Exclusive Reactions at High Momentum Transfer

Organizing Committee

Preface

Contents

The various factorization schemes for hard exclusive processes and the status of their applications is briefly reviewed.

The AdS/CFT correspondence between string theory in AdS space and conformal field theories in physical space-time leads to an analytic, semiclassical model for strongly-coupled QCD which has scale invariance and dimensional counting at short distances and color confinement at large distances. One can use holography to map the amplitude describing the hadronic state in the fifth dimension of Anti-de Sitter space AdS₅