Search

An overwhelming number of theoretical predictions for hadron colliders require parton distribution functions (PDFs), which are an important ingredient of theory infrastructure for the next generation of high-energy experiments. This whitepaper summarizes the status and future prospects for determination of high-precision PDFs applicable in a wide range of energies and experiments, in particular in precision tests of the Standard Model and in new physics searches at the high-luminosity Large Hadron Collider and Electron-Ion Collider. We discuss the envisioned advancements in experimental measurements, QCD theory, global analysis methodology, and computing that are necessary to bring unpolarized PDFs in the nucleon to the N2LO and N3LO accuracy in the QCD coupling strength. Special attention is given to the new tasks that emerge in the era of the precision PDF analysis, such as those focusing on the robust control of systematic factors both in experimental measurements and theoretical computations. Various synergies between experimental and theoretical studies of the hadron structure are explored, including opportunities for studying PDFs for nuclear and meson targets, PDFs with electroweak contributions or dependence on the transverse momentum, for incisive comparisons between phenomenological models for the PDFs and computations on discrete lattice, and for cross-fertilization with machine learning/AI approaches. [Submitted to the US Community Study on the Future of Particle Physics (Snowmass 2021).], Comment: 83 pages, 27 figures, contribution to Snowmass 2021; v.3: journal version

Novel considerations are presented on the physics, apparatus and accelerator designs for a future, luminous, energy frontier electron-hadron ($eh$) scattering experiment at the LHC in the thirties for which key physics topics and their relation to the hadron-hadron HL-LHC physics programme are discussed. Demands are derived set by these physics topics on the design of the LHeC detector, a corresponding update of which is described. Optimisations on the accelerator design, especially the interaction region (IR), are presented. Initial accelerator considerations indicate that a common IR is possible to be built which alternately could serve $eh$ and $hh$ collisions while other experiments would stay on $hh$ in either condition. A forward-backward symmetrised option of the LHeC detector is sketched which would permit extending the LHeC physics programme to also include aspects of hadron-hadron physics. The vision of a joint $eh$ and $hh$ physics experiment is shown to open new prospects for solving fundamental problems of high energy heavy-ion physics including the partonic structure of nuclei and the emergence of hydrodynamics in quantum field theory while the genuine TeV scale DIS physics is of unprecedented rank., Comment: 27 pages, 24 figures, 6 tables; to appear in Eur. Phys. J. C

This report describes the physics case, the resulting detector requirements, and the evolving detector concepts for the experimental program at the Electron-Ion Collider (EIC). The EIC will be a powerful new high-luminosity facility in the United States with the capability to collide high-energy electron beams with high-energy proton and ion beams, providing access to those regions in the nucleon and nuclei where their structure is dominated by gluons. Moreover, polarized beams in the EIC will give unprecedented access to the spatial and spin structure of the proton, neutron, and light ions. The studies leading to this document were commissioned and organized by the EIC User Group with the objective of advancing the state and detail of the physics program and developing detector concepts that meet the emerging requirements in preparation for the realization of the EIC. The effort aims to provide the basis for further development of concepts for experimental equipment best suited for the science needs, including the importance of two complementary detectors and interaction regions. This report consists of three volumes. Volume I is an executive summary of our findings and developed concepts. In Volume II we describe studies of a wide range of physics measurements and the emerging requirements on detector acceptance and performance. Volume III discusses general-purpose detector concepts and the underlying technologies to meet the physics requirements. These considerations will form the basis for a world-class experimental program that aims to increase our understanding of the fundamental structure of all visible matter, Comment: 902 pages, 415 authors, 151 institutions

The Large Hadron electron Collider (LHeC) is designed to move the field of deep inelastic scattering (DIS) to the energy and intensity frontier of particle physics. Exploiting energy recovery technology, it collides a novel, intense electron beam with a proton or ion beam from the High Luminosity--Large Hadron Collider (HL-LHC). The accelerator and interaction region are designed for concurrent electron-proton and proton-proton operation. This report represents an update of the Conceptual Design Report (CDR) of the LHeC, published in 2012. It comprises new results on parton structure of the proton and heavier nuclei, QCD dynamics, electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics in extending the accessible kinematic range in lepton-nucleus scattering by several orders of magnitude. Due to enhanced luminosity, large energy and the cleanliness of the hadronic final states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, the report represents a detailed updated design of the energy recovery electron linac (ERL) including new lattice, magnet, superconducting radio frequency technology and further components. Challenges of energy recovery are described and the lower energy, high current, 3-turn ERL facility, PERLE at Orsay, is presented which uses the LHeC characteristics serving as a development facility for the design and operation of the LHeC. An updated detector design is presented corresponding to the acceptance, resolution and calibration goals which arise from the Higgs and parton density function physics programmes. The paper also presents novel results on the Future Circular Collider in electron-hadron mode, FCC-eh, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies., Comment: 373 pages, many figures, to be published by J. Phys. G

