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The Electron–Ion Collider (EIC) is under construction at Brookhaven National Laboratory partnering with Jefferson Laboratory. The collider is designed for collisions of 70% polarized electrons and ions with luminosities up to \(L = 1\times 10^{34}~\mathrm {cm}^{-2}\mathrm {sec}^{-1}\) at the center-of-mass energies up to 140 GeV. The report summarizes the requirements, describes the design of the collider, and presents the present status of the project.

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In this paper, the current status of the studies on the electron-beam polarization at the Electron–Ion Collider are summarized.

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Spin is a unique probe to unravel the internal structure and QCD dynamics of nucleons. The exploration of the spin structure of nucleons is based on the complementarity of lepton scattering processes and purely hadronic probes. One of the main questions that physicists have been trying to address in spin experiments involving different interactions and probes is: how does the spin of the nucleon originate from its quark, anti-quark, and gluon constituents and their dynamics? These proceedings provide a snapshot of selected recent experimental results probing the longitudinal spin structure of nucleons utilizing both lepton scattering processes and hadron–hadron interactions, such as Deep Inelastic Scattering experiments in Jefferson Lab, CERN, and DESY, as well as the RHIC spin program with \(pp\) collisions. The future opportunities at the Electron–Ion Collider are also briefly described.

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The goal of LHCspin is to develop innovative solutions and cutting-edge technologies to access the field of spin physics over the next few years by exploring a unique kinematic regime and exploiting new reaction processes. To this end, a polarized gaseous target, operated in combination with the high-energy, high-intensity LHC beams and the highly performing LHCb particle detector, has the potential to open new physics frontiers and deepen our understanding of the intricacies of the strong interaction in the non-perturbative regime of QCD. This configuration, with center-of-mass energies per nucleon up to 115 GeV, using both proton and heavy-ion beams, covers a wide backward rapidity region, including the poorly explored high Bjorken-\(x\) and high Feynman-\(x\) regimes. This ambitious task is based on the recent installation of an unpolarised gas target (SMOG2) in the LHCb spectrometer. This setup not only constitutes a unique project but also provides an invaluable playground for its polarized upgrade. This article provides an overview of the physics potential, a description of the LHCspin experimental setup, and the first output of the SMOG2 system.

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Both deeply-virtual and photoproduction of mesons offer promising access to generalized parton distributions and complementary description of different kinematical regions. The higher-order contributions offer stabilizing effect with respect to the dependence on renormalization scales, while higher-twist effects have been identified as especially important in the case of the production of pseudo-scalar mesons. This was confirmed by the recent evaluation of the complete twist-3 contribution to \(\pi \) and \(\eta \)/\(\eta '\) photoproduction and its confrontation with experimental data.

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In recent years, there has been a breakthrough in lattice calculations of \(x\)-dependent partonic distributions. This encompasses also distributions describing the 3D structure of the nucleon, such as generalized parton distributions (GPDs). We report on a new method of accessing GPDs in asymmetric frames of reference, relying on a novel Lorentz-covariant parametrization of the accessed off-forward matrix elements in boosted nucleon states. The approach offers the possibility of computationally more efficient determination of the full parameter dependence of GPDs and as such, it can contribute to better understanding of nucleon’s structure.

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We analyze off-shell effects in the generalized parton distributions (GPDs) of the pion in the context of the Sullivan electroproduction process, as well as the corresponding half-off-shell electromagnetic and gravitational form factors. We illustrate our general results within a chiral quark model, where the off-shell effects show up at a significant level, indicating their contribution to uncertainties in the extraction of the GPDs from future experimental data.

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A small-\(x\) helicity evolution has been derived in 2016–2018 and received an important modification in 2022. This article discusses its general framework and summarizes recent theoretical developments, including the asymptotic behaviors of helicity PDFs and \(g_1\) structure function at small \(x\). The latest fits to various polarized scattering data are also discussed. The results from this research program will provide important theoretical inputs for the future polarized small-\(x\) measurements at the EIC.

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We make predictions for the cross section of coherent \(J/\psi \) photoproduction in Pb–Pb and O–O ultraperipheral collisions (UPCs) at the LHC as a function of the \(J/\psi \) rapidity \(y\) in the framework of collinear factorization and next-to-leading order (NLO) perturbative QCD. We quantify the strong scale dependence and significant uncertainties due to nuclear PDFs and show that our approach provides a reasonable description of the LHC data on coherent \(J/\psi \) photoproduction in Pb–Pb UPCs. We demonstrate that these uncertainties are reduced by approximately a factor of 10 in the scaled ratio of the O–O and Pb–Pb UPC cross sections. Our analysis indicates the dominance of the quark contribution to the UPC cross section at central rapidities, which affects the interpretation of the UPC data.

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At the LHC we are colliding protons, but it is not the protons that are doing the interacting. It is their constituents: the quarks, antiquarks, and gluons — collectively known as partons. We need to know what fractional momentum of the proton each of these partons takes at the energy scale of LHC collisions, in order to understand the LHC physics. Such parton momentum distributions are known as PDFs (Parton Distribution Functions) and are a field of study in their own right. However, it is now the case that the uncertainties on PDFs are a major contributor to the background to the discovery of physics Beyond the Standard Model (BSM). Firstly, in searches at the highest energy scales of a few TeV, and secondly, in precision measurements of Standard Model (SM) parameters such as the mass of the \(W\) boson, \(m_W\), or the weak mixing angle, \(\sin ^2\theta _\mathrm {W}\), which can provide indirect evidence for the BSM physics in their deviations from SM values.

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In the framework of collinear factorization and next-to-leading order (NLO) perturbative QCD, we make predictions for inclusive and diffractive dijet photoproduction in electron–proton and electron–nucleus scattering in the EIC kinematics. We establish kinematic ranges in the \({\bar p}_{\mathrm {T}}\), \({\bar \eta }\), \(x_A^{\mathrm {obs}}\), and \(x_{\gamma }^{\mathrm {obs}}\) variables, quantify sensitivity to small-\(x\) nuclear PDFs, and analyze various scenarios of factorization breaking in the case of diffractive scattering.

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The High-Luminosity Large Hadron Collider (HL-LHC), a major upgrade of the LHC, is set to operate in 2029. The HL-LHC aims to achieve higher instantaneous luminosities to allow exploration of the rarest production processes of the Standard Model (SM). The central exclusive production (CEP) process in proton–proton collisions at the HL-LHC can only be explored using a forward proton spectrometer (FPS), a set of near-beam detectors located a few hundred meters from the proton–proton interaction point. During LHC Run 2, the ATLAS and CMS collaborations installed FPSs delivering a broad range of physics results. The accelerator complex will be rearranged for the HL-LHC, and a new FPS detector design is under development. The CEP study offers a unique opportunity to observe the rarest SM processes and search for physics beyond the SM, including axion-like particles or anomalous gauge couplings.

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The Electron–Ion Collider provides the opportunity to drastically advance our understanding of QCD and the multidimensional structure of both protons and nuclei. An essential component of the EIC physics program is the identification and characterization of exclusive, diffractive, and tagged events using detectors integrated with the outgoing hadron beam-line, the so-called “far-forward” detectors. The ePIC experiment includes a suite of far-forward detectors designed to deliver the necessary geometric coverage and resolution required to achieve the exclusive physics program envisioned at the EIC. In addition to the multidimensional imaging program at the EIC, topics such as spectator tagging in \(e+d\) and \(e+{^3}\)He reactions to access structure functions and searches for gluon saturation in \(e + A\) collisions are also enabled by this experimental apparatus. In these proceedings, the ePIC far-forward detectors will be briefly introduced, and a few selected physics topics focused on tagged deep-inelastic scattering will be discussed.

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We discuss recent developments towards next-to-leading order (NLO) accuracy in the dipole picture. We review recent NLO results for exclusive vector meson production and diffractive structure functions, and discuss how it is becoming possible to describe both inclusive and exclusive DIS data simultaneously within the Color Glass Condensate framework at NLO accuracy. These developments will make it possible to probe the gluon saturation phenomena in detail, especially when nuclear-DIS data from the EIC become available.

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The two-tensor-Pomeron model is applied to deeply virtual Compton scattering (DVCS) on a proton. A good description of the DVCS HERA data at small Bjorken-\(x\) is achieved due to a sizeable interference of soft- and hard-Pomeron contributions. We present two fits which differ somewhat in the strength of the hard-Pomeron contribution. We describe, in the same framework, both the low-\(Q^{2}\) and high-\(Q^{2}\) regimes and the transition between them. We find that the soft-Pomeron contribution is considerable up to \(Q^{2} \sim 20\) GeV\(^{2}\). The reggeon exchange term is particularly relevant for describing the scattering of a real photon on a proton measured at lower \(\gamma p\) energies at FNAL. We find that the ratio of \(\gamma ^{*} p \to \gamma p\) cross sections for longitudinally and transversely polarized virtual photons strongly increases with \(t\). Our findings may be checked in future lepton–nucleon scattering experiments in the low-\(x\) regime, for instance, at a future Electron–Ion Collider (EIC) at the BNL and LHeC at the LHC.

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In these proceedings, we calculate double-spin asymmetry (DSA) in exclusive dijet production in \(ep\) collisions and we demonstrate for the first time that the \(\cos (\phi )\) angular correlation between the scattered electron and proton is a simultaneous probe of the gluon orbital angular momentum and its interplay with the gluon helicity. We make a rough estimate of the DSA for the kinematics of the Electron–Ion Collider.

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A new physics program has been initiated as part of the ongoing LHC physics run in the far-forward region, where dedicated FASER and SND@LHC experiments are currently taking data. We discuss the possible discovery prospects of this program in the search for signatures of beyond the Standard Model physics. We focus on both the present period and the proposed future Forward Physics Facility (FPF) that will operate in the high luminosity LHC era.

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Exotic hadrons are particles with quantum numbers that do not fit into three-quarks or quark–antiquark patterns. In this paper, very recent discoveries are presented: first pentaquark with a strange content, tetraquark isospin pair in decays to \(D_s\pi \), and another tetraquark in \(D_sD_s\) final state.

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We clarify two issues related to the so-called \(D\)-term in matrix elements of the energy-momentum tensor. First, we show that in a stable system, the \(D\)-term can have either sign, contrary to claims that it must be negative. Second, we demonstrate a logarithmic enhancement of the \(\mathcal {\alpha }\) correction to the \(D\)-term in any state of the hydrogen atom. We contrast this enhancement with the Lamb shift where it is present only in \(S\)-states.

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Here, we review the physics programme at the proposed Large Hadron-electron Collider at the High Luminosity Large Hadron Collider, and Future Circular Collider in electron–hadron mode. We consider Quantum Chromodynamics in both electron–proton and electron–nucleus collisions, and Electroweak, Top, Higgs, and Beyond the Standard Model physics. We comment on the synergies with other collision systems, \(e^+e^-\) and hadron–hadron, and the physics possibilities with a joint electron–hadron/hadron–hadron detector.

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The development of ERLs has been recognized as one of the five main pillars of accelerators R&D in support of the European Strategy for Particle Physics (ESPP). The ERL Roadmap Panel recognized the PERLE project as “a central part of the roadmap for the development of energy-recovery linacs”, with milestones to be achieved by the next ESPP in 2026. PERLE at Orsay is a project aiming at the construction of a novel ERL machine for the development and application of the energy recovery technique in multi-turn configuration, large current, and large energy regime. It will operate in a 3-turns mode, first at 250 MeV, then upgraded to 500 MeV with 20 mA beam current. Such challenging parameters make PERLE a unique multi-turn ERL facility operating at an unexplored operational power regime (10 MW), studying and validating a broad range of accelerator phenomena, paving the way for the future larger-scale ERLs. The PERLE machine opens a new frontier for the physics of “the electromagnetic probe”. It will be the first ERL dedicated to Nuclear Physics for studying the \(eN\) interaction with radioactive nuclei. PERLE is also the necessary demonstrator for the future HEP machine (LHeC/FCC-eh) (the same technological choices and beam parameters). PERLE could also host elastic \(ep\) scattering experiments and experiments on Nuclear Photonics using inverse Compton scattering gammas. In this paper, we will present the PERLE project focusing on the challenges of accelerators physics and presenting the possible physics applications. We will also show the project structuration in an international collaboration and a timeline for the TDR phase and the following staged construction steps toward the PERLE machine at its nominal performances.

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Deep Inelastic Scattering would be brought into the unexplored TeV regime by the proposed Large Hadron Electron Collider at CERN. Its rich physics program includes both precision Standard Model measurements to complement LHC physics as well as studies of QCD in the high-energy limit. The present contribution reports on studies included in the updated LHeC Conceptual Design Report. We study the impact of LHeC simulated data on Parton Distribution Functions uncertainties. We also assess the LHeC potential to allow for the determination of the strong coupling constant \(\alpha _\mathrm {S}\), at the per-mille level as well as to disentangle between various scenarios of small-\(x\) QCD.

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Large Hadron electron Collider (LHeC) and its more energetic counterpart, the Future Circular electron–hadron Collider (FCC-eh), are proposals for next-generation Deep Inelastic Scattering facilities at CERN. Both experiments would perform electron–proton and electron–nucleus collisions at high energy and luminosity. In this paper, I present an overview of the possibilities for exploring nuclear physics with \(eA\) collisions at the LHeC and FCC-eh.

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Double deeply virtual Compton scattering (DDVCS) is the process where an electron scatters off a nucleon and produces a lepton pair. The main advantage of this process in contrast with deeply virtual and timelike Compton scatterings (DVCS and TCS) is the possibility of directly measuring GPDs for \(x\neq \pm \xi \) at leading order in \(\alpha _{\mathrm {s}}\) (LO). We present a new calculation of the DDVCS amplitude based on the methods developed by R. Kleiss and W.J. Stirling in the 1980s. These techniques produce expressions for amplitudes that are perfectly suited for implementation in numerical simulations. Via the PARTONS software, the correctness of this new formulation has been tested by comparing the DVCS and TCS limits of DDVCS with independent calculations of DVCS and TCS.

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In this work, we derive the cross section for inclusive DIS dijet production at full next-to-eikonal order. We include the corrections that stem from taking a finite width of the target, the interaction of the quark with the transverse component of the background field, and also the dynamics of the target.

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Studying high-energy hadronic scattering processes to understand the structure of nuclei has been the focus of experimental and theoretical studies for more than three decades now. The Color Glass Condensate effective theory has been developed and used to study high-energy proton–nucleus collisions in particular. One of the main approximations adopted in the Color Glass Condensate is the so-called eikonal approximation, which amounts to neglecting power-suppressed corrections in the high-energy limit. This approximation is well justified for asymptotically high energies, however, corrections to it might be sizable in practice, in particular at the Relativistic Heavy Ion Collider and upcoming Electron Ion Collider. Here, we will briefly review the eikonal approximation and present the computation of a gluon propagator through the target at next-to-eikonal accuracy. Furthermore, we will present its application to gluon production in proton–nucleus collisions.

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The first observation of the \({\mit \Lambda }_b^0 \rightarrow D_s^- p\) decay is presented using proton–proton collision data collected by the LHCb experiment at a centre-of-mass energy of \(\sqrt {s}=13\) TeV, corresponding to a total integrated luminosity of \(6\,{\mathrm {fb}}^{-1}\). Using the \({\mit \Lambda }_b^0 \rightarrow {\mit \Lambda }_c^+ \pi ^-\) decay as the normalisation mode, the branching fraction of the \({\mit \Lambda }_b^0 \rightarrow D_s^- p\) decay is measured to be \(\mathcal {B}({\mit \Lambda }_b^0 \rightarrow D_s^- p)\) \(= (12.6 \pm 0.5 \pm 0.3 \pm 1.2) \times 10^{-6}\), where the first uncertainty is statistical, the second systematic, and the third due to uncertainties in the branching fractions of the \({\mit \Lambda }_b^0 \rightarrow {\mit \Lambda }_c^+ \pi ^-\), \(D_s^- \rightarrow K^- K^+ \pi ^-\), and \({\mit \Lambda }_c^+ \rightarrow p K^- \pi ^+\) decays.

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The one-loop contributions to the branching ratios for leptonic \(\tau \) decays are calculated in two Higgs doublet models. The analysis focuses on the effect of charged Higgs and on the basic supersymmetric extension, the minimal supersymmetric Standard Model (MSSM).

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We present our results concerning elastic and semi-elastic photon-initiated \(e^{+}e^{-}\) pair production processes in proton–nucleus collisions at the LHC energy. In the calculations, the \(k_{\mathrm {T}}\)-factorization approach was used, and the research area was divided into low-mass region (LMR) and intermediate-mass region (IMR) according to the ALICE Collaboration definition. The one- and two-dimensional distributions of various kinematic variables obtained on the basis of various parameterizations of the proton structure function tested here in the non-perturbative region of small \(Q^{2}\) and small \(W\) are discussed further on. The values of the gap survival factor for this type of processes are also presented.

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A significant part of the particle physics programme at the Large Ha-dron Collider (LHC) at CERN focuses on searching for potential signs of processes beyond the Standard Model. An example of such phenomena would be the discovery of the charged Higgs boson decaying into \(\tau \) lepton and neutrino that is predicted by theories such as Supersymmetry. Identification of hadronically decaying \(\tau \) leptons plays a crucial role in \(\tau \)-related studies and misidentification of such decays can lead to extra background events. This paper presents an overview of the \(H^{\pm }\to \tau \nu \) analysis based on 2015+2016 data recorded with the ATLAS detector at the LHC and shows the usage of the data-driven Fake Factor method for fake \(\tau \) background modelling. The systematics associated with the method is also discussed.

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This contribution summarizes motivation and experimental methodology of lepton-flavour violation searches, based on the \(B^0 \to K^{*0}\mu ^\pm e^\mp \) and \(B_s^0\to \phi \mu ^\pm e^\mp \) decays.

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We calculate the differential cross section d\(\sigma /\)d\(t\) for the diffractive photoproduction process \(\gamma p \to \rho p\) and compare it to recent experimental data extracted by the CMS Collaboration. Our model is based on two-gluon exchange in the non-perturbative domain. We take into account both the helicity-conserving and the often neglected helicity-flip amplitudes in the \(\gamma \to V\) transition, which can contribute at finite \(t\). The shape of the differential crosssection as well as the role of helicity-flip processes is strongly related to the dependence of the unintegrated gluon distribution on the transverse momenta in the non-perturbative region. Results for different unintegrated gluon distribution are shown.

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Nuclear parton distribution functions (nPDFs) are crucial in studying nuclear structure and high-energy nuclear collisions. nPDFs have been determined via ‘global QCD analyses’, in which the nPDF-dependent predictions for a given process are compared with their actual measurements. One of the challenging parts of nPDF extractions is the estimation of uncertainties. The most common approach for this purpose is the Hessian method, which, however, has certain shortcomings, especially in the case of weaker data constraints. Here, we will show a case study for an alternative approach where nPDF uncertainties are estimated using Markov Chain Monte Carlo (MCMC) methods.

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This document presents the LHCb results for the published analyses of Central Exclusive Production of \(J/\psi \) and \(\psi (2S)\) mesons with 13 TeV \(pp\) data, together with a summary of the ongoing \(\phi \rightarrow \mu \mu \) analysis. The first results in a unique LHCb acceptance at as-of-today highest collision energies make a valuable contribution to probe QCD predictions.