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As seen above, the case for $\epem$ collisions with centre-of-mass energy of 500 GeV and above is not compelling for the study of the H(126) particle alone. A stronger motivation would exist if a new particle were found (or inferred) at LHC during the next run at 13-14 TeV, if and only if $\epem$ collisions could bring substantial new information about it.   Typically, $\epem$ colliders can pair-produce new particles with masses up to half the centre-of-mass energy, if they are either electrically charged or have a non-vanishing coupling to the Z. The reach of ILC500, ILC1000 and CLIC is therefore limited to particles lighter than 250, 500 and 1500 GeV/$c^2$, 1500~GeV,  respectively. The lowest threshold for new particles could be that for pair-production of dark matter particles, such as the lightest neutralinos of supersymmetric models, through their Z or Higgs couplings, in association with an initial-state-radition photon. This search was performed at LEP, but was limited by the kinematic reach and the large background from conventional neutrinos. Similar searches are performed at the LHC (mono-photon, mono-jet, accompanied with missing energy), but are competitive with astrophysical searches only for very small dark-matter particle masses. The high luminosity of TLEP up to centre-of-mass energies of 350 to 500~GeV, associated with the absence of photon background from beamstrahlung, may provide a promising opportunity to extend the sensitivity of such single-photon searches for dark matter. The absence of new phenomena at the LHC so far has reduced the prospects for direct new physics discovery in $\epem$ collisions below 1~TeV in the centre of mass (with few exceptions like the aforementioned possible observation of light dark matter). The next LHC run at 13-14 TeV, to start in 2015, will bring clarity in this respect. Discovery of a new particle lighter than 1.5 TeV/$c^2$ 1.5~TeV  in the 13-14 TeV LHC data would rejuvenate the proposal of CLIC at $\sqrt{s} =$ 3 TeV. A 100 TeV proton-proton collider, the natural successor of TLEP in the same tunnel, would instead be able to produce new particles up to several tens of TeV/$c^2$, of~TeV,  thus opening a unique window at high energy. A detailed study of the VHE-LHC physics case is therefore in order, and is foreseen to start at the beginning of 2014, in order to have relevant answers ready for the next European Strategy update, to take place around 2018.