The operation of the Future Circular Collider (FCC) with heavy ions would provide Pb-Pb and p-Pb collisions at sqrt{s_NN}= 39 and 63 TeV, respectively, per nucleon-nucleon collision, with projected per-month integrated luminosities of up to 110/nb and 29/pb, respectively. This document outlines the unique and broad physics opportunities with heavy ions at the energy frontier opened by FCC., Comment: 14 pages, 8 figures, Proceedings of the Hard Probes 2018 International Conference, largely similar to the HI contribution to the FCC CDR Volume 1 http://cds.cern.ch/record/2651294

The future opportunities for high-density QCD studies with ion and proton beams at the LHC are presented. Four major scientific goals are identified: the characterisation of the macroscopic long wavelength Quark-Gluon Plasma (QGP) properties with unprecedented precision, the investigation of the microscopic parton dynamics underlying QGP properties, the development of a unified picture of particle production and QCD dynamics from small (pp) to large (nucleus--nucleus) systems, the exploration of parton densities in nuclei in a broad ($x$, $Q^2$) kinematic range and the search for the possible onset of parton saturation. In order to address these scientific goals, high-luminosity Pb-Pb and p-Pb programmes are considered as priorities for Runs 3 and 4, complemented by high-multiplicity studies in pp collisions and a short run with oxygen ions. High-luminosity runs with intermediate-mass nuclei, for example Ar or Kr, are considered as an appealing case for extending the heavy-ion programme at the LHC beyond Run 4. The potential of the High-Energy LHC to probe QCD matter with newly-available observables, at twice larger center-of-mass energies than the LHC, is investigated., Comment: 209 pages; Report from Working Group 5 of the Workshop on the Physics of the CERN HL-LHC, and Perspectives at the HE-LHC (v2: Minor updates to text and figures. Added one author.)

The unique physics opportunities accessible with nuclear collisions at the CERN Future Circular Collider (FCC) are summarized. Lead-lead (PbPb) and proton-lead (pPb) collisions at $\sqrt{s_{NN}}$ = 39 and 63 TeV respectively with $\mathcal{L}_{int}$ = 33 nb$^{-1}$ and 8 pb$^{-1}$ monthly integrated luminosities, will provide unprecedented experimental conditions to study quark-gluon matter at temperatures ${\cal O}$(1 GeV). The following topics are succinctly discussed: (i) charm-quark densities thrice larger than at the LHC, leading to direct heavy-quark impact in the bulk QGP properties, (ii) quarkonia, including $\Upsilon(1S)$, melting at temperatures up to five times above the QCD critical temperature, (iii) access to initial-state nuclear parton distributions (nPDF) at fractional momenta as low as $x\approx 10^{-7}$, (iv) availability of $5\cdot 10^5$ top-quark pairs per run to study the high-$x$ gluon nPDF and the energy loss properties of boosted colour-antennas, (v) study of possible Higgs boson suppression in the QGP, and (vi) high-luminosity $\gamma\gamma$ (ultraperipheral) collisions at c.m. energies up to 1 TeV., Comment: 4 pages, 6 figures. Proceedings Quark Matter'17 (Chicago, Feb. 2017). Nucl.Phys.A, to appear

The Future Circular Collider (FCC) Study is aimed at assessing the physics potential and the technical feasibility of a new collider with centre-of-mass energies, in the hadron-hadron collision mode, seven times larger than the nominal LHC energies. Operating such machine with heavy ions is an option that is being considered in the accelerator design studies. It would provide, for example, Pb-Pb and p-Pb collisions at sqrt{s_NN} = 39 and 63 TeV, respectively, per nucleon-nucleon collision, with integrated luminosities above 30 nb^-1 per month for Pb-Pb. This is a report by the working group on heavy-ion physics of the FCC Study. First ideas on the physics opportunities with heavy ions at the FCC are presented, covering the physics of the Quark-Gluon Plasma, of gluon saturation, of photon-induced collisions, as well as connections with other fields of high-energy physics., Comment: 57 pages, 28 figures. This document will be part of a CERN Yellow Report on Physics at FCC-hh

