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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 phenomeno-logical models for the PDFs and computations on discrete lattice, and for cross-fertilization with machine learning/AI approaches. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Large Hadronâ€"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 electronâ€"proton and protonâ€"proton operations. This report represents an update to the LHeC’s conceptual design report (CDR), published in 2012. It comprises new results on the parton structure of the proton and heavier nuclei, QCD dynamics, and electroweak and top-quark physics. It is shown how the LHeC will open a new chapter of nuclear particle physics by extending the accessible kinematic range of leptonâ€"nucleus scattering by several orders of magnitude. Due to its enhanced luminosity and large energy and the cleanliness of the final hadronic states, the LHeC has a strong Higgs physics programme and its own discovery potential for new physics. Building on the 2012 CDR, this report contains a detailed updated design for the energy-recovery electron linac (ERL), including a new lattice, magnet and superconducting radio-frequency technology, and further components. Challenges of energy recovery are described, and the lower-energy, high-current, three-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 that arise from the Higgs and parton-density-function physics programmes. This paper also presents novel results for the Future Circular Collider in electronâ€"hadron (FCC-eh) mode, which utilises the same ERL technology to further extend the reach of DIS to even higher centre-of-mass energies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The 〈 p t 〉 N ch - N ch correlations experimentally observed in the central rapidity region in pp and p $$ \bar p $$ collisions, in a wide energy range from the ISR to Tevatron, are described in the framework of a multi-Pomeron exchange model in which string collectivity has been included in an effective way. Three parameters are obtained from the fit to data: the string tension, the average number of particles per string, and a parameter which effectively introduces string collective effects. The model successfully reproduces the rise of 〈 p t 〉 of charged particles, the flattening with growing rapidity density of charged particles and with the collision energy, and the negative p t - N ch correlation at low energies. The string tension and the average number of particles per string are energy independent, while the parameter that includes effectively string collective effects shows a smooth increasing behavior with energy. [ABSTRACT FROM AUTHOR]

We study the effects of low- pT collective flow on radiative energy loss from high- pT 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- pT trigger at RHIC become different. Finally, transverse flow implies an increase of high- pT v2 at RHIC. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Nuclear structure functions at small x and small or moderate Q2 are studied using the relation with diffraction on nucleons which arises from Gribov's reggeon calculus. A reasonable description of the 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. [ABSTRACT FROM AUTHOR]

A simple model for nuclear structure functions in the region of small x and small and moderate Q2 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 the ratios of nuclear structure functions is obtained. Nuclear effects in the longitudinal-to-transverse cross section ratios are found to be small. Predictions of the model for values of x smaller than those available to present experiments are given. The unintegrated gluon distribution and the behaviour of the saturation scale which result from this model are shown and discussed. [ABSTRACT FROM AUTHOR]

Nuclear structure functions and cross-sections for heavy flavour production in lepton–nucleus collisions are investigated in the low x region accessible now or in the near future. The scattering on a heavy nucleus is described by the sum of fan diagrams of BFKL pomerons, which is exact in the high-colour limit. The initial condition for the evolution at x=0.01 is taken from a saturation model, which reproduces the experimental data on the proton. The $A$ dependence of the structure functions is well described by a power factor $A^\alpha$, with $\alpha$ reaching values as low as 1/2 at extremely low x. The total cross-sections for heavy flavour production reach values of the order of mb, and the corresponding transverse momentum distributions are sizable up to transverse momenta larger than the initial large scale $(Q^2+4m_f^2)^{1/2}$. [ABSTRACT FROM AUTHOR]

A Monte Carlo model to simulate nuclear collisions in the energy range going from SPS to LHC is presented. The model includes in its initial stage both soft and semihard components, which lead to the formation of color strings. Collectivity is taken into account considering the possibility of strings in color representations higher than triplet or antitriplet, by means of string fusion. String breaking leads to the production of secondaries. At this point, the model can be used as an initial condition for the further evolution by a transport model. In order to tune the parameters and see the results in nucleus–nucleus collisions, a naive model for rescattering of secondaries is introduced. Results of the model are compared with experimental data, and predictions for RHIC and LHC are shown. [ABSTRACT FROM AUTHOR]

Unintegrated gluon densities in nuclei, dipole-nucleus cross-sections and quark densities are numerically investigated in the high-color limit, with the scattering on a heavy nucleus exactly described by the sum of fan diagrams of BFKL pomerons. The initial condition for the evolution in rapidity is quickly forgotten, and the gluon density presents a “supersaturation” pattern, as previous studies indicated. Both dipole-nucleus cross-sections and quark densities present the expected saturation features. Identifying the position in transverse momentum l of the maximum of the gluon distribution with the saturation momentum $Q_{\mathrm{s}}(y,b)$, at large rapidities all distributions depend on only one variable, $l/Q_{\mathrm{s}}(y,b)$ or $rQ_{\mathrm{s}}(y,b)$. [ABSTRACT FROM AUTHOR]

Predictions on central rapidity densities of charged particles at energies of the relativistic heavy ion collider and the large hadron collider, for central collisions between the largest nuclei that will be available at these accelerators, are reviewed. Differences among the results of the existing models are discussed in relation with their underlying physical basis and with the possibilities to discriminate them. [ABSTRACT FROM AUTHOR]

The KNO scaling, the scaling of multiplicities, the behaviour of fluctuations in the transverse momentum as a function of the multiplicity and the long range correlations in nucleus-nucleus collisions are studied by a Monte Carlo code based on the string fusion model. It is shown that the fusion of strings produces a strong reduction of the long range correlations at high multiplicities, which could be detected experimentally. On the contrary the KNO scaling, the scaling of multiplicities and the behaviour of fluctuations in the transverse momentum are not modified when string fusion is included. [ABSTRACT FROM AUTHOR]

The EMC effect is studied in the perturbative QCD hard pomeron approach. In this framework the nuclear structure function can be expressed directly in terms of the proton one. In the limit x → 0 and for a nucleus with a constant density the effect is found to be a function of a single variable which combines its x-, Q- and A-dependence. The EMC ratio of the nuclear to nucleon structure functions goes to zero for x → 0 or/and A ≫ 1. At large Q the effect dies out as ln Q/ Q. To describe the present data at 0. 005 < x < 0. 05 an attempt is made to take into account subasymptotic effects by introducing an anomalous dimension falling with x. This leads to a weaker x- and Q-dependence, which almost disappears as x grows and the anomalous dimension becomes small. [ABSTRACT FROM AUTHOR]

Arguments are presented for the odderon intercept being exactly equal to unity. A variational method is presented based on a complete system of one-gluon functions. For the odderon, the highest intercept calculated by this method is 1 - (3 α/ π) 0.45. [ABSTRACT FROM AUTHOR]

The inclusion of string fusion in Dual Parton Model results in the appearance of diquark-antidiquark pairs in the sea with comparatively large Feynman- x. Such antidiquarks can fragment into fast antibaryons, thus increasing several times the corresponding yields in high energy pp collisions for x ∼ 0.8 ÷ 0.9. String fusion also results in an unusual dependence of inclusive spectra on the multiplicity of secondaries. Some numerical estimations are presented. [ABSTRACT FROM AUTHOR]