Distinguishing electroweak EFTs with WLWL→n x h

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Amer Physical Soc
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The electroweak symmetry-breaking sector is one of the most promising and uncharted parts of the Standard Model (SM); but it seems likely that new electroweak physics may be out of reach of the present accelerator effort and the hope is to observe small deviations from the SM. Given that, effective field theory (EFT) becomes the logic method to use, and Standard Model effective field theory (SMEFT) has become the standard. However, the most general theory with the known particle content is Higgs effective field theory (HEFT), and whether SMEFT suffices should be investigated in future experimental efforts. Building on investigations by other groups that established geometric criteria to distinguish SMEFT from HEFT (useful for theorists examining specific beyond-SM completions), we seek more phenomenological understanding and present an analogous discussion aimed at a broader audience. We discuss various aspects of (multi)Higgs boson production from longitudinal electroweak gauge bosons WLWL -> n x h in the TeV region as the necessary information to characterize the flare function, F(h), that determines whether SMEFT or HEFT is needed. We also present tree-level amplitudes including contact and exchange channels, as well as a short discussion on accessing F from the statistical limit of many bosons. We also discuss the status of the coefficients of the series expansion of F(h), its validity, whether its complex -h extension can be used to predict or not a tell-tale zero, and how they relate to the dimension-six and-eight SMEFT operators in the electroweak sector. We derive a set of new correlations among beyond the standard model corrections to the HEFT coefficients that help decide, from experimental data, whether we have a viable SMEFT. This analysis can be useful for machines beyond the LHC that could address the challenging final state with several Higgs bosons.
© Amer Physical Soc 2022 This work was supported by Spanish MICINN No. PID2019 - 108655 GB -I00 Grant, and Universidad Complutense de Madrid under research group 910309 and the IPARCOS institute; ERC Starting Grants No. REINVENT -714788; No. UCM CT42/18-CT43/18; the Fondazione Cariplo and Regione Lombardia, Grant No. 2017-2070. A. S. B. thanks Professor Juan Ferrera- Cuesta for pointing out the relevance of using Schwarz ? s lemma. We also thank Carlos Quezada-Calonge for dis- cussions on WW ? hh scattering.
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