Energy frontier DIS at CERN: the LHeC and the FCC-eh, PERLE

Energy-frontier Deep Inelastic Scattering (DIS) can be realised at CERN through an energy recovery linac (ERL) that would produce 60 GeV electrons to collide with the High Luminosity (HL)-Large Hadron Collider (LHC) or, eventually, with the High Energy (HE)-LHC or the Future Circular Collider (FCC) hadron beams. It would deliver lepton-proton (nucleus) collisions with centre of mass energies in the range 0.8-3.5 TeV per nucleon, and luminosities exceeding 1034 (5×10^32) cm^−2s^−1 in electron-proton (electron-lead ion) beam operation. Such machine would provide a huge physics program, with the highest resolution microscope for hadron structure, rich Higgs, top and precision Electro-Weak (EW) physics, large possibilities for Beyond Standard Model (BSM) searches, and a unique top-energy nuclear physics facility with eventual access to a new regime of QCD at high partonic densities. All these aspects have strong complementarities with the respective, concurrent pp and AA programs. In this paper we review the LHeC, HE-LHeC and FCC-eh proposals at CERN, with emphasis on the accelerator and infrastructure aspects. We also review the project of an ERL demonstrator, PERLE, under consideration to be built at LAL Orsay.