Future strategies for the discovery and the precise measurement of the Higgs self coupling

Abstract

The European Strategy for Particle Physics (ESSP) submitted in 2013 a deliberation document to the CERN council explaining that a lepton collider with "energies of 500\,GeV or higher could explore the Higgs properties further, for example the [Yukawa] coupling to the top quark, the [trilinear] self-coupling and the total width.". In view of the forthcoming ESPP update in 2020, variations on this qualitative theme have been applied, inaccurately, to the case of the ILC, to argue that an upgrade to 500\,GeV would allow the measurement of the Higgs potential and would increase the potential for new particle searches. As a consequence, the strategic question was raised again whether the FCC-ee design study ought to consider a 500 GeV energy upgrade. In this note, we revisit the ESSP 2013 statement quantitatively and find [...] that 500 GeV is not a particularly useful energy for the lepton colliders under consideration, especially for the FCC-ee. A 5 sigma demonstration of the existence of the Higgs self-coupling is within reach at the energies foreseen for the FCC-ee, with a moderate change of configuration, which certainly deserves consideration.