Abstract
In this paper, we promote the convex cone method of positive bounds from tree level to loop level. This method is general and can be applied to obtain leading s2 positivity bounds on the forward scattering process in the standard model effective field theory. To obtain the loop level bounds, the original tree level bounds are modified by loop corrections, which involve low dimensional coefficients. New positivity bounds being valid at one loop level on the four-Higgs scattering have been provided. We study some specific ultraviolet models to check the validity of the new bounds. In addition, the renormalisation group effect on positivity is explored. We point out that as long as the new bounds are satisfied at the cutoff scale Λ, they will also be satisfied at all scales below Λ.
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Acknowledgments
The author would like to thank Profs. Shun Zhou, Shuang-Yong Zhou for helpful discussions and their valuable suggestions. And the author especially thanks Mikael Chala for the discussion. This work was supported in part by the National Natural Science Foundation of China under grant No. 11835013 and the Key Research Program of the Chinese Academy of Sciences under grant No. XDPB15.
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Li, X. Positivity bounds at one-loop level: the Higgs sector. J. High Energ. Phys. 2023, 230 (2023). https://doi.org/10.1007/JHEP05(2023)230
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DOI: https://doi.org/10.1007/JHEP05(2023)230