SMEFT is falsifiable through multi-Higgs measurements (even in the absence of new light particles)

Abstract By embedding the Standard Model effective field theory (SMEFT) in the more general Higgs effective field theory (HEFT), we expose correlations among the coefficients of the latter that, if found to be violated in future data, would lead to the experimental falsification of the SMEFT framework. These are derived from the necessary symmetric point of HEFT and analyticity of the SMEFT Lagrangian that allows the construction of the SMEFT expansion, as laid out by other groups, and properties at that point of the Higgs-flare function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>h</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> coupling Goldstone and Higgs bosons, of the Higgs potential V ( h ) and of the Higgs-top quark coupling function <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi mathvariant="italic"></mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>h</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> .