The Future Circular Collider is a new proposed collider at CERN with centre-of-mass energies around 100 TeV in the pp mode. Ongoing studies aim at assessing its physics potential and technical feasibility. Here we focus on updates in physics opportunities accessible in pA and AA collisions not covered in previous Quark Matter contributions, including Quark-Gluon Plasma and gluon saturation studies, novel hard probes of QCD matter, and photon-induced collisions., Comment: 4 pages, 5 figures, proceedings of Quark Matter 2015

We present an overview of the results obtained in pPb and PbPb collisions at the Large Hadron Collider during Run 1. We first discuss the results for global characteristics: cross sections, hadron multiplicities, azimuthal asymmetries, correlations at low transverse momentum, hadrochemistry, and femtoscopy. We then review hard and electromagnetic probes: particles with high transverse momentum, jets, heavy quarks, quarkonium, electroweak bosons and high transverse momentum photons, low transverse momentum photons and dileptons, and ultraperipheral collisions. We mainly focus on the experimental results, and present very briefly the main current theoretical explanations., Comment: 33 pages, 29 figures

We point out that current calculations of inclusive two-particle correlations in p-A collisions based on the Color Glass Condensate approach exhibit a contribution from Hanbury-Brown-Twiss correlations. These HBT correlations are quite distinct from the standard ones, in that they are apparent for particles widely separated in rapidity. The transverse size of the emitter which is reflected in these correlations is the gluonic size of the proton. This raises an interesting possibility of measuring the proton size directly by the HBT effect of particle pairs produced in p-A collisions., Comment: 11 pages, 3 eps figures; v2: comments, discussions, references and acknowledgements added, conclusions unchanged, final version

Predictions for charged hadron, identified light hadron, quarkonium, photon, jet and gauge bosons in p+Pb collisions at sqrt s_NN = 5 TeV are compiled and compared. When test run data are available, they are compared to the model predictions., Comment: 84 pages

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 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, and it benefited from inputs from the users' communities of BNL and JLab. This White Paper offers the promise to propel the QCD science program in the U.S., established with the CEBAF accelerator at JLab and the RHIC collider at BNL, to the next QCD frontier., Comment: The Second Edition, 164 pages

The present note relies on the recently published conceptual design report of the LHeC and extends the first contribution to the European strategy debate in emphasising the role of the LHeC to complement and complete the high luminosity LHC programme. The brief discussion therefore focuses on the importance of high precision PDF and $\alpha_s$ determinations for the physics beyond the Standard Model (GUTs, SUSY, Higgs). Emphasis is also given to the importance of high parton density phenomena in nuclei and their relevance to the heavy ion physics programme at the LHC.

Proton-nucleus (p+A) collisions have long been recognized as a crucial component of the physics programme with nuclear beams at high energies, in particular for their reference role to interpret and understand nucleus-nucleus data as well as for their potential to elucidate the partonic structure of matter at low parton fractional momenta (small-x). Here, we summarize the main motivations that make a proton-nucleus run a decisive ingredient for a successful heavy-ion programme at the Large Hadron Collider (LHC) and we present unique scientific opportunities arising from these collisions. We also review the status of ongoing discussions about operation plans for the p+A mode at the LHC., Comment: 33 pages, 15 Figures

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., Comment: 17 pages, 4 figures

We discuss the longitudinal structure function in nuclear DIS at small $x$. We work within the framework of universal parton densities obtained in DGLAP analyses at NLO. We show that the nuclear effects on the longitudinal structure function closely follow those on the gluon distribution. The error analyses available from newest sets of nuclear PDFs also allow to propagate the uncertainties from present data. In this way, we evaluate the minimal sensitivity required in future experiments for this observable to improve the knowledge of the nuclear glue. We further discuss the uncertainties on the extraction of $F_2$ off nuclear targets, introduced by the usual assumption that the ratio $F_L/F_2$ is independent of the nuclear size. We focus on the kinematical regions relevant for future lepton-ion colliders., Comment: LaTeX, 12 pages, 4 eps figures; v2: reference added; v3: comments and references added, results and conclusions unchanged, final version

We present a Monte Carlo implementation, within PYTHIA, of medium-induced gluon radiation in the final state branching process. Medium effects are introduced through an additive term in the splitting functions computed in the multiple-soft scattering approximation. The observable effects of this modification are studied for different quantities as fragmentation functions and the hump-backed plateau, and transverse momentum and angular distributions. The anticipated increase of intra-jet multiplicities, energy loss of the leading particle and jet broadening are observed as well as modifications of naive expectations based solely on analytical calculations. This shows the adequacy of a Monte Carlo simulator for jet analyses. Effects of hadronization are found to wash out medium effects in the soft region, while the main features remain. To show the performance of the implementation and the feasibility of our approach in realistic experimental situations we provide some examples: fragmentation functions, nuclear suppression factors, jet shapes and jet multiplicities. The package containing the modified routines is available for public use. This code, which is not an official PYTHIA release, is called Q-PYTHIA. We also include a short manual to perform the simulations of jet quenching., Comment: 21 pages, 8 figures

