Particle loss due to the emission of single energetic beamstrahlung photons in beam collisions is shown to impose a fundamental limit on storage-ring luminosities at energies greater than 2E~140 GeV for head-on collisions and 2E~40 GeV for crab-waist
collisions. Above these threshold energies, the suppression factor due to beamstrahlung scales as 1/E^{4/3}, and for a fixed power of synchrotron radiation, the luminosity L is proportional to R/E^{13/3}, where R is the collider radius. For 2E > 150 GeV, both collision schemes have similar luminosity limits. The luminosities attainable at storage-ring and linear-collider (LC) 2E=240 GeV Higgs factories are comparable; at higher energies, LCs are preferable. This conference paper is based on my recent PRL publication [1], supplemented with additional comments on linac-ring e+e- colliders and ring e+e- colliders with charge compensation (four-beam collisions).
Over the past two decades, the high energy physics community has been actively discussing and developing a number of post-LHC collider projects; however, none of them have been approved due to high costs and the uncertainty in post-LHC physics scenar
ios. There have been great expectations of rich new physics in the 0.1-1 TeV mass region: the Higgs boson (one or several), supersymmetry, or perhaps new particles from the dark-matter family. It has been the general consensus that the best machine for the detailed study of new physics to be discovered at the LHC would be an energy-frontier linear e+e- collider. Physicists held their breath waiting for the results from the LHC. In summer 2012, two LHC detectors, ATLAS and CMS, announced the discovery of a Higgs boson with the mass of 126 GeV and (still) nothing else. The absence of new physics in the region below 1 TeV has changed the post-LHC collider R&D priorities and triggered a zoo of project proposals for the precision study of the 126 GeV Higgs boson, possibly with further upgrades to higher energies. This paper gives an overview of these projects; it is based largely on the reports presented at the first workshop on Higgs factories held at FNAL a few days prior to the present workshop in Protvino.
