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In this article we address the physical basis of the deviation of hadron shapes from spherical symmetry (non-spherical amplitudes) with focus on the nucleon and $Delta$. An overview of both the experimental methods and results and the current theoretical understanding of the issue is presented. At the present time the most quantitative method is the $gamma^{*} p to Delta$ reaction for which significant non-spherical electric (E2) and Coulomb quadrupole (C2) amplitudes have been observed with good precision as a function of Q^{2} from the photon point through 6 GeV^{2}. Quark model calculations for these quadrupole amplitudes are at least an order of magnitude too small and even have the wrong sign. Lattice QCD, chiral effective field theory, and dynamic model calculations which include the effects of the pion-cloud are in approximate agreement with experiment. This is expected due to the spontaneous breaking of chiral symmetry in QCD and the resulting, long range (low Q^{2}) effects of the pion-cloud. Other observables such as nucleon form factors and virtual Compton scattering experiments indicate that the pion-cloud is playing a significant role in nucleon structure. Semi-inclusive deep inelastic scattering experiments with transverse polarized beam and target also show the effect of non-zero quark angular momentum.
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Surprisingly enough, the ratio of elastic to inelastic cross sections of proton interactions increases with energy in the interval correspond- ing to ISR - LHC (i.e. from 10 GeV to 10 TeV). That leads to special features of their spatial interaction region at these and higher ener- gies. Within the framework of some phenomenological models, we show how the particular ranges of the transferred momenta measured in elastic scattering experiments expose the spatial features of the in- elastic interaction region according to the unitarity condition. The difference between their predictions at higher energies is discussed. The notion of central and peripheral collisions of hadrons is treated in terms of the impact parameters description. It is shown that the shape of the differential cross section in the diffraction cone is mostly determined by collisions with intermediate impact parameters. Elastic scattering at very small transferred momenta is sensitive to peripheral processes with large impact parameters. The role of central collisions in formation of the diffraction cone is less significant.
Hadron spectroscopy provides direct physical measurements that shed light on the non-perturbative behavior of quantum chromodynamics (QCD). In particular, various exotic hadrons such as the newly observed $T_{cc}^+$ by the LHCb collaboration, offer unique insights on the QCD dynamics in hadron structures. In this letter, we demonstrate how heavy ion collisions can serve as a powerful venue for hadron spectroscopy study of doubly charmed exotic hadrons by virtue of the extremely charm-rich environment created in such collisions. The yields of $T_{cc}^+$ as well as its potential isospin partners are computed within the molecular picture for Pb-Pb collisions at center-of-mass energy $2.76~mathrm{TeV}$. We find about three-order-of-magnitude enhancement in the production of $T_{cc}^+$ in Pb-Pb collisions as compared with the yield in proton-proton collisions, with a moderately smaller enhancement in the yields of the isospin partners $T_{cc}^0$ and $T_{cc}^{++}$. The $T_{cc}^+$ yield is comparable to that of the $X(3872)$ in the most central collisions while shows a considerably stronger decrease toward peripheral collisions, due to a threshold effect of the required double charm quarks for $T_{cc}^+$. Final results for their rapidity and transverse momentum $p_T$ dependence as well as the elliptic flow coefficient are reported and can be tested by future experimental measurements.
The propagation of colored quarks through strongly interacting systems, and their subsequent evolution into color-singlet hadrons, are phenomena that showcase unique facets of Quantum Chromodynamics (QCD). Medium-stimulated gluon bremsstrahlung, a fundamental QCD process, induces broadening of the transverse momentum of the parton, and creates partonic energy loss manifesting itself in experimental observables that are accessible in high energy interactions in hot and cold systems. The formation of hadrons, which is the dynamical enforcement of the QCD confinement principle, is very poorly understood on the basis of fundamental theory, although detailed models such as the Lund string model or cluster hadronization models can generally be tuned to capture the main features of hadronic final states. With the advent of the technical capability to study hadronic final states from lepton scattering with good particle identification and at high luminosity, a new opportunity has appeared. Study of the characteristics of parton propagation and hadron formation as they unfold within atomic nuclei are now being used to understand the coherence and spatial features of these processes and to refine new experimental tools that will be used in future experiments. Fixed-target data on nuclei with lepton and hadron beams, and collider experiments involving nuclei, all make essential contact with these topics and they elucidate different aspects of these same themes. In this paper, a survey of the most relevant recent data and its potential interpretation will be followed by descriptions of planned experiments at Jefferson Lab following the completion of the 12 GeV upgrade, and feasible measurements at a future Electron-Ion Collider.
Colliding high energy hadrons either produce new particles or scatter elastically with their quantum numbers conserved and no other particles produced. We consider the latter case here. Although inelastic processes dominate at high energies, elastic scattering contributes considerably (18-25%) to the total cross section. Its share first decreases and then increases at higher energies. Small-angle scattering prevails at all energies. Some characteristic features are seen that provide informationon the geometrical structure of the colliding particles and the relevant dynamical mechanisms. The steep Gaussian peak at small angles is followed by the exponential (Orear) regime with some shoulders and dips, and then by a power-law drop. Results from various theoretical approaches are compared with experimental data. Phenomenological models claiming to describe this process are reviewed. The unitarity condition predicts an exponential fall for the differential cross section with an additional substructure to occur exactly between the low momentum transfer diffraction cone and a power-law, hard parton scattering regime under high momentum transfer. Data on the interference of the Coulomb and nuclear parts of amplitudes at extremely small angles provide the value of the real part of the forward scattering nuclear amplitude. The real part of the elastic scattering amplitude and the contribution of inelastic processes to the imaginary part of this amplitude (the so-called overlap function) at nonforward transferred momenta are also discussed. Problems related to the scaling behavior of the differential cross section are considered. The power-law regime at highest momentum transfer is briefly described.
We calculate the transverse momentum dependence in the production of two back-to-back hadrons in electron-positron annihilations at the medium/large energy scales of BES-III and BELLE experiments. We use the parameters of the transverse-momentum-dependent (TMD) fragmentation functions that were recently extracted from the semi-inclusive deep-inelastic-scattering multiplicities at low energy from HERMES. TMD evolution is applied according to different approaches and using different parameters for the nonperturbative part of the evolution kernel, thus exploring the sensitivity of our results to these different choices and to the flavor dependence of parton fragmentation functions. We discuss how experimental measurements could discriminate among the various scenarios.
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