Electrons for the HL-LHC

The Large Hadron-electron Collider is the opportunity for DIS at the TeV scale in the HL-LHC era. An energy recovery linac in racetrack configuration would provide 20-60 GeV electrons to collide with the HL-LHC hadron and nuclear beams, providing instantaneous luminosities around $10^{34}$ and $5\cdot 10^{32}$ cm$^{-2}$s$^{-1}$ per nucleon respectively. It would extend the kinematic $x-Q^2$ plane down in $x$ and up in $Q^2$ by around two and four orders of magnitude in $ep$ and $eA$ respectively. A comprehensive physics programme on precision QCD, top, EW , Higgs, BSM and nuclear physics would be achievable with such machine. In this talk we will review accelerator, physics and detector aspects of the proposal, following the update [1] of the 2012 CDR [2]. Besides, the studies on the recent proposal of a detector in IP2 able to study both ep/A and pp/pA/AA collision will be presented, including a new detector and IR design [3]. [1] LHeC Collaboration and FCC-he Study Group, P. Agostini et al., e-Print: 2007.14491 [hep-ex], to appear in J. Phys. G. [2] LHeC Study Group, J.L. Abelleira Fernandez et al., J.Phys.G 39 (2012) 075001, e-Print: 1206.2913 [physics.acc-ph]. [3] LHeC talks at Offshell-2021 — The virtual HEP conference on Run4@LHC (https://indico.cern.ch/event/968055/