ForewordThe study of the fundamental structure of nuclear matter is a central thrust of physics research in the United States. As indicated in Frontiers of Nuclear Science, the 2007 Nuclear Science Advisory Committee long range plan, consideration of a future Electron-Ion Collider (EIC) is a priority and will likely be a significant focus of discussion at the next long range plan. We are therefore pleased to have supported the ten week program in fall 2010 at the Institute of Nuclear Theory which examined at length the science case for the EIC. This program was a major effort; it attracted the maximum allowable attendance over ten weeks.This report summarizes the current understanding of the physics and articulates important open questions that can be addressed by an EIC. It converges towards a set of "golden" experiments that illustrate both the science reach and the technical demands on such a facility, and thereby establishes a firm ground from which to launch the next phase in preparation for the upcoming long range plan discussions. We thank all the participants in this productive program. In particular, we would like to acknowledge the leadership and dedication of the five co-organizers of the program who are also the co-editors of this report.David Kaplan, Director, National Institute for Nuclear Theory Hugh Montgomery, Director, Thomas Jefferson National Accelerator Facility Steven Vigdor, Associate Lab Director, Brookhaven National Laboratory iii Preface This volume is based on a ten-week program on "Gluons and the quark sea at high energies", which took place at the Institute for Nuclear Theory (INT) in Seattle from September 13 to November 19, 2010. The principal aim of the program was to develop and sharpen the science case for an Electron-Ion Collider (EIC), a facility that will be able to collide electrons and positrons with polarized protons and with light to heavy nuclei at high energies, offering unprecedented possibilities for in-depth studies of quantum chromodynamics. Guiding questions were• What are the crucial science issues?• How do they fit within the overall goals for nuclear physics?• Why can't they be addressed adequately at existing facilities?• Will they still be interesting in the 2020's, when a suitable facility might be realized?The program started with a five-day workshop on "Perturbative and Non-Perturbative Aspects of QCD at Collider Energies", which was followed by eight weeks of regular program and a concluding four-day workshop on "The Science Case for an EIC".More than 120 theorists and experimentalists took part in the program over ten weeks. It was only possible to smoothly accommodate such a large number of participants because of the extraordinary efforts of the INT staff, to whom we extend our warm thanks and appreciation. We thank the INT Director, David Kaplan, for his strong support of the program and for covering a significant portion of the costs for printing this volume. We gratefully acknowledge additional financial support provided by BNL and JLab.The program w...

In this paper, we perform the first simultaneous QCD global analysis of data from semi-inclusive deep inelastic scattering, Drell-Yan, e þ e − annihilation into hadron pairs, and proton-proton collisions. Consequently, we are able to extract a universal set of nonperturbative functions that describes the observed asymmetries in these reactions. The outcome of our analysis indicates single transverse-spin asymmetries in high-energy collisions have a common origin. Furthermore, we achieve the first phenomenological agreement with lattice QCD on the up and down quark tensor charges.

The T -odd distribution functions contributing to transversity properties of the nucleon and their role in fueling nontrivial contributions to azimuthal asymmetries in semi-inclusive deep inelastic scattering are investigated. We use a dynamical model to evaluate these quantities in terms of HERMES kinematics.