We present a global fit to the structure function F_2 measured in lepton-proton experiments at small values of Bjorken-x, x< 0.01, for all experimentally available values of Q^2, 0.045< Q^2 < 800 GeV^2, using the Balitsky -Kovchegov equation including running coupling corrections. Using our fits to F_2, we reproduce available data for F_L and perform predictions, parameter-free and completely driven by small-x evolution, to the kinematic range relevant for the LHeC., Comment: To appear in the proceedings of the XVII International Workshop on Deep-Inelastic Scattering and Related Subjects DIS 2009, 26-30 April 2009, Madrid. 5 pages, 3 figures

I review the main predictions for the heavy-ion programme at the Large Hadron Collider (LHC) at CERN, as available in early April 2009. I begin by remembering the standard claims made in view of the experimental data measured at the Super Proton Synchrotron (SPS) at CERN and at the Relativistic Heavy Ion Collider (RHIC) at the BNL. These claims will be used for later discussion of the new opportunities at the LHC. Next I review the generic, qualitative expectations for the LHC. Then I turn to quantitative predictions: First I analyze observables which characterize directly the medium produced in the collisions - bulk observables or soft probes -: multiplicities, collective flow, hadrochemistry at low transverse momentum, correlations and fluctuations. Second, I move to calibrated probes of the medium i.e. typically those whose expectation in the absence of any medium can be described in Quantum Chromodynamics (QCD) using perturbative techniques (pQCD), usually called hard probes. I discuss particle production at large transverse momentum and jets, heavy-quark and quarkonium production, and photons and dileptons. Finally, after a brief review of pA collisions, I end with a summary and a discussion about the potentiality of the measurements at the LHC - particularly those made during the first run - to further substantiate or, on the contrary, disproof the picture of the medium that has arisen from the confrontation between the SPS and RHIC data, and theoretical models., Comment: 64 pages, 40 figures, 7 tables; invited review for "Quark-Gluon Plasma 4"; v2: small changes, some predictions and references added, final version

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 GeV^2\le Q^2 \le 800 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 non-linear 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 excellent fits to data with \chi^2/d.o.f.<1.1. Data for the proton longitudinal structure function F_L, not included in the fits, are also well described. We provide predictions for F_2 and F_L in the kinematical regions of interest for future colliders and ultra-high energy cosmic rays. Our analysis allows to perform a first principle extrapolation of the proton-dipole scattering amplitude. A numerical implementation of our results down to x=10^{-12} is released as a computer code for public use., Comment: 24 pages and 6 figures, revised version

We present a Monte Carlo implementation of medium-induced gluon radiation in the final-state branching process. Medium effects are introduced through an additive term in the splitting functions. We have implemented such modification within PYTHIA. We show the medium effects on the hump-backed plateau, and the transverse momentum and angular distributions with respect to the parent parton. As expected, with increasing medium densities there is an increase (decrease) of partons with small (large) momentum fraction, and angular broadening is observed. The effects on the transverse-momentum distributions are more involved, with an enhancement of low- and intermediate-$p_T$ partons and a decrease at large $p_T$, which is related to energy conservation, and to the lack of momentum exchange with the medium in our approach., Comment: LaTeX, 6 pages, 2 eps figures; proceedings of the 3rd International Conference on Hard and Electromagnetic Probes in High-Energy Nuclear Collisions - Hard Probes 2008 (Illa de A Toxa, Spain, June 8th-14th 2008)

We study the modification of the multiplicity distributions in MLLA due to the presence of a QCD medium. The medium is introduced though a multiplicative constant ($f_{med}$) in the soft infrared parts of the kernels of QCD evolution equations. Using the asymptotic ansatz for quark and gluons mean multiplicities $=e^{\gamma y}$ and $=r^{-1}e^{\gamma y}$ respectively, we study two cases: fixed $\gamma$ as previously considered in the literature, and fixed $\alpha_s$. We find opposite behaviors of the dispersion of the multiplicity distributions with increasing $f_{med}$ in both cases. For fixed $\gamma$ the dispersion decreases, while for fixed $\alpha_s$ it increases., Comment: LaTeX, 9 pages, 4 eps figures; proceedings of the 3rd International Conference on Hard and Electromagnetic Probes in High-Energy Nuclear Collisions - Hard Probes 2008 (Illa de A Toxa, Spain, June 8th-14th 2008)

