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 linear seesaw mechanism provides a simple way to generate neutrino masses. In addition to Standard Model particles, it includes quasi-Dirac leptons as neutrino mass mediators, and a leptophilic scalar doublet seeding small neutrino masses. Here we review its associated physics, including restrictions from theory and phenomenology. The model yields potentially detectable μ-> e gamma rates as well as distinctive signatures in the production and decay of heavy neutrinos ( N-i) and the charged Higgs boson (H-+/-) arising from the second scalar doublet. We have found that production processes such as e(+) e(-) -> NN, e- gamma -> NH- and e(+) e(-) -> H (+) H- followed by the decay chain H-+/--> l(+/-) (i) N, N -> l`(+/-) (j) W (-/+) leads to striking lepton number violation signatures at high energies which may probe the Majorana nature of neutrinos.

Abstract: The minimal U(1)(X) extension of the Standard Model (SM) is a well-motivated new physics scenario, where anomaly cancellation dictates new neutral gauge boson (Z') couplings with the SM fermions in terms of the U(1)(X) charges of the new scalar fields. We investigate the SM charged fermion pair-production process for different values of these U(1)(X) charges at future e(-)e(+) colliders: e(+)e(-) -> f (f) over bar Apart from the standard gamma and Z-mediated processes, this model features additional s-channel (or both s and t-channel when f = e(-)) Z' exchange which interferes with the SM processes. We first estimate the bounds on the U(1)(X) coupling (g') and the Z' mass (M-Z') considering the latest dilepton and dijet constraints from the heavy resonance searches at the LHC. Then using the allowed values of g', we study the angular distributions, forward-backward (A(FB)), left-right (A(LB)), and left-right forward-backward (A(LR-FB)) asymmetries of the final states. We fmd that these observables can show substantial deviations from the SM results in the U(1)(X) model, thus providing a powerful probe of the multi-TeV Z' bosons at future e(+)e(-) colliders.

Abstract: The addition of SU(2)(L) triplet fermions of zero hypercharge with the Standard Model (SM) helps to explain the origin of the neutrino mass by the so-called seesaw mechanism. Such a scenario is commonly known as the type-III seesaw model. After the electroweak symmetry breaking, the mixings between the light and heavy mass eigenstates of the neutral leptons are developed and play important roles in the study of the charged and neutral multiplets of the triplet fermions at the colliders. In this article, we study such interactions to produce these multiplets of the triplet fermion at the electron-positron and electron-proton colliders at different center-of-mass energies. We focus on the heavy triplets, for example, having mass in the TeV scale so that their decay products including the SM, the gauge bosons, or the Higgs boson can be sufficiently boosted, leading to a fat jet. Hence, we probe the mixing between light-heavy mass eigenstates of the neutrinos and compare the results with the bounds obtained by the electroweak precision study.

Abstract: Axion like particles (ALPs) and right-handed neutrinos (RHNs) are two well-motivated dark matter (DM) candidates. However, these two particles have a completely different origin. Axion was proposed to solve the strong CP problem, whereas RHNs were introduced to explain light neutrino masses through seesaw mechanisms. We study the case of ALP portal RHN DM (Majorana DM) taking into account existing constraints on ALPs. We consider the leading effective operators mediating interactions between the ALP and Standard Model (SM) particles and three RHNs to generate light neutrino masses through type-I seesaw. Further, ALP-RHN neutrino coupling is introduced to generalize the model which is restricted by the relic density and indirect detection constraint.