Physics case for an $e^+e^-$ collider at 500 GeV and above
Philip Bechtle, Sven Heinemeyer, Jenny List, Gudrid Moortgat-Pick and, Georg Weiglein

TL;DR
This paper discusses the physics potential of a 500 GeV or higher energy electron-positron collider, focusing on probing the Higgs potential through di-Higgs and triple Higgs production, and compares it with other collider options.
Contribution
It highlights the experimental opportunities for studying the Higgs potential at high-energy $e^+e^-$ colliders, emphasizing the unique access to di-Higgs and triple Higgs production.
Findings
Potential to measure Higgs pair production at 500 GeV
Comparison with HL-LHC and lower-energy Higgs factories
Feasibility of accessing the Higgs potential via collider experiments
Abstract
Some highlights of the physics case for running an collider at 500 GeV and above are discussed with a particular emphasis on the experimental access to the Higgs potential via di-Higgs and (at sufficiently high energy) triple Higgs production. The information obtainable from Higgs pair production at about 500 GeV is compared with the prospects for the HL-LHC and with the indirect information that can be obtained from a Higgs factory running at lower energies.
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