Abstract: We consider the NMSSM extended to include one vector-like family of quarks and leptons. If (some of) these vector-like matter particles, as the Higgs doublets, have Yukawa couplings to the singlet S that exceed unity at about the same scale Λ ≲ 103 TeV, this gives the order 40% enhancement of the tree level Higgs boson mass required in the MSSM to reach 125 GeV. It is conceivable that the Yukawa couplings to the singlet S, although naively blowing up close to Λ, will not spoil gauge coupling unification. In such a case the unified coupling αX could be interestingly led to a value not far from unity, thus providing a possible explanation for the number of generations. The characteristic signal is an enhanced resonant production of neutral spin zero particles at LHC, that could even explain the putative diphoton resonance hinted by the recent LHC data at 750 GeV.

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10 TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work.

The original online version of this article was revised: The additional reference [139] has been added. Tao Han’s ORICD ID has been incorrectly assigned to Chengcheng Han and Chengcheng Han’s ORCID ID to Tao Han. Yang Ma’s ORCID ID has been incorrectly assigned to Lianliang Ma, and Lianliang Ma’s ORCID ID to Yang Ma. The original article has been corrected.