Constraining the Higgs potential at the Multi-TeV Muon Collider

Multi Higgs production at a future high-energy muon collider provides a unique opportunity to gather information on the Higgs potential, ie. the determination of the triple and quartic self-couplings. We explore the potential of combining information from H,HH,HHH production to constrain possible coupling deformations induced by new physics at high scales, including the first matrix-element based evaluation of the irreducible backgrounds.