Higgs Pair Production and Triple Higgs Couplings at the LHC in the 2HDM

Gaining information about the shape of the Higgs potential is one of the main goals of particle
physics for the coming years. The trilinear Higgs self-interactions can directly be probed via Higgs
pair production, which at the LHC happens dominantly through gluon fusion. In models with
extended Higgs sectors the trilinear self-coupling of the detected Higgs boson can strongly deviate
from the prediction of the Standard Model (SM) due to large loop corrections even in scenarios
where all couplings to gauge bosons and fermions are very close to their SM values. Furthermore,
triple Higgs couplings involving additional Higgs bosons can have an important impact on the pair
production process of the SM-like Higgs boson via the resonant contribution of the heavy Higgs.
We study the phenomenological implications for Higgs pair production in the framework of the
Two Higgs Doublet Model (THDM). We analyze the potential sensitivity to both, the SM-like
trilinear Higgs self-coupling and the beyond-the-SM triple Higgs coupling involving a resonantly
produced CP-even Higgs. In particular, we focus on the theoretical predictions of two observable
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quantities: the total Higgs pair production cross section and the invariant mass distribution of the
two Higgs bosons in the final state. We show that the inclusion of loop corrections to the trilinear
Higgs couplings as well as the resonant heavy Higgs contribution are crucial in this context.