Sensitivity to Triple Higgs Couplings via Di-Higgs Production in the 2HDM at the (HL-)LHC

Abstract: An important task of the LHC is the investigation of the Higgs-boson sector. Of particular interest is the reconstruction of the Higgs potential, i.e. the measurement of the Higgs self-couplings. Based on previous analyses, within the 2HDMs type~I and~II, we analyze several two-dimensional benchmark planes that are over large parts in agreement with all theoretical and experimental constraints. For these planes we evaluate di-Higgs production cross sections at the (HL-)LHC with a center-of-mass energy of 13 TeV at NLO in the heavy top-quark limit with the code HPAIR. We investige in particular the process $gg \to hh$, with $h$ being the Higgs boson discovered at the LHC with a mass of about 125 GeV. The top box diagram of the loop-mediated gluon fusion process into Higgs pairs interferes with the $s$-channel exchange of the two CP-even 2HDM Higgs bosons $h$ and $H$ involving the trilinear couplings $\lambda_{hhh}$ and $\lambda_{hhH}$, respectively. Depending on the size of the involved top-Yukawa and triple Higgs couplings as well as on the mass of $H$, the contribution of the $s$-channel $H$~diagram can be dominating or be highly suppressed. We find regions of the allowed parameter space in which the di-Higgs production cross section can differ by many standard deviations from its SM prediction, indicating possible access to deviations in $\lambda_{hhh}$ from the SM value $\lambda_{\rm SM}$ and/or contributions involving $\lambda_{hhH}$. The sensitivity to $\lambda_{hhH}$ is further analyzed employing the $m_{hh}$ distributions. We demonstrate how a possible measurement of $\lambda_{hhH}$ depends on the various experimenal uncertainties. Depending on the underlying parameter space, the HL-LHC may have the option not only to detect beyond-the-Standard-Model triple Higgs couplings, but also to provide a first rough measurement of their sizes.