The Large Hadron–Electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy-recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High-Luminosity Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron–proton and proton–proton operations. This report represents an update to the LHeC’s conceptual design report (CDR), published in 2012. It comprises new results on the parton structure of the proton and heavier nuclei, QCD dynamics, and electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics by extending the accessible kinematic range of lepton–nucleus scattering by several orders of magnitude. Due to its enhanced luminosity and large energy and the cleanliness of the final hadronic states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, this report contains a detailed updated design for the energy-recovery electron linac (ERL), including a new lattice, magnet and superconducting radio-frequency technology, and further components. Challenges of energy recovery are described, and the lower-energy, high-current, three-turn ERL facility, PERLE at Orsay, is presented, which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution, and calibration goals that arise from the Higgs and parton-density-function physics programmes. This paper also presents novel results for the Future Circular Collider in electron–hadron (FCC-eh) mode, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies.

We calculate the prediction for the anomalous weak-magnetic form factor of the tau lepton at q 2 = M 2 Z within the Standard Model. With all particles on-shell, this is a electroweak gauge invariant quantity. Its value is a w τ (M 2 Z ) = − (2.10 + 0.61 i) × 10 −6 . We show that the transverse and normal components of the single-tau polarization of tau pairs produced at e + e − unpolarized collisions are sensitive to the real and absorptive parts of the anomalous weak-magnetic dipole moment of the tau. The sensitivity one can achieve at LEP in the measurement of this dipole moment is discussed.

Using LEP1, SLD and LEP2 data, for tau lepton production, and data from pp colliders and LEP2, for W decays into tau leptons, we set model independent limits on non-standard electromagnetic and weak magnetic moments of the tau lepton. The most general effective Lagrangian giving rise to tau moments is used without further assumptions. Precise bounds (2σ) on the non-standard model contributions to tau electromagnetic (−0.007 < a γ < 0.005), tau Z-magnetic (−0.0024 < a Z < 0.0025) and tau W-magnetic (−0.003 < κ W < 0.004) dipole moments are set from the analysis.

The proposed high-luminosity B/Flavor factories offer new opportunities for the improved determination of the fundamental physical parameters of standard heavy leptons. Compared to the electron or the muon case, the magnetic properties of the τ lepton are largely unexplored. We show that the electromagnetic properties of the τ , and in particular its magnetic form factor, may be measured competitively in these facilities, using unpolarized or polarized electron beams. Various observables of the τ 's produced on top of the Υ resonances, such as cross-section and normal polarization for unpolarized electrons or longitudinal and transverse asymmetries for polarized beams, can be combined in order to increase the sensitivity on the magnetic moment form factor. In the case of polarized electrons, we identify a special combination of transverse and longitudinal τ polarizations able to disentangle this anomalous magnetic form factor from both the charge form factor and the interference with the Z-mediating amplitude. For an integrated luminosity of 15 × 10 18 b −1 one could achieve a sensitivity of about 10 −6 , which is several orders of magnitude below any other existing high-or low-energy bound on the magnetic moment. Thus one may obtain a QED test of this fundamental quantity to a few % precision.

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