The physics programme and the design are described of a new collider for particle and nuclear physics, the Large Hadron Electron Collider (LHeC), in which a newly built electron beam of 60 GeV, to possibly 140 GeV, energy collides with the intense hadron beams of the LHC. Compared to the first ep collider, HERA, the kinematic range covered is extended by a factor of twenty in the negative four-momentum squared, Q² , and in the inverse Bjorken x, while with the design luminosity of 10³³ cm^-2 s^-1 the LHeC is projected to exceed the integrated HERA luminosity by two orders of magnitude. The physics programme is devoted to an exploration of the energy frontier, complementing the LHC and its discovery potential for physics beyond the Standard Model with high precision deep inelastic scattering measurements. These are designed to investigate a variety of fundamental questions in strong and electroweak interactions. The LHeC thus continues the path of deep inelastic scattering (DIS) into unknown areas of physics and kinematics. The physics programme also includes electron-deuteron and electron-ion scattering in a (Q ²1/x) range extended by four orders of magnitude as compared to previous lepton-nucleus DIS experiments for novel investigations of neutron's and nuclear structure, the initial conditions of Quark-Gluon Plasma formation and further quantum chromodynamic phenomena. The LHeC may be realised either as a ring-ring or as a linac-ring collider. Optics and beam dynamics studies are presented for both versions, along with technical design considerations on the interaction region, magnets including new dipole prototypes, cryogenics, RF, and further components. A design study is also presented of a detector suitable to perform high precision DIS measurements in a wide range of acceptance using state-of-the art detector technology, which is modular and of limited size enabling its fast installation. The detector includes tagging devices for electron, photon, proton and neutron detection near to the beam pipe. Civil engineering and installation studies are presented for the accelerator and the detector. The LHeC can be built within a decade and thus be operated while the LHC runs in its high-luminosity phase. It so represents a major opportunity for progress in particle physics exploiting the investment made in the LHC.

We calculate the prompt neutrino flux from atmospheric charm production by cosmic rays, using the dipole picture in a perturbative QCD framework, which incorporates the parton saturation effects present at high energies. We compare our results with the next-to-leading-order perturbative QCD result and find that saturation effects are large for neutrino energies above ${10}^6\mathrm{GeV}$, leading to a substantial suppression of the prompt neutrino flux. We comment on the range of prompt neutrino fluxes due to theoretical uncertainties.

We evaluate the prompt atmospheric neutrino flux at high energies using three different frameworks for calculating the heavy quark production cross section in QCD: NLO perturbative QCD, k_T factorization including low-x resummation, and the dipole model including parton saturation. We use QCD parameters, the value for the charm quark mass and the range for the factorization and renormalization scales that provide the best description of the total charm cross section measured at fixed target experiments, at RHIC and at LHC. Using these parameters we calculate differential cross sections for charm and bottom production and compare with the latest data on forward charm meson production from LHCb at 7 TeV and at 13 TeV, finding good agreement with the data. In addition, we investigate the role of nuclear shadowing by including nuclear parton distribution functions (PDF) for the target air nucleus using two different nuclear PDF schemes. Depending on the scheme used, we find the reduction of the flux due to nuclear effects varies from 10% to 50% at the highest energies. Finally, we compare our results with the IceCube limit on the prompt neutrino flux, which is already providing valuable information about some of the QCD models.

We re-evaluate the prompt atmospheric neutrino flux, using the measured charm cross sections at RHIC and the Large Hadron Collider to constrain perturbative QCD parameters such as the factorization and renormalization scales, as well as modern parton distribution functions and recent estimates of the cosmic-ray spectra. We find that our result for the prompt neutrino flux is lower than previous perturbative QCD estimates and, consequently, alters the signal-to-background statistics of the recent IceCube measurements at high energies.

We explore the phenomenology of models containing one Vector-Like Quark (VLQ), t′, which can decay into the Standard Model (SM) top quark, t, and a new spin-0 neutral boson, S, the latter being either a scalar or pseudoscalar state. We parametrise the underlying interactions in terms of a simplified model which enables us to capture possible Beyond the SM (BSM) scenarios. We discuss in particular three such scenarios: one where the SM state is supplemented by an additional scalar, one which builds upon a 2-Higgs Doublet Model (2HDM) framework and another which realises a Composite Higgs Model (CHM) through partial compositeness. Such exotic decays of the t′ can be competitive with decays into SM particles, leading to new possible discovery channels at the Large Hadron Collider (LHC). Assuming t′ pair production via strong interactions, we design signal regions optimised for one t′ → S t transition (while being inclusive on the other $$ \overline{t} $$ t ¯ ′ decay, and vice versa), followed by the decay of S into the two very clean experimental signatures S → γ γ and S → Z (→ ℓ ⁺ ℓ ⁻ )γ. We perform a dedicated signal- to-background analysis in both channels, by using Monte Carlo (MC) event simulations modelling the dynamics from the proton-proton to the detector level. Under the assumption of BR(t′ → S t) = 100%, we are therefore able to realistically quantify the sensitivity of the LHC to both the t′ and S masses, assuming both current and foreseen luminosities. This approach paves the way for the LHC experiments to surpass current VLQ search strategies based solely on t′ decays into SM bosons (W ^± , Z , h).