The Large Hadron-Electron Collider at the HL-LHC

The Large Hadron electron Collider, LHeC, is the means to move deep inelastic physics following HERA to the energy frontier of particle physics as it is being exploited by the HL-LHC. The paper presents a thorough update of the initial LHeC Conceptual Design Report (CDR) published in 2012. It comprises new results on the far reaching physics programme on parton structure, QCD dynamics, electroweak and top physics. It is shown how LHeC will open a new chapter of nuclear particle physics by extending the kinematic range in lepton-nucleus scattering by several orders of magnitude. Owing to an enhanced luminosity goal, the high centre of mass energy and the cleanliness of the neutral and charged current final states, the LHeC has a very remarkable Higgs programme and a promising potential to discover new physics beyond the Standard Model. The design is for concurrent LHeC and HL-LHC operation which paves the way for transforming the LHC in its final phase of operation to a high precision Higgs and electroweak physics facility with also a much increased range to explore new physics up to 100 TeV mass, as is demonstrated in a separate chapter. Building on the CDR, the paper presents a detailed updated design of the energy recovery electron linac (ERL) including new lattice, magnet, SRF technology and interaction region designs. A lower energy, high current ERL facility, PERLE at Orsay, is described which uses the basic LHeC configuration parameters, a 3-turn racetrack, the source, and cryo-module designs, enabling it to serve as a development facility assisting the design and anticipated operation of the LHeC. The electron accelerator frequency is now chosen to be $801.58$\,MHz and the first 5-cell Niobium cavity is presented which has reached a $Q_0$ of $3 \cdot 10^{10}$ exceeding the design goal. An updated detector design, including a forward hadron tagger, is presented as a base for the acceptance, resolution and calibration goals which arise from the Higgs and PDF physics programme. The detector is shown to require an installation time of two years which is commensurate with typical LHC shutdown durations. The paper comprises a brief report of the LHeC international advisory committee with recommendations on the next steps to be made in preparing the possible endorsement of the LHeC as part of the LHC project. While the paper is dedicated to the LHeC, it also presents novel results on the FCC-eh which is designed to utilise the same ERL technology, or a relocated LHeC depending on future developments of the energy frontier collider landscape.