We consider a simple rescattering mechanism to calculate a leading twist T-odd pion fragmentation function, a favored candidate for filtering the transversity properties of the nucleon. We evaluate the single spin azimuthal asymmetry for a transversely polarized target in semi-inclusive deep inelastic scattering ͑for HERMES kinematics͒. Additionally, we calculate the double T-odd cos 2 asymmetry in this framework.The transversity distribution h 1 ͑also known as ␦q), which measures the probability to find a transversely polarized quark in the transversely polarized nucleon, is as important for the description of the internal nucleon structure and its spin properties as the more familiar longitudinal distribution function g 1 . However, it still remains unmeasured, unlike the spin-average and helicity distribution functions, which are known experimentally and extensively modeled theoretically. The difficulty is that h 1 is a chiral-odd function, and consequently suppressed in inclusive deep inelastic scattering ͑DIS͒ processes ͓1͔; it has to be accompanied by a second chiral-odd quantity. In semi-inclusive deep inelastic scattering ͑SIDIS͒ of transversely polarized nucleons several methods have been proposed to access transversity distributions. The more promising one relies on the so called Collins fragmentation function ͓2͔, which correlates the transverse spin of the fragmenting quark to the transverse momentum of the produced hadron. In addition to being chiral odd, this fragmentation function is also time-reversal odd (T odd, see, e.g., ͓3,4͔͒, which makes its calculation challenging. Earlier, in addition to the Collins parametrization ͓2͔, a theoretical attempt was made to estimate the Collins function for pions ͓5͔. More recently, a nonvanishing T-odd fragmentation function was obtained through a consistent one-loop calculation, where massive constituent quarks and pions are the only effective degrees of freedom ͓6͔. In addition to parametrizations from data indicating a nonzero Collins function ͓7͔, the nonzero single spin asymmetries in recent measurements ͓8-10͔ signal the existence of a nontrivial T-odd effect. These indications of the T-odd fragmentation functions taken together call for deeper investigations, both theoretical and experimental.In this paper we explore an alternative one-gluon exchange mechanism, for the fragmentation of a transversely polarized quark into a spinless hadron similar to the approach we applied ͓11,12͔ to the distribution of the transversely polarized quarks in both the unpolarized and transversely polarized nucleons ͑in this context see also ͓13-15͔͒. Within this consistent framework we now make predictions for the leading twist T-odd pion fragmentation function, and the resulting single transverse-spin azimuthal asymmetry, sin(ϩ S ), as well as the spin-independent, cos 2, asymmetry in SIDIS.The nonperturbative information about the quark content of the target and the fragmentation of quarks into hadrons in SIDIS is encoded in the general form of the factorized cross sect...

The naive time-reversal-odd (''T-odd'') parton distribution h ? 1 , the so-called Boer-Mulders function, for both up (u) and down (d) quarks is considered in the diquark spectator model. While the results of different articles in the literature suggest that the signs of the Boer-Mulders function in semi-inclusive deep inelastic scattering (SIDIS) for both flavors u and d are the same and negative, a previous calculation in the diquark spectator model found that h ?ðuÞ 1 and h ?ðdÞ 1 have different signs. The flavor dependence is of significance for the analysis of the azimuthal cosð2Þ asymmetries in unpolarized SIDIS and Drell-Yan processes, as well as for the overall physical understanding of the distribution of transversely polarized quarks in unpolarized nucleons. We find substantial differences with previous work. In particular, we obtain half and first moments of the Boer-Mulders function that are negative over the full range in Bjorken x for both the u and d quarks. In conjunction with the Collins function, we then predict the cosð2Þ azimuthal asymmetry for þ and À in this framework. We also find that the Sivers u and d quarks are negative and positive, respectively. As a by-product of the formalism, we calculate the chiral-odd but ''T-even'' function h ?1L , which allows us to present a prediction for the single-spin asymmetry A sinð2Þ UL for a longitudinally polarized target in SIDIS.

We calculate the Collins fragmentation function in the framework of a spectator model with pseudoscalar pion-quark coupling and a Gaussian form factor at the vertex. We determine the model parameters by fitting the unpolarized fragmentation function for pions and kaons. We show that the Collins function for the pions in this model is in reasonable agreement with recent parametrizations obtained by fits of the available data. In addition, we compute for the first time the Collins function for the kaons.

We provide a consistent regularization procedure for calculating hadron structure functions in a chiral quark model. The structure functions are extracted from the absorptive part of the forward Compton amplitude in the Bjorken limit. Since this amplitude is obtained as a time-ordered correlation function its regularization is consistently determined from the regularization of the bosonized action. We find that the Pauli-Villars regularization scheme is most suitable because it preserves both the anomaly structure of QCD and the leading scaling behavior of hadron structure functions in the Bjorken limit. We show that this procedure yields the correct pion structure function. In order to render the sum rules of the regularized polarized nucleon structure functions consistent with their corresponding axial charges we find it mandatory to further specify the regularization procedure. This specification goes beyond the double subtraction scheme commonly employed when studying static hadron properties in this model. In particular the present approach serves to determine the regularization prescription for structure functions whose leading moments are not given by matrix elements of local operators. In this regard we conclude somewhat surprisingly that in this model the Gottfried sum rule does not undergo regularization.

We construct an improved implementation for combining transverse-momentum-dependent (TMD) factorization and collinear factorization. TMD factorization is suitable for low transverse momentum physics, while collinear factorization is suitable for high transverse momenta and for a cross section integrated over transverse momentum. The result is a modified version of the standard W + Y prescription traditionally used in the Collins-Soper-Sterman (CSS) formalism and related approaches. We further argue that questions regarding the shape and Q-dependence of the cross sections at lower Q are largely governed by the matching to the Y -term.