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 $e^+e^-$ colliders of assuming anomalous couplings of the Higgs boson to gauge bosons $HVV$ and $HHVV$ ($V=W,Z$) given by the $κ$-modifiers with respect to the Standard Model couplings, $κ_V$ and $κ_{2V}$, respectively. For this study we use the Higgs Effective Field Theory (HEFT) where these two $κ$ parameters are identified with the two most relevant effective couplings at leading order, concretely $a=κ_V$ and $b=κ_{2V}$. 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 $e^+e^- \to HH ν\bar ν$, where the vector boson scattering subprocess $WW \to HH$ 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 $κ_V^2 \neq κ_{2V}$. In order to enhance the sensitivity to these HEFT parameters $κ_V$ and $κ_{2V}$ and their potential correlations we propose here some selected differential cross sections for the $e^+e^- \to HH ν\barν$ 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 $b \bar b$ 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 $(κ_V,κ_{2V})$ effective couplings and their potential correlations. In our study we will consider the three projected energies for $e^+e^-$ colliders of 500 GeV, 1000 GeV and 3000 GeV.