the massless shift-symmetric scalar with g4(∂ϕ)4/Λ4 and g6(∂ϕ)6/Λ8, we derive the dispersion relation, whose cuts start at zero energy, and study the large-s growth at fixed t<0 of the tree, the one-loop bubble and the three-loop banana. The partial-wave sum is split at a transition spin: low spins are bounded by unitarity, channel by channel, and high spins are evaluated with the eikonal phase of the crossed-channel logarithms by stationary phase. The same construction is applied in the forward limit required by the dispersion relation, and we use the one- and three-loop absorptive parts below the cutoff to constrain g4 and g6.
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BibTeX
@misc{li2026regge,
title = {{Regge bounds and eikonal scaling in a four-dimensional scalar EFT}},
author = {Ji Li},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04505},
eprint = {2611.04505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04505},
}
RIS
TY - UNPB
TI - Regge bounds and eikonal scaling in a four-dimensional scalar EFT
AU - Ji Li
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04505
UR - https://arxiv.org/abs/2611.04505
AB - Positivity bounds rest on twice-subtracted dispersion relations, which assume that the amplitude grows more slowly than s^2. For the massless shift-symmetric scalar with g_4(∂ϕ)^4/Λ^4 and g_6(∂ϕ)^6/Λ^8, we derive the dispersion relation, whose cuts start at zero energy, and study the large-s growth at fixed t<0 of the tree, the one-loop bubble and the three-loop banana. The partial-wave sum is split at a transition spin: low spins are bounded by unitarity, channel by channel, and high spins are evaluated with the eikonal phase of the crossed-channel logarithms by stationary phase. The same construction is applied in the forward limit required by the dispersion relation, and we use the one- and three-loop absorptive parts below the cutoff to constrain g_4 and g_6.
ER -