Revisiting the <math><mrow><mi>t</mi><mover><mrow><mi>t</mi></mrow><mrow><mo>¯</mo></mrow></mover><mi>h</mi><mi>h</mi></mrow></math> channel at the FCC-hh

The exploration of the scalar sector of the Standard Model is at the core of current and future science programs at collider experiments, with increasing focus on the self-interaction of the Higgs boson. This important parameter of the Higgs sector can be measured in various channels, among the production of a Higgs boson associated with a top-quark pair, t&#175;thh. In this paper we study this channel and its potential to measure or constrain the self-coupling and possible new physics contributions at a future 100 TeV proton-proton collider. Analyzing this highly complex final state adds to the sensitivity for enhanced self-coupling interactions, and we argue that a measurement of this process is a necessity to constrain blind directions in the multidimensional parameter space of well-motivated new physics scenarios.