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...

We analyze the one-loop vacuum stability and perturbativity bounds on a singlet extension of the Standard Model (SM) scalar sector containing a scalar dark matter candidate. We show that the presence of the singlet-doublet quartic interaction relaxes the vacuum stability lower bound on the SM Higgs mass as a function of the cutoff and lowers the corresponding upper bound based on perturbativity considerations. We also find that vacuum stability requirements may place a lower bound on the singlet dark matter mass for given singlet quartic self coupling, leading to restrictions on the parameter space consistent with the observed relic density. We argue that discovery of a light singlet scalar dark matter particle could provide indirect information on the singlet quartic self-coupling.

We analyze one-loop vacuum stability, perturbativity, and phenomenological constraints on a complex singlet extension of the Standard Model (SM) scalar sector containing a scalar dark matter candidate. We study vacuum stability considerations using a gauge-invariant approach and compare with the conventional gauge-dependent procedure. We show that, if new physics exists at the TeV scale, the vacuum stability analysis and experimental constraints from the dark matter sector, electroweak precision data, and LEP allow both a Higgs-like scalar in the mass range allowed by the latest results from CMS and ATLAS and a lighter singlet-like scalar with weak couplings to SM particles. If instead no new physics appears until higher energy scales, there may be significant tension between the vacuum stability analysis and phenomenological constraints (in particular electroweak precision data) to the extent that the complex singlet extension with light Higgs and singlet masses would be ruled out. We comment on the possible implications of a scalar with ∼ 125 GeV mass and future ATLAS invisible decay searches.

Recent results from ATLAS and CMS point to a narrow range for the Higgs mass: M H ∈ [124, 126] GeV. Given this range, a case may be made for new physics beyond the Standard Model (SM) because of the resultant vacuum stability problem, i.e., the SM Higgs quartic coupling may run to negative values at a scale below the Planck scale. We study representative minimal extensions of the SM that can keep the SM Higgs vacuum stable to the Planck scale by introducing new scalar or fermion interactions at the TeV scale while solving other phenomenological problems.In particular, we consider the type-II seesaw model, which is introduced to explain the non-zero Majorana masses of the active neutrinos. Similarly, we observe that if the stability of the SM Higgs vacuum is ensured by the running of the gauge sector couplings, then one may require a series of new electroweak multiplets, the neutral component of which can be cold dark matter candidate.Stability may also point to a new U (1) gauge symmetry, in which the SM Higgs carries non-zero charge.

We analyze the potential sensitivity of a search for e → τ conversion at a proposed electronion collider (EIC) facility. To that end, we calculate the cross sections for e → τ events in a leptoquark framework assuming that the leptoquark masses are on the order of several hundred GeV or more. Given present limits on leptoquarks from direct searches at HERA and rare decay processes, an EIC sensitive to 0.1 f b e → τ cross sections could probe previously unexplored regions of parameter space for these lepton flavor violating events (assuming 90 GeV center-of-mass energy and 10 f b −1 integrated luminosity). Depending on the species of leptoquark and flavor structure of the couplings, an EIC search could surpass the HERA and rare process sensitivity to e → τ conversion amplitudes by as much as an order of magnitude or more. We also derive updated limits on quark flavor-diagonal LFV leptoquark interactions using the most recent BaBar τ → eγ search. We find that limits from an EIC e → τ search could be competitive with the most recent τ → eγ limit for a subset of the quark flavor-diagonal leptoquark couplings. Using an SU(5) GUT model in which leptoquark couplings are constrained by the neutrino masses and mixing, we illustrate how observable leptoquark-induced e → τ conversion can be consistent with stringent LFV limits imposed by µ → eγ and µ → e conversion searches. *