Maximal value for trilinear Higgs coupling in a 3-3-1 EFT

Recent theoretical and experimental efforts have increasingly focused on the scalar potential of the Standard Model, particularly the trilinear Higgs coupling. This parameter is crucial for testing Beyond-Standard-Model theories and understanding early cosmological dynamics. Advances in experimental techniques are making precise measurements of this coupling feasible. In this work, we develop a consistent EFT framework for models based on \(SU(3)_c \times SU(3)_L \times U(1)_Y\) and show how to match the UV-complete theory to a unique class of Two-Higgs-Doublet Models (2HDMs). We impose various bounds—theoretical, electroweak precision observables, collider, and flavor—and determine the maximum allowed value of the trilinear Higgs coupling, which can reach four times the Standard Model prediction. This is testable at the LHC Hi-Lumi upgrade and future colliders. Importantly, such high values are achievable only in an out-of-alignment scenario, even with minimal deviation, which has often been overlooked in the literature.