This White Paper presents the science case of an Electron-Ion Collider (EIC), focused on the structure and interactions of gluon-dominated matter, with the intent to articulate it to the broader...

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 present a global analysis of available data on inclusive structure functions and reduced cross sections measured in electron-proton scattering at small values of Bjorken-x, x<0.01, including the latest data from HERA on reduced cross sections. Our approach relies on the dipole formulation of DIS together with the use of the non-linear running coupling BK equation for the description of the small-x dynamics. We improve our previous studies by including the heavy quark (charm and beauty) contribution to the reduced cross sections, and also by considering a variable flavor scheme for the running of the coupling. We obtain a good description of data, the fit parameters remaining stable with respect to our previous analyses where only light quarks were considered. The inclusion of the heavy quark contributions resulted in a good description of available experimental data for the charm component of the structure function and reduced cross section provide the initial transverse distribution of heavy quarks was allowed to differ (more specifically, to have a smaller radius) from that of the light flavors.

We perform a global fit to the structure function $F_2$ measured in lepton-proton experiments at small values of Bjorken-$x$, $x\le 0.01$, for all experimentally available values of $Q^2$, $0.045{\mathrm{GeV}}^2\le Q^2\le 800{\mathrm{GeV}}^2$. We show that the recent improvements resulting from the inclusion of running coupling corrections allow for a description of data in terms of nonlinear QCD evolution equations. In this approach $F_2$ is calculated within the dipole model with all Bjorken-$x$ dependence described by the running coupling Balitsky-Kovchegov equation. Two different initial conditions for the evolution are used, both yielding good fits to data with ${\chi }^2/\mathrm{d}.\mathrm{o}.\mathrm{f}.<1.1$. The proton longitudinal structure function $F_L$, not included in the fits, is also well described. Our analysis allows to perform a first principle extrapolation of the proton-dipole scattering amplitude once the initial condition has been fitted to presently available data. We provide predictions for $F_2$ and $F_L$ in the kinematical regions of interest for future colliders and ultra-high energy cosmic rays. A numerical implementation of our results down to $x={10}^{-12}$ is released as a computer code for public use.