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In this work we explore the low energy effects induced from the integrationof the heavy Higgs boson modes, $H$, $A$ and $H^\pm$, within the Two HiggsDoublet Model (2HDM) by assuming that the lightest Higgs boson $h$ is the oneobserved experimentally at $m_h \sim 125$ GeV. We work within the context ofEffective Field Theories, focusing on the Higgs Effective Field Theory (HEFT),although some comparisons with the Standard Model Effective Field Theory(SMEFT) case are also discussed through this work. Our main focus is placed inthe computation of the non-decoupling effects from the heavy Higgs bosons andthe capture of such effects by means of the HEFT coefficients which areexpressed in terms of the input parameters of the 2HDM. Our approach to solvethis issue is by matching the amplitudes of the 2HDM and the HEFT for physicalprocesses involving the light Higgs boson $h$ in the external legs, instead ofthe most frequently used matching procedure at the Lagrangian level. Moreconcretely, we perform the matching at the amplitudes level for the followingphysical processes, including scattering and decays: $h\to WW^*\to Wf\bar{f'}$,$h\to ZZ^*\to Zf\bar{f}$, $WW \to hh$, $ZZ \to hh$, $hh \to hh$, $h \to \gamma\gamma$ and $h \to \gamma Z$. One important point of this work is that thematching is required to happen at low energies compared to the heavy Higgsboson masses, and these are heavier than the other particle masses. The properexpansion for this heavy mass limit is also defined here, which provides theresults for the non-decoupling effects presented in this work. We finallydiscuss the implications of the resulting effective coefficients, and remark onthe interesting correlations detected among them.

Non-decoupling effects from heavy Higgs bosons by matching 2HDM to HEFT amplitudes