There was a time when CERN was the Mecca of deep inelastic lepton-hadron scattering (DIS). Roughly 30-40 years ago, various muon and neutrino scattering experiments were pursued to develop the Quark-Parton Model of hadronic matter establishing Quantum Chromodynamics as the appropriate gauge field theory of strong interactions. At that time, CERN also hosted the proton-antiproton collider using the SPS for the discovery of the weak bosons W and Z. Not long ago, in 2012, the Conceptual Design Report of the Large Hadron Electron Collider (LHeC) was published , an approximately circular energy recovery linac (see Figure 1), with which electron-proton scattering would be able to complement searches, Higgs, QCD and heavy ion physics with the LHC, in its later phase of operation. Recently, the FCC study was launched at CERN and again the idea of synchronous hadron-hadron and hadron-lepton operation and physics analysis is under study, with perhaps an initial e+e- phase.
Why has DIS been such an interesting process that it is continuously developed? Much of this fascination had come with HERA at DESY, the first ever built ep collider. Without HERA we would know very little about the partonic structure of the proton and thus hardly be able to come to a quantitative understanding of the LHC physics. An example is the Higgs production cross section, which is proportional to the gluon momentum distribution squared, for which HERA delivered the only reliable information at the Bjorken x values of ~0.01 relevant to Higgs production at the LHC. DIS experiments resolve proton structure at dimensions 1/√Q2, where Q2 is the variable 4-momentum transfer squared. The LHeC [1,2] and its possible successor, the FCC-he collider , are designed to have a luminosity about 100-1000 times higher than HERA and will extend its Q2 range by a factor of more than 10 and 100, respectively. They can thus be expected to lead to a new understanding of quark-gluon dynamics, to possibly a discovery of deeper substructure or the spectroscopy of lepton-parton bound states as well as to new insight into the unification of forces. This may be crucial for the interpretation of new physics at the LHC in its high luminosity phase of operation, and later the FCC-hh, when the discovery ranges approach the large mass region, corresponding to Bjorken x values, for which the parton distributions in the proton are poorly known. With energy frontier electron-hadron colliders one will develop QCD much deeper and may possibly see it break.
Figure 1: Default configuration of the energy recovery linac, with which an electron beam of Ee=60 GeV energy can be generated and ep luminosities close to 1034cm-2 s-1 may be achieved in ep collisions, designed to proceed synchronous to pp operation. For the FCC there are two options under consideration, a combination of the LHeC ERL with the 50 TeV proton beam, which would be limited to the ERL energy and to smaller positron intensities, and the combination of the electron and proton FCC rings to achieve even higher energies, with Ee up to 175 GeV, and high luminosity for both electrons and positrons. The development of superconducting RF and the design of an ERL test facility at CERN has begun in international collaborations. It promises exciting technology developments of principal importance since the ERL technique is a unique way of economising the power consumption which possibly is the biggest common challenge of the next generation of energy frontier accelerators. An ep detector for the LHeC is under design, and its extension to the FCC-he is being considered. Clearly, these developments are open for participation - in physics, the accelerator and detector areas.
The discovery of the Higgs boson at CERN has opened a new era of particle physics. It is exciting to realise that with a cross section of 200 fb at the LHeC, and even 1-2 pb at the FCC-he, genuine Higgs factories can be built with the ep colliders under design at moderate cost. In charged and neutral current DIS, see Figure 2, rare and complicated decay channels, such as H into charm or bottom quark pairs and the Higgs self-coupling (at FCC-he) will become accessible, and H decay distributions can be measured accurately. At very low parton momentum fractions, x down to 10-7, the famous but linear DGLAP evolution equations are expected to break, QCD may relate to SUSY, and data will become accessible, which are of crucial relevance for the 100 TeV pp collider as well as for ultra-high energy neutrino scattering. With the extension of the kinematic range by 4-5 orders of magnitude, deep inelastic lepton-ion (eA) scattering at CERN has the potential to revolutionise the physics of neutron, deuteron and nuclear substructure and of the Quark-Gluon Plasma, a vital complement to AA and pA physics.
Figure 2: Leading order diagram for the production and decays of the Higgs boson in charged and neutral current deep inelastic electron-proton scattering. The cross section at the LHeC is about 200 fb and at the FCC-he it reaches 1-2 pb giving access to the Higgs self-coupling. The unique CC or NC final state, which is free of pile-up, allows precision H measurements to be made, complementing the LHC, which are being studied further [2,3], following . With its unprecedented precision in the determination of PDFs and the strong coupling, the LHeC may assist in transforming the LHC into a precision Higgs factory. Since the Higgs in pp collisions at the FCC-hh is produced at even lower x than at the LHC (x ~MH/√s), it will be crucial to measure PDFs down to very small x (10-6) in ep, and to establish the likely new, non-linear laws of their Q2 evolution. All this challenges the theoretical development of QCD considerably.
The envisaged operation of ep and eA colliders would lead to a renaissance of deep inelastic scattering and complement the pp and ee exploration of new energy frontier phenomena which are still hidden by nature. Direction for this development is provided by a dedicated International Advisory Committee, chaired by emeritus DG of CERN, Herwig Schopper, which together with a new ep coordination group was recently established by CERN for a period of four years, the envisaged duration of the FCC study. With the CERN hadron beams, the future of energy frontier DIS is open for jointly shaping it.
 The LHeC Study Group, “A Large Hadron Electron Collider at CERN”, JPhysG:39(2012)075001, arXiv:1206.2913.
 LHeC web page with recent papers, talks and workshop documentation: http://cern.ch/lhec
 Max Klein, “Deep Inelastic Scattering at High Energy”, Summary Talk on FCC-he at the FCC kickoff meeting, Geneva, 15.2.2014, see .
Convenor of the FCC-he Physics and Experiments group for the FCC Kick-off & Study Preparation Team is: M. Klein