We evaluate both the tau lepton energy loss produced by photonuclear interactions and the neutrino charged current cross section at ultra-high energies, both relevant to neutrino bounds with Earth-skimming tau neutrinos., Comment: Contribution to the Proceedings of the XLIII Rencontres de Moriond: QCD and High Energy Interactions, La Thulile, Italy, 8-15 March 2008. Talk presented by G. Parente (4 pages and 3 figures)

I present an overview of predictions for the heavy ion program at the Large Hadron Collider. It is mainly based on the material presented during the workshop 'Heavy Ion Collisions at the LHC - Last Call for Predictions', held in the frame of the CERN Theory Institute from May 14th to June 10th 2007. Predictions on both bulk properties and hard probes are reviewed., Comment: 8 pages, 3 eps figures included using graphicx; proceedings of Quark Matter 2008 (Jaipur, India, february 4th-10th 2008)

This writeup is a compilation of the predictions for the forthcoming Heavy Ion Program at the Large Hadron Collider, as presented at the CERN Theory Institute 'Heavy Ion Collisions at the LHC - Last Call for Predictions', held from May 14th to June 10th 2007., Comment: LaTeX, 185 pages, uses iop styles; writeup of the CERN Theory Institute 'Heavy Ion Collisions at the LHC - Last Call for Predictions', held from May 14th to June 10th 2007

Medium-induced gluon radiation is usually identified as the dominant dynamical mechanism underling the {\it jet quenching} phenomenon observed in heavy-ion collisions. In its actual implementation, multiple medium-induced gluon emissions are assumed to be independent, leading, in the eikonal approximation, to a Poisson distribution. Here, we introduce a medium term in the splitting probabilities so that both medium and vacuum contributions are included on the same footing in a DGLAP approach. The improvements include energy-momentum conservation at each individual splitting, medium-modified virtuality evolution and a coherent implementation of vacuum and medium splitting probabilities. Noticeably, the usual formalism is recovered when the virtuality and the energy of the parton are very large. This leads to a similar description of the suppression observed in heavy-ion collisions with values of the transport coefficient of the same order as those obtained using the {\it quenching weights}., Comment: LaTeX, 18 pages, 13 figures included using epsfig, uses JHEP3; v2: enlarged discussions, one figure replaced, some references added, final version

We evaluate both the tau lepton energy loss produced by photonuclear interactions and the neutrino charged current cross section at ultra-high energies, relevant to neutrino bounds with Earth-skimming tau neutrinos, using different theoretical and phenomenological models for nucleon and nucleus structure functions. The theoretical uncertainty is estimated by taking different extrapolations of the structure function F2 to very low values of x, in the low and moderate Q2 range for the tau lepton interaction and at high Q2 for the neutrino-nucleus inelastic cross section. It is at these extremely low values of x where nuclear shadowing and parton saturation effects are unknown and could be stronger than usually considered. For tau and neutrino energies E=10^9 GeV we find uncertainties of a factor 4 for the tau energy loss and of a factor 2 for the charged current neutrino-nucleus cross section., Comment: 20 pages and 11 figures

Long-range correlations between multiplicities in different rapidity windows in hadron-nucleus collisions are analyzed. After recalling the standard results in the probabilistic model, we study them in the framework of perturbative QCD. Considering interacting BFKL pomerons in the form of fan diagrams coupled to a dilute projectile, analytic estimates are done for very large rapidities. The correlation strength results weakly depending on energy and centrality or nuclear size, and generically greater than unity. Finally, we turn to the Color Glass Condensate framework. For a saturated projectile and considering the most feasible experimental situation of forward and backward rapidity windows symmetric around the center-of-mass, the resulting correlation strength turns out to be larger than unity and shows a non-monotonic behavior with increasing energy, first increasing and then decreasing to a limiting value. Its behavior with increasing centrality or nuclear size depends on the considered rapidity windows., Comment: 17 pages, LaTeX, 6 eps figures included using graphicx; v2: error in the CGC formula corrected, conclusions of the corresponding section changed accordingly

We calculate some ${\cal O}(\alpha_s^2)$ corrections to the JIMWLK kernel in the framework of the light-cone wave function approach to the high energy limit of QCD. The contributions that we consider originate from higher order corrections in the strong coupling and in the density of the projectile to the solution of the classical Yang-Mills equations of motion that determine the Weizs\"acker-Williams fields of the projectile. We study the structure of these corrections in the dipole limit, showing that they are subleading in the limit of large number of colours $N$, and that they cannot be fully recast in the form of dipole degrees of freedom., Comment: 4 pages, LaTeX, 2 eps figures included using graphicx, uses enclosed iopart.cls; contribution to the proceedings of Quark Matter 2006 (Shanghai, November 14th-20th 2006)

