The EIC Collaboration

We outline the compelling physics case for e+A collisions at an Electron Ion Collider (EIC). With its wide range in energy, nuclear beams, high luminosity and clean collider environment, the EIC offers an unprecedented opportunity for discovery and for the precision study of a novel universal regime of strong gluon fields in Quantum Chromodynamics (QCD). The EIC will measure, in a wide kinematic regime, the momentum and space-time distribution of gluons and sea-quarks in nuclei, the scattering of fast, compact probes in extended nuclear media and role of color neutral (Pomeron) excitations in scattering off nuclei. These measurements at the EIC will also deepen and corroborate our understanding of the formation and properties of the strongly interacting Quark Gluon Plasma (QGP) in high energy heavy ion collisions at RHIC and the LHC. Q uantum Chromodynamics (QCD), the theory of strong interactions, is a cornerstone of the standard model of physics. Approximately 99% of the mass of baryonic matter in the universe can be attributed to QCD. This mass derives from “emergent phenomena” of the QCD vacuum that are not evident from the Lagrangian. These phenomena include chiral symmetry breaking and confinement that are fundamental features of the strong interactions. Lattice gauge theory and effective field theories have taught us that the rich and complex structure of the QCD vacuum arises primarily from the dynamics of gluons with small contributions from the quark sea. Experiments probe the QCD vacuum in a variety of ways. In electron-positron annihilation, we observe the response of the vacuum to the deposition of enormous amounts of energy into minuscule space-time volumes. In hadron spectroscopy, we observe the way in which configurations of quarks and gluons carve out and inhabit bubbles in the vacuum. In relativistic heavy ion collisions, we observe the evolution of the vacuum after first heating a macroscopic ( 1 fm ) chunk of it to trillions of degrees Kelvin. Precision measurements of deep inelastic scattering (DIS) of leptons with hadrons study properties of the QCD vacuum that are manifest in the structure of matter at resolution scales of less than a femtometer. DIS experiments with nuclei can identify those features of the short distance structure of matter which are common to all strongly interacting states. The kinematic invariants in fully inclusive DIS are the Bjorken variable x, the momentum transfer squared Q2 > 0, the inelasticity y and s, the c.m. energy squared 1. For fixed y, x ∝ Q2/s; thus high energies allow us to probe small values of x. DIS experiments of electrons off protons at the HERA collider at DESY have shown that, for Q2 ΛQCD (where ΛQCD ∼ 200 MeV), the gluon density grows rapidly with decreasing x. For x < 0.01 the proton wave function is predominantly gluonic. DIS experiments with nuclei have established that quark and gluon distributions in nuclei exhibit shadowing; they are modified significantly relative to their distributions in the nucleon wave function. However, in sharp contrast to the proton, the gluonic structure of nuclei is not known for x < 0.01. The nature of gluon shadowing is terra incognita in QCD at high energies. We will discuss in the following how an Electron Ion Collider (EIC) can enhance our understanding of universal features of the dynamics of gluons in nuclei. At large x and at large Q2, the properties of quarks and gluons in the hadron are well described by the linear evolution equations of perturbative QCD (pQCD). The rapid growth in gluon densities with decreasing x is understood to follow from a self similar Bremsstrahlung cascade where harder (large x) parent gluons successively shed softer daughter gluons. Gluon saturation is a simple mechanism for nature to tame this growth. When the density of gluons becomes large, softer gluons can recombine into harder gluons. The competition between linear QCD Bremsstrahlung and non-linear gluon recombination causes the gluon distributions to saturate at small x. The onset of saturation and the properties of the saturated phase are characterized by a dynamical scale Qs which grows with increasing energy (smaller x) and increasing nuclear size A. The nucleus is an efficient amplifier of the universal physics of high gluon densities. Simple considerations 2 suggest that Qs ∝ (A/x)1/3. Therefore DIS with large nuclei probes the same universal physics as seen in DIS with protons at x’s at least two orders of magnitude lower (or equivalently an order of magnitude larger √ s). Fig. 1 shows the saturation scale for protons and nuclei as a function of x in relation to the kinematic reach in x and Q2 of EIC. When Q2 Qs , one is in the well understood “linear” regime of QCD. For large nuclei there is a significant window at small x where Qs Q2 ΛQCD and where one is in the domain of strong non-linear gluon fields. The intensity of the chromo-electric and chromomagnetic fields in the strong gluon field regime is of order O(1/αS), where the asymptotic freedom of QCD dictates that the fine structure constant αS(Qs ) 1. These fields are therefore the strongest fields in nature! Remarkably, the weak coupling suggests that the onset and properties of this regime may be computed systematically in a QCD framework. The high occupation numbers of gluons ensures that their dynamics is classical and their piling up at a characteristic momentum scale (QA s ) is reminiscent of a Bose–Einstein condensate. Further, kinematic arguments suggest that the time scales of in1. For a brief primer on DIS kinematics, we refer the reader to the text box on page 4 2. For an expanded discussion, see the text box on page 9. Physics with an Electron Ion Collider 1 eRHIC e+Au, (20 GeV + 100 GeV/n) eRHIC e+Au, (10 GeV + 100 GeV/n) ELIC e+Ca, (7 GeV + 75 GeV/n) EIC 1 = y Q 2 s roton Q 2 s Ca (ntral) Q 2 s,q Au (ntral) ×9/4 Q 2 s,g 10 -1 1 10 10 2 10 3 10 4 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 1 x Q 2 V e G ( 2 ) Figure 1: Kinematic acceptance in the (Q2, x) plane for the EIC. Shown are lines for two complementary concepts to realize EIC, eRHIC and ELIC (see page 14 for details). Lines showing the quark saturation scale Qs for protons, Ca, and Au nuclei are superposed on the kinematic acceptance. As indicated, the gluon saturation scale in Au nuclei is larger by the color factor 9/4. teractions of gluons are in practice time dilated well beyond characteristic time scales for gluon interactions. This slowing down is analogous to what happens in spin glasses. These dynamical and kinematic considerations have led to a suggestion that the matter in nuclear wave functions at high energies is universal and can be described as a Color Glass Condensate (CGC) [1, 2]. Alternative candidates for the appropriate degrees of freedom in QCD at high energies include color neutral excitations with vacuum quantum numbers called Pomerons. These come in soft (non-perturbative) or hard (perturbative) varieties [3]. A wide range of measurements with EIC, which we shall discuss shortly, can distinguish between predictions in the CGC (or other “unconventional” frameworks) and those following from the linear evolution equations of pQCD. The nucleus is also a powerful analyzer of physics across the full range of x, Q2 and A. In e+A collisions at high energies, the virtual photon mediating the interaction splits into a compact qq̄ “dipole” which scatters off the nuclear medium. The interaction of these fast, compact dipoles with an extended gluon medium provides insight into how partons lose energy, are absorbed, and how hadron formation is modified in the presence of a colored medium. VaryR g ( x , Q 2 = 5 G e V 2 )