Abstract
SMEFT Wilson coefficients are subject to various positivity bounds in order to be consistent with the fundamental principles of S-matrix. Previous bounds on dimension-8 SMEFT operators have been obtained using the positivity part of UV partial wave unitarity and form a (projective) convex cone. We derive a set of linear UV unitarity conditions that go beyond positivity and are easy to implement in an optimization scheme with dispersion relations in a multi-field EFT. Using Higgs scattering as an example, we demonstrate how to obtain closed bounds in the space of the three relevant dimension-8 coefficients, making use of the UV unitarity conditions as well as so-called null constraints that arise from full crossing symmetry. Specifically, we show that they are bounded by inequalities schematically going like C < \( \mathcal{O} \) ((4π)2). We compare the newly obtained upper bounds with the traditional perturbative unitarity bounds from within the EFT, and discuss some phenomenological implications of the two-sided positivity bounds in the context of experimental probes of Vector Boson Scattering.
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Acknowledgments
We would like to thank Dong-Yu Hong, Yue-Zhou Li, Andrew Tolley, Shi-Lin Wan and Zhuo-Hui Wang for helpful discussions. SYZ acknowledges support from the Fundamental Research Funds for the Central Universities under grant No. WK2030000036 and from the National Natural Science Foundation of China under grant No. 12075233 and 12247103. QC acknowledges a postdoctorate fellowship supported by University of Science and Technology of China and Peng Huanwu Center for Fundamental Theory (PCFT), Hefei. PCFT is supported by National Natural Science Foundation of China under grant No. 12247103.
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Chen, Q., Mimasu, K., Wu, T.A. et al. Capping the positivity cone: dimension-8 Higgs operators in the SMEFT. J. High Energ. Phys. 2024, 180 (2024). https://doi.org/10.1007/JHEP03(2024)180
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DOI: https://doi.org/10.1007/JHEP03(2024)180