In this work we calculate some O(\alpha_s^2) corrections to the JIMWLK kernel in the framework of the light-cone wave function approach to the high energy limit of QCD. The contributions that we consider originate from higher order corrections in the strong coupling and in the density of the projectile to the solution of the classical equations of motion that determine the Weizs\"acker-Williams fields of the projectile. We study the structure of these corrections in the dipole limit, showing that they are subleading in the large-N limit and that they cannot be fully recast in the form of dipole degrees of freedom, but rather present a complicated color structure., Comment: 17 pages, 3 figures. Comments added and typos corrected

The phenomenon of shadowing of nuclear structure functions at small values of Bjorken-$x$ is analyzed. First, multiple scattering is discussed as the underlying physical mechanism. In this context three different but related approaches are presented: Glauber-like rescatterings, Gribov inelastic shadowing and ideas based on high-density Quantum Chromodynamics. Next, different parametrizations of nuclear partonic distributions based on fit analysis to existing data combined with Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution, are reviewed. Finally, a comparison of the different approaches is shown, and a few phenomenological consequences of nuclear shadowing in high-energy nuclear collisions are presented., Comment: 33 pages, LaTeX, uses iopart and iopams styles; 22 eps figures included using graphicx. v2: comments and references added, results and conclusions unchanged, final version

We consider modifications of the standard non-linear QCD evolution in an attempt to account for some of the missing ingredients discussed recently, such as correlations, discreteness in gluon emission and Pomeron loops. The evolution is numerically performed using the Balitsky-Kovchegov equation on individual configurations defined by a given initial value of the saturation scale, for reduced rapidities $y=(\alpha_s N_c/\pi) Y<10$. We consider the effects of averaging over configurations as a way to implement correlations, using three types of Gaussian averaging around a mean saturation scale. Further, we heuristically mimic discreteness in gluon emission by considering a modified evolution in which the tails of the gluon distributions are cut-off. The approach to scaling and the behavior of the saturation scale with rapidity in these modified evolutions are studied and compared with the standard mean-field results. For the large but finite values of rapidity explored, no strong quantitative difference in scaling for transverse momenta around the saturation scale is observed. At larger transverse momenta, the influence of the modifications in the evolution seems most noticeable in the first steps of the evolution. No influence on the rapidity behavior of the saturation scale due to the averaging procedure is found. In the cut-off evolution the rapidity evolution of the saturation scale is slowed down and strongly depends on the value of the cut-off. Our results stress the need to go beyond simple modifications of evolution by developing proper theoretical tools that implement such recently discussed ingredients., Comment: 20 pages, LaTeX, 18 eps figures included using epsfig; changes in v3: new kind of averaging added, 5 new plots, discussions and conclusions extended, final version

The attenuation of heavy-flavored particles in nucleus-nucleus collisions tests the microscopic dynamics of medium-induced parton energy loss and, in particular, its expected dependence on the identity (color charge and mass) of the parent parton. We discuss the comparison of theoretical calculations with recent single-electron data from RHIC experiments. Then, we present predictions for the heavy-to-light ratios of D and B mesons at LHC energy., Comment: 3 pages, 2 figures, prepared for the PANIC 2005 Conference proceedings

In nucleus-nucleus collisions, high-pt electron spectra depend on the medium modified fragmentation of their massive quark parents, thus giving novel access to the predicted mass hierarchy of parton energy loss. Here we calculate these spectra in a model, which supplements the perturbative QCD factorization formalism with parton energy loss. In general, we find - within large errors - rough agreement between theory and data on the single inclusive electron spectrum in pp, its nuclear modification factor, and its azimuthal anisotropy. However, the nuclear modification factor depends on the relative contribution of charm and bottom production, which we find to be affected by large perturbative uncertainties. In order for electron measurements to provide a significantly more stringent test of the expected mass hierarchy, one must then disentangle the b- and c-decay contributions, for instance by reconstructing the displaced decay vertices., Comment: 9 pages RevTex, 4 eps-figures, asci-file containing numerical tables of results included

The ratio of nuclear modification factors of high-$p_T$ heavy-flavored mesons tolight-flavored hadrons (heavy-to-light ratio) is shown to be a sensitive tool to test medium-induced energy loss at RHIC and LHC energies. Heavy-to-light ratios of $D$ mesons at RHIC in the region $7

The solutions of the Balitsky-Kovchegov evolution equations are studied numerically and compared with known analytical estimations. The rapidity and nuclear size dependences of the saturation scale are obtained for the cases of fixed and running coupling constant. These same dependences are studied in experimental data, on lepton-nucleus, deuteron-nucleus and nucleus-nucleus collisions, through geometric scaling and compared with the theoretical calculations., Comment: 8 pages, 8 figures. Contribution based on talks given by J. G. Milhano and C. A. Salgado to the proceedings of ``Hard Probes 2004'', Ericeira (Portugal), November 4-10, 2004

We study the effects of low-$p_T$ collective flow on radiative energy loss from high-$p_T$ partons traversing the QCD medium created in high-energy nucleus-nucleus collisions. We illustrate this idea through three examples. Due to longitudinal flow, jet profiles at the LHC present marked asymmetries in the $\eta\times \phi$-plane, and widths in $\eta$ and $\phi$ of particle distributions associated with a high-$p_T$ trigger at RHIC become different. Finally, transverse flow implies an increase of high-$p_T$ $v_2$ at RHIC., Comment: LaTeX, 4 pages, 4 eps figs included using graphics, uses enclosed svepj.clo and svjour.cls; proceedings of Hard Probes 2004, Ericeira, Portugal, November 4th-10th 2004

The relation between diffraction in lepton-proton collisions and shadowing of nuclear structure functions which arises from Gribov inelastic shadowing, is described. A model realizing such relation, which produces a parameter-free description of experimental data on nuclear structure functions at small $x$, is presented. The application to the description of multiplicities in nuclear collisions is discussed and related to other approaches., Comment: LaTeX, 6 pages, 5 eps figures, uses enclosed ws-ijmpa.cls; invited talk given by N. Armesto at the Eighth Workshop on Non-Perturbative Quantum Chromodynamics, Paris, France, June 7th-11th 2004

Jet quenching studies play a prominent role in our current understanding of ultra-relativistic heavy ion collisions. In this review I first present the available formalism to compute medium-induced gluon radiation. Then I discuss its effect on single particle spectra, with dedicated attention to the case of the radiating parton being a massive quark. Next I examine more differential observables like jet shapes and multiplicities, and the consequences of flow on radiative energy loss. I conclude with some remarks., Comment: LaTeX, 8 pages, 7 eps figures, uses enclosed cjpsuppl.cls; invited talk at Physics at LHC, Vienna, Austria, July 13th-17th 2004

I present a brief review of the existing models for particle multiplicity evaluation in heavy ion collisions which are at our disposal in the form of Monte Carlo simulators. Models are classified according to the physical mechanisms with which they try to describe the different stages of a high-energy collision between heavy nuclei. A comparison of predictions, as available at the beginning of year 2000, for multiplicities in central AuAu collisions at the BNL Relativistic Heavy Ion Collider (RHIC) and PbPb collisions at the CERN Large Hadron Collider (LHC) is provided., Comment: LaTeX, 11 pages, 3 eps figures, uses enclosed jpconf.cls; invited talk at Focus on MULTIPLICITY: International Workshop on Particle Multiplicity in Relativistic Heavy Ion Collisions, Bari, Italy, June 17th-19th 2004

We study the effects of including a running coupling constant in high-density QCD evolution. For fixed coupling constant, QCD evolution preserves the initial dependence of the saturation momentum $Q_s$ on the nuclear size $A$ and results in an exponential dependence on rapidity $Y$, $Q^2_s(Y) = Q^2_s(Y_0) \exp{[ \bar\alpha_s d (Y-Y_0) ]}$. For the running coupling case, we re-derive analytical estimates for the $A$- and $Y$-dependences of the saturation scale and test them numerically. The $A$-dependence of $Q_s$ vanishes $\propto 1/ \sqrt{Y}$ for large $A$ and $Y$. The $Y$-dependence is reduced to $Q_s^2(Y) \propto \exp{(\Delta^\prime\sqrt{Y+X})}$ where we find numerically $\Delta^\prime\simeq 3.2$. We study the behaviour of the gluon distribution at large transverse momentum, characterizing it by an anomalous dimension $1-\gamma$ which we define in a fixed region of small dipole sizes. In contrast to previous analytical work, we find a marked difference between the fixed coupling ($\gamma \simeq 0.65$) and running coupling ($\gamma \sim 0.85$) results. Our numerical findings show that both a scaling function depending only on the variable $r Q_s$ and the perturbative double-leading-logarithmic expression, provide equally good descriptions of the numerical solutions for very small $r$-values below the so-called scaling window., Comment: LaTeX, 29 pages, 7 eps figures; discussion on DLL enlarged and comparison with sub-leading terms in the rapidity behaviour of the saturation scale added

Medium-induced gluon radiation from massless and massive quarks is treated in the same formalism. The dead cone which regulates gluon radiation from massive quarks in the vacuum at small angles, is filled in the medium but constitutes a small fraction of the available phase space. Our study indicates that the energy loss for charmed hadrons at RHIC should be smaller than for light hadrons, but still sizable., Comment: 4 pages, uses enclosed moriond.sty, 3 eps figures included using epsfig; presented by N. Armesto at the XXXIXth Rencontres de Moriond: QCD and High Energy Hadronic Interactions, La Thuile, March 28th-April 4th 2004, to appear in the proceedings

The idea of saturation of parton densities in small x physics is briefly introduced. Some aspects of saturation are described, mainly focusing on the status of our knowledge on the non-linear equations describing the high parton density regime. Implications of saturation ideas on the description of nuclear collisions at the Relativistic Heavy Ion Collider are discussed., Comment: 8 pages in LaTeX using enclosed appolb.cls, 3 eps figures included using epsfig; minireview at the XXXIIIrd International Symposium on Multiparticle Dynamics (Kracow, Poland, September 5th-11th 2003)

We discuss the importance of high-pT hadron and jet measurements in nucleus-nucleus collisions at the CERN Large Hadron Collider., Comment: The writeup of the working group "Jet Physics" for the CERN Yellow Report on "Hard Probes in Heavy Ion Collisions at the LHC", 123 pages. Subgroup convenors: R. Baier, X.N. Wang, U.A. Wiedemann (theory) and I.P. Lokhtin, A. Morsch (experiment). Editor: U.A. Wiedemann

This manuscript is the outcome of the subgroup ``PDFs, shadowing and $pA$ collisions'' from the CERN workshop ``Hard Probes in Heavy Ion Collisions at the LHC''. In addition to the experimental parameters for $pA$ collisions at the LHC, the issues discussed are factorization in nuclear collisions, nuclear parton distributions (nPDFs), hard probes as the benchmark tests of factorization in $pA$ collisions at the LHC, and semi-hard probes as observables with potentially large nuclear effects. Also, novel QCD phenomena in $pA$ collisions at the LHC are considered. The importance of the $pA$ program at the LHC is emphasized., Comment: The writeup of the working group "PDFs, shadowing and $pA$ collisions" for the CERN Yellow Report on Hard Probes in Heavy Ion Collisions at the LHC, 121 pages. Subgroup convenors: K.J. Eskola, J.w. Qiu (theory) and W. Geist (experiment). Editor: K.J. Eskola

A model for shadowing in nuclear structure functions at small $x$ and small or moderate $Q^2$ is presented using the relation with diffraction that arises from Gribov's reggeon calculus. A reasonable description of the experimental data is obtained with no fitted parameters. A comparison with predictions from other models is performed., Comment: 4 pages, LaTeX, uses enclosed moriond.sty, 2 eps figs included using epsfig; contribution to Rencontres de Moriond: QCD and High Energy Hadronic Interactions (Les Arcs, France, March 22nd-29th 2003)

A simple model for nuclear structure functions in the region of small $x$ and small and moderate $Q^2$, is presented. It is a parameter-free extension, in the Glauber-Gribov approach to nuclear collisions, of a saturation model for the nucleon. A reasonable agreement with experimental data on ratios of nuclear structure functions is obtained. The unintegrated gluon distribution and the behavior of the saturation scale which result from this model are discussed., Comment: LaTeX2e, uses enclosed moriond.sty, 4 pages, 2 eps figures included using epsfig, contribution to the XXXVIIIth Rencontres de Moriond: QCD and Hadronic Interactions, Les Arcs, France, March 22nd-29th 2003

Nuclear structure functions at small x and small or moderate $Q^2$ are studied using the relation with diffraction on nucleons which arises from Gribov's Reggeon Calculus. A reasonable description of experimental data is obtained with no fitted parameters. A comparison with other models and predictions for future lepton-ion colliders are provided. Consequences for the reduction of multiplicities in nucleus-nucleus collisions at energies of RHIC and LHC are examined., Comment: LaTeX, 32 pages, 14 eps figures included using epsfig; 1 reference updated

Different approaches to gluon shadowing at small x are reviewed. Some available results relevant for RHIC and LHC are compared., Comment: 6 pages, LaTeX2e, uses enclosed cernrep.cls, one eps figure enclosed using graphicx, contribution to the Yellow Report on Hard Probes in Heavy Ion Collisions at the LHC