Abstract: 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.

Abstract: The simplest linear seesaw mechanism can accommodate the new CDF-II W mass measurement. In addition to Standard Model particles, the model includes quasi-Dirac leptons, and a second, leptophilic, scalar doublet seeding small neutrino masses. Our proposal is consistent with electroweak precision tests, neutrino physics, rare decays and collider restrictions, requiring a new charged scalar below a few TeV, split in mass from the new degenerate scalar and pseudoscalar neutral Higgs bosons.

Abstract: Type-III seesaw is a simple extension of the Standard Model (SM) with the SU(2)(L) triplet fermion with zero hypercharge. It can explain the origin of the tiny neutrino mass and flavor mixing. After the electroweak symmetry breaking the light neutrino mass is generated by the seesaw mechanism which further ensures the mixings between the light neutrino and heavy neutral lepton mass eigenstates. If the triplet fermions are around the electroweak scale having sizable mixings with the SM sector allowed by the correct gauge symmetry, they can be produced at the high energy colliders leaving a variety of characteristic signatures. Based on a simple and concrete realizations of the model we employ a general parametrization for the neutrino Dirac mass matrix and perform a parameter scan to identify the allowed regions satisfying the experimental constraints from the neutrino oscillation data, the electroweak precision measurements and the lepton-flavor violating processes, respectively considering the normal and inverted neutrino mass hierarchies. These parameter regions can be probed at the different collider experiments.

Abstract: We study the effect of interference on the lepton number violating (LNV) and lepton number conserving (LNC) three-bodymeson decaysM(1)(+)-> l(i) (+) l(j)(+)pi(+/-) that arise in a TeV-scale left-right symmetric model (LRSM) with degenerate or nearly degenerate right-handed (RH) neutrinos. The LRSM contains three RH neutrinos and a RH gauge boson. The RH neutrinos with masses in the range of M-N similar to (MeV-few GeV) can give resonant enhancement in the semileptonic LNV and LNC meson decays. In the case where only one RH neutrino contributes to these decays, the predicted new physics branching ratios of semileptonic LNV and LNC meson decaysM(1)(+)-> l(i)(+) l(j)(+) pi(-) andM(+) 1 -> l(i)(+)l(j)(-) pi(+) are equal. We find that with at least two RH neutrinos contributing to the process, the LNV and LNC decay rates can differ. Depending on the neutrino mixing angles and CP-violating phases, the branching ratios of LNVand LNC decay channelsmediated by the heavy neutrinos can be either enhanced or suppressed, and the ratio of these two rates can differ from unity.

Abstract: The triplet or type-II seesaw mechanism is the simplest way to endow neutrinos with mass in the Standard Model (SM). Here we review its associated theory and phenomenology, including restrictions from S, T, U parameters, neutrino experiments, charged lepton flavor violation as well as collider searches. We also examine restrictions coming from requiring consistency of electroweak symmetry breaking, i.e., perturbative unitarity and stability of the vacuum. Finally, we discuss novel effects associated to the scalar mediator of neutrino mass generation namely, (i) rare processes, e.g., l(alpha)-> l(beta)gamma decays, at the intensity frontier, and also (ii) four-lepton signatures in colliders at the high-energy frontier. These can be used to probe neutrino properties in an important way, providing a test of the absolute neutrino mass and mass ordering, as well as of the atmospheric octant. They may also provide the first evidence for charged lepton flavor violation in nature. In contrast, neutrino nonstandard interaction strengths are found to lie below current detectability.