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 discuss B c → η c and B c → J/ψ semileptonic decays within the Standard Model (SM) and beyond. The relevant transition form factors, being the main source of theoretical uncertainties, are calculated in the sum rule approach and are provided in a full q 2 range. We calculate the semileptonic branching fractions and find for the ratios, R ηc | SM = 0.32 ± 0.02, R J/ψ | SM = 0.23 ± 0.01. Both predictions are in agreement with other existing calculations and support the current tension in R J/ψ at 2σ level with the experiment. To extend the potential of testing the SM in the semileptonic B c decays, we consider the forward-backward asymmetry and polarization observables. We also study the 4-fold differential distributions of B c → J/ψ(J/ψ →˜ −˜ +) −ν , where˜ = e, µ, in the presence of different new physics scenarios and find that the new physics effects can significantly modify the angular observables and can also produce effects which do not exist in the SM. Using the constraints on the new physics couplings from the recent combined analysis of BaBar, Belle and LHCb data on semileptonic B → D (*) decays, where the effects of new physics could be visible, we find that these different new physics scenarios are not able to simultaneously explain the current experimental value of R J/ψ .

We revisit the process e + e − → γZ at the ILC with transverse beam polarization in the presence of anomalous CP-violating γZZ coupling λ1 and γγZ coupling λ2. We point out that if the finalstate spins are resolved, then it becomes possible to fingerprint the anomalous coupling Reλ1. 90% confidence level limit on Reλ1 achievable at ILC with center-of-mass energy of 500 GeV or 800 GeV with realistic initial beam polarization and integrated luminosity is of the order of few times of 10 −2 when the helicity of Z is used and 10 −3 when the helicity of γ is used. The resulting corrections at quadratic order to the cross section and its influence on these limits are also evaluated and are shown to be small. The benefits of such polarization programmes at the ILC are compared and contrasted for the process at hand. We also discuss possible methods by which one can isolate events with a definite helicity for one of the final-state particles.

We consider the Higgs-radion mixing in the context of warped space extra dimensional models with custodial symmetry and investigate the prospects of detecting the mixed radion. Custodial symmetries allow the Kaluza-Klein excitations to be lighter, and protect Zb b to be in agreement with experimental constraints. We perform a complementary study of discovery reaches of the Higgsradion mixed state at the 13 and 14 TeV LHC and at the 500 and 1000 GeV ILC. We carry out a comprehensive analysis of the most significant production and decay modes of the mixed radion in the 80 GeV − 1 TeV mass range, and indicate the parameter space that can be probed at the LHC and the ILC. There exists a region of the parameter space which can be probed, at the LHC, through the diphoton channel even for a relatively low luminosity of 50 fb −1 . The reach of the 4-lepton final state, in probing the parameter space is also studied in the context of 14 TeV LHC, for a luminosity of 1000 fb −1 . At the ILC, with an integrated luminosity of 500 fb −1 , we analyze the Z-radion associated production and the W W fusion production, followed by the radion decay into b b and W + W − . The W W fusion production is favored over the Z-radion associated channel in probing regions of the parameter space beyond the LHC reach. The complementary study at the LHC and the ILC is useful both for the discovery of the radion and the understanding of its mixing sector.

We consider supersymmetric models in which the lightest Higgs scalar can decay invisibly consistent with the constraints on the 126 GeV state discovered at the CERN LHC. We consider the invisible decay in the minimal supersymmetric standard model (MSSM), as well its extension containing an additional chiral singlet superfield, the so-called next-to-minimal or nonminimal supersymmetric standard model (NMSSM). We consider the case of MSSM with both universal as well as nonuniversal gaugino masses at the grand unified scale, and find that only an E6 grand unified model with unnaturally large representation can give rise to sufficiently light neutralinos which can possibly lead to the invisible decay h 0 →χ 0 1χ 0 1 . Following this, we consider the case of NMSSM in detail, where also we find that it is not possible to have the invisible decay of the lightest Higgs scalar with universal gaugino masses at the grand unified scale. We delineate the regions of the NMSSM parameter space where it is possible to have the lightest Higgs boson to have a mass of about 126 GeV, and then concentrate on the region where this Higgs can decay into light neutralinos, with the soft gaugino masses M1 and M2 as two independent parameters, unconstrained by grand unification. We also consider, simultaneously, the other important invisible Higgs decay channel in the NMSSM, namely the decay into the lightest CP odd scalars, h1 → a1a1, which is studied in detail. With the invisible Higgs branching ratio being constrained by the present LHC results, we find that µ ef f < 170 GeV and M1 < 80 GeV is disfavored in NMSSM for fixed values of the other input parameters. The dependence of our results on the parameters of NMSSM is discussed in detail.