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In this paper we will provide an overview of the hadron colliders built to date and the design and operational challenges that each of these machines has faced. Many of these are inherent to the ongoing effort to optimise the instantaneous and integrated luminosity of the machines, which inevitably lead to many technological challenges that must be met and overcome. We will summarise how these challenges have been successfully met in the past and present machines and outline the role they could play in ambitious future accelerator projects such as the HL-LHC upgrade and the FCC project.

We present the formalism of hadron-to-two-hadron transition generalized parton distributions (GPDs) for spinless hadron case. Definitions of the twist-2 unpolarized and polarized $π\toππ$ transition GPDs are introduced with a particular choice of kinematic variables that characterize the produced two-pion system. In the vicinity of $ρ(770)$, we work out the two-pion decay angular distributions of the $e^-π\to e^-γππ$ cross section, incorporating both the Bethe-Heitler and deeply virtual Compton scattering processes. Each cross section exhibits a distinctive angular distribution, which is sensitive to the polarization states of the produced $ρ(770)$ resonance. In addition, we construct the double partial-wave expansion of $π\toππ$ transition GPDs in the two-pion decay angles as a generalization of GPDs for transition from a pion to a spin-$\ell$ resonance state. With the help of the Omnès representation, we constrain the $π\toππ$ transition GPDs in terms of the low energy $ππ$ scattering phase shift and build a phenomenological model for these GPDs.

The emergence of hadron mass represents one of the most challenging and still open problems in contemporary hadron physics. The results on the nucleon resonance electroexcitation amplitudes available from the CLAS data on $πN$ and $π^+π^-p$ electroproduction analyzed within the continuum Schwinger method open up a new avenue for gaining insight into the strong interaction dynamics that are responsible for the generation of the dominant part of hadron mass. Future prospects of these studies in experiments of the 12-GeV era with CLAS12 and after a potential increase of the CEBAF energy up to 22 GeV will offer a unique opportunity to explore the full range of distances where the dominant part of hadron mass and $N^*$ structure emerge from QCD.

We discuss the general behavior of the near-threshold scattering amplitude with channel couplings. The signal of the exotic hadrons near the threshold may manifest as a dip structure in the cross section originated from a zero point of the scattering amplitude. Such a dip structure by the zero point cannot be reproduced by the Flatté amplitude which is widely used for the analysis of exotic hadrons, because of the constraints imposed on the Flatté amplitude near the threshold. In this work, we propose the General amplitude which can describe the dip structure near the threshold, in contrast to the Flatté amplitude. Moreover, we numerically study the behavior of the near-threshold cross section in relation to the zero point.

We compute total and differential elastic cross sections of high-energy hadronic collisions in the loop-loop correlation model that provides a unified description of hadron-hadron, photon-hadron, and photon-photon reactions. The impact parameter profiles of pp and gamma*p collisions are calculated. For ultra-high energies the hadron opacity saturates at the black disc limit which tames the growth of the hadronic cross sections in agreement with the Froissart bound. We compute the impact parameter dependent gluon distribution of the proton xG(x,Q^2,b) and find gluon saturation at small Bjorken x. These saturation effects manifest S-matrix unitarity in hadronic collisions and should be observable in future cosmic ray and accelerator experiments at ultra-high energies. The c.m. energies and Bjorken x at which saturation sets in are determined and LHC and THERA predictions are given.

The string+${}^3P_0$ model of spin-dependent hadronization is applied to the fragmentation of a string stretched between a quark and an antiquark with entangled spin states, assumed to be produced in the $e^+e^-$ annihilation process. The model accounts systematically for the spin correlations in the hadronization chain and is formulated as a recursive recipe suitable for the implementation in a Monte Carlo event generator. The recipe is applied to the production of two back-to-back pseudoscalar mesons produced in $e^+e^-$ annihilation, and it is shown to reproduce the form of the azimuthal distribution of the hadrons as expected in QCD.

Recent developments in hadron spectroscopy triggers the discussion on various exotic configurations beyond the simple three-quark state for baryons and quark-anti-quark pair for mesons. In particular, the states observed near a two-hadron threshold are often regarded as candidates of hadronic molecules, which are made of constituent hadrons and dynamically generated by the hadronic interactions. However, identification of the hadronic molecules involves several subtle difficulties which are often overlooked or underestimated. Here we summarize these subtleties and present a promising approach to distinguish the dynamically generated states from others using observable quantities.

Baryon-strangeness correlations ($C_{BS}$) are studied with a hadron/string transport approach (UrQMD) and a dynamical quark recombination model (quark molecular dynamics, qMD) for various energies from $E_{lab}=4A$ GeV to $\sqrt{s_{NN}}=200$ GeV. As expected, we find that the hadron/string dynamics shows correlations similar to a simple hadron gas. In case of the quark molecular dynamics, we find that initially the $C_{BS}$ correlation is that of a weakly interacting QGP but changes in the process of hadronization also to the value for a hadron gas. Therefore, we conclude that the hadronization process itself makes the initial baryon strangeness correlation unobservable. To make an experimental study of this observable more feasible, we also investigate how a restriction to only charged kaons and $Λ$'s (instead of all baryons and all strange particles) influences the theoretical result on $C_{BS}$. We find that a good approximation of the full result can be obtained in this limit in the present simulation.

We discuss coexistence/mixing of different natures of hadronic composite (molecule) and elementary (quark-intrinsic) ones in hadron resonances. The discussions here are based on our previous publications on the origin of hadron resonances \cite{Hyodo:2008xr}, exotic $\bar D$ meson-nucleons as hadronic composites containing one anti-heavy quark \cite{Yamaguchi:2011xb}, and the study of $a_1$ as a typical example to show explicitly the mixing of the two different natures \cite{Nagahiro:2011jn}. In all cases, interactions are derived from the chiral dynamics of the light flavor sector. These interactions generate in various cases hadronic composite/molecule states, serving varieties of structure beyond the conventional quark model.

The ability to reliably measure the energy of an excited hadron in Lattice QCD simulations hinges on the accurate determination of all lower-lying energies in the same symmetry channel. These include not only single-particle energies, but also the energies of multi-hadron states. This talk deals with the determination of multi-hadron energies in Lattice QCD. The group-theoretical derivation of lattice interpolating operators that couple optimally to multi-hadron states is described. We briefly discuss recent algorithmic developments which allow for the efficient implementation of these operators in software, and present numerical results from the Hadron Spectrum Collaboration.

Nucleus-nucleus collisions offer a great opportunity for analyzing and determining the intrinsic nature of heavy and exotic hadrons. In this sense, here we discuss how the production and dissociation of hadron states are affected by reactions during the expansion of hadronic matter in a heavy-ion collision environment. We give emphasis to recent works on exotic states, revisiting as a case study the time evolution of the abundances of the $X_{0,1}(2900)$ states.

Most of the exotic hidden-charm hadrons discovered over the last 20 years fit neatly into the quark model as normal mesons and baryons if the existence of a seventh flavor of quark is hypothesized. For the quark to reproduce the spectrum (mass, spin, parity) of exotic hadrons, it would have to have a mass of $\sim$2.9 GeV and a charge of $-\tfrac{1}{3}$. The observed production and decay modes of these hadrons can be reproduced by a model that also includes light scalar bosons.

We study the effect of hadron masses on the leading power correction of dijet event-shape distributions. We define the transverse velocity operator, that describes the effects of hadron masses. It depends on the "transverse velocity" r, which is different from one only for non-vanishing hadron masses. We find that hadron-mass effects in general break universality. However we provide a simple method to identify universality classes of event shapes with a common power correction. We also compute the anomalous dimension of the power correction and the structure of the corresponding Wilson coefficient, finding a nontrivial result.

In order to get a more realistic description of the hadron spectrum we extend a constituent-quark model by explicit mesonic degrees of freedom. The resulting system of constituent (anti)quarks, which are subject to an instantaneous confining force, and mesons, which couple directly to the quarks, is treated by means of a relativistic coupled-channel framework. It can be formally shown that the mass-eigenvalue problem for such a system is equivalent to a hadronic eigenvalue problem in which the eigenstates of the pure confinement potential (bare hadrons) are coupled via meson loops. Following this kind of approach we have calculated hadron masses and decay widths for a simple toy model.

Today, hadron physics research occurs at Fermilab as parts of broader experimental programs. This is very likely to be the case in the future. Thus, much of this presentation focuses on our vision of that future - a future aimed at making Fermilab the host laboratory for the International Linear Collider (ILC). Given the uncertainties associated with the ILC - the level of needed R&D, the ILC costs, and the timing - Fermilab is also preparing for other program choices. I will describe these latter efforts, efforts focused on a Proton Driver to increase the numbers of protons available for experiments. As examples of the hadron physics which will be coming from Fermilab, I summarize three experiments: MIPP/E907 which is running currently, and MINER A and Drell-Yan/E906 which are scheduled for future running periods. Hadron physics coming from the Tevatron Collider program will be summarized by Arthur Maciel in another talk at Hadron05.

In this talk, I focus on the quark-gluon structure of hadrons probed using high-energy hadron beams. I start with a brief review on recent major achievements in measuring parton distributions of the nucleon, pion, and kaon, with hadron facilities at CERN and FNAL\@. Then I discuss a number of outstanding questions and interesting physics issues in the field, and point out their intellectual impact on nuclear physics as a whole. While advocating a continuing exploitation of hadron beams at CERN and FNAL, I strongly emphasize the role of a polarized RHIC, where a major nuclear physics program on the structure of hadrons can thrive.

High energy hadron colliders have been the tools for discovery at the highest mass scales of the energy frontier from the SppS, to the Tevatron and now the LHC. This report reviews future hadron collider projects from the high luminosity LHC upgrade to a 100 TeV hadron collider in a large tunnel, the underlying technology challenges and R&D directions and presents a series of recommendations for the future development of hadron collider research and technology.

The BaBar Collaboration has an intensive program of studying hadronic cross sections at low-energy $e^+e^-$ collisions, accessible via initial-state radiation. Our measurements allow significant improvements in the precision of the predicted value of the muon anomalous magnetic moment, that shed light on the current $\approx$ 3.5 sigma difference between the predicted and the experimental values. We have published results on a number of processes with two to six hadrons in the final state. We report here the results of recent studies with the final states that constitute the main contribution to the hadronic cross section below 3 GeV, as $e^+e^- \rightarrow π^+π^-$, $K^+K^-$, $K_S K_L$ and $e^+e^- \rightarrow 4$ hadrons.

In these lectures I first give a motivation for investigations of in-medium properties of hadrons. I discuss the relevant symmetries of QCD and how they might affect the observed hadron properties. I then discuss at length the observable consequences of in-medium changes of hadronic properties in reactions with elementary probes, and in particular photons, on nuclei. Here I put an emphasis on new experiments on changes of the sigma and omega mesons in medium.