Exploring correlations between HEFT Higgs couplings κ V and κ 2V via HH production at e⁺e⁻ colliders

In this work we explore the phenomenological implications at future e⁺e⁻ e + e - colliders of assuming anomalous couplings of the Higgs boson to gauge bosons HVV and HHVV $$(V=W,Z)$$ ( V = W , Z ) given by the κ κ -modifiers with respect to the Standard Model couplings, κ V κ V and κ 2V, κ 2 V , respectively. For this study we use the Higgs Effective Field Theory (HEFT) where these two κ κ parameters are identified with the two most relevant effective couplings at leading order, concretely a=κ V a = κ V and b=κ 2V. b = κ 2 V . Our focus is put on these two couplings and their potential correlations which we believe carry interesting information on the underlying ultraviolet theory. The particular studied process is e⁺e⁻ → HH ν ν ̄, e + e - → H H ν ν ¯ , where the vector boson scattering subprocess WW → HH W W → H H plays a central role, specially at the largest planned energy colliders. Our detailed study of this process as a function of the energy and the angular variables indicates that the produced Higgs bosons in the BSM scenarios will have in general a high transversality as compared to the SM case if κ V² ≠ κ 2V. κ V 2 ≠ κ 2 V . In order to enhance the sensitivity to these HEFT parameters κ V κ V and κ 2V κ 2 V and their potential correlations we propose here some selected differential cross sections for the e⁺e⁻ → HH ν ν ̄ e + e - → H H ν ν ¯ process, where different kinematic properties of the BSM case with respect to the SM are manifested. Finally, we will focus on the dominant Higgs decays to b b̄ b b ¯ pairs leading to final events with 4 b -jets and missing transverse energy from the undetected neutrinos and will provide the expected accessibility to the (κ V,κ 2V) ( κ V , κ 2 V ) effective couplings and their potential correlations. In our study we will consider the three projected energies for e⁺e⁻ e + e - colliders of 500 GeV, 1000 GeV and 3000 GeV.