Abstract. 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 nuclear science community. It was commissioned by the managements of Brookhaven National Laboratory (BNL) and Thomas Jefferson National Accelerator Facility (JLab) with the objective of presenting a summary of scientific opportunities and goals of the EIC as a follow-up to the 2007 NSAC Long Range plan. This document is a culmination of a community-wide effort in nuclear science following a series of workshops on EIC physics over the past decades and, in particular, the focused ten-week program on "Gluons and quark sea at high energies" at the Institute for Nuclear Theory in Fall 2010. It contains a brief description of a few golden physics measurements along with accelerator and detector concepts required to achieve them. It has been benefited profoundly from inputs by the users' communities of BNL and JLab. This White Paper offers the promise to propel the QCD science program in the US, established with the CEBAF accelerator at JLab and the RHIC collider at BNL, to the next QCD frontier. Preamble Editors' note for the second editionThe first edition of this White Paper was released in 2012. In the current (second) edition, the science case for the EIC is further sharpened in view of the recent data from BNL, CERN and JLab experiments and the lessons learnt from them. Additional improvements were made by taking into account suggestions from the larger nuclear physics community including those made at the EIC Users Group meeting at Stony Brook University in July 2014, and the QCD Town Meeting at Temple University in September 2014.Abhay Deshpande, Zein-Eddine Meziani and Jian-Wei Qiu November 2014 Editors' note for the third edition Since the 2nd release of this White Paper, the NSAC's Long Range Plan (2015) was successfully completed. The EIC is a major recommendation of the US nuclear science community. In the current release (version 3) we have fixed some minor remaining errors in the text, and have added a few new references. While the core science case for the EIC remains the same, the machine designs of both options, the eRHIC at BNL and the JLEIC at JLab keep evolving. In this 3rd release of the EIC White Paper instead of making substantial changes to the machine design sections (5.1 and 5.2), we give references to the most recent machine design documents.

We demonstrate a factorization formula for semi-inclusive deep-inelastic scattering with hadrons in the current fragmentation region detected at low transverse momentum. To facilitate the factorization, we introduce the transverse-momentum dependent parton distributions and fragmentation functions with gauge links slightly off the light-cone, and with soft-gluon radiations subtracted. We verify the factorization to one-loop order in perturbative quantum chromodynamics and argue that it is valid to all orders in perturbation theory.

Parton distributions contain factorizable final state interaction effects originating from the fast-moving struck quark interacting with the target spectators in deeply inelastic scattering. We show that these interactions give rise to gauge invariance of the transverse momentum-dependent parton distributions. As compared to previous analyses, our study demonstrates the existence of extra scaling contributions from transverse components of the gauge potential at the light-cone infinity. They form a transverse gauge link which is indispensable for restoration of the gauge invariance of parton distributions in the light-cone gauge where the gauge potential does not vanish asymptotically. Our finding helps to explain a number of features observed in a model calculation of structure functions in the light-cone gauge.Keywords: parton distributions, light-cone gauge, final state interactions, dipole scattering PACS numbers: 12.38.Bx, 13.60.Nb 1 Parton model and QCD Hadron structure functions, measurable in deeply inelastic scattering, are genuine physical observables which provide direct access to the microscopic constituents of matter and their intricate interaction dynamics. In the naive parton model [1], the structure function is expressed in terms of a probability density q(x) to find a parton of a specific flavor with a certain fraction x of the parent hadron's momentum. The underlying probabilistic picture for the scattering process relies on the fact that the constituents in a hadron boosted to the infinite momentum frame behave as a collections of noninteracting quanta due to time dilation. This simple and intuitive description of hard reactions has found its firm foundation in rigorous field theoretical approach based on asymptotically free Quantum Chromodynamics (QCD). The result is factorization theorems which separate incoherent contributions responsible for physics of large and small distances involved in hard reactions in a universal and controllable manner: The physical observables such as structure functions are calculated as a convolution of QCD parton distributions in the hadrons and parton scattering cross sections. The parton model result arises as a lowest order term in the expansion in the coupling constant and inverse power of the hard momentum transfer of QCD factorization formulas.The QCD quark distribution follows from the factorization theorem in deeply inelastic scat-whereis the gauge link between the quark fields, which arises from final state interactions between the struck quark and the target spectators. This interaction does not ruin factorization and is in fact much needed to maintain gauge invariance. On the other hand, the presence of this gauge link seems to spoil the interpretation of q(x) as a pure quark distribution, as the bilocal operator in the above expression is not obviously a quark number operator. The probabilistic interpretation is expected to hold only in the light-cone gauge [3,4],since only the physical degrees of freedom remain with this choice. In this spec...

We systematically study dijet production in various processes in the small-x limit and establish an effective k t -factorization for hard processes in a system with dilute probes scattering on a dense target. We find that the well-known Weizsäcker-Williams gluon distribution can be directly probed in the quark-antiquark jet correlation in deep inelastic scattering and the dipole gluon distribution can be directly measured in the direct photon-jet correlation in pA collisions. In the large-N c limit, the unintegrated gluon distributions involved in other different dijet channels in pA collisions are shown to be related to two widely proposed ones: the Weizsäcker-Williams gluon distribution and the dipole gluon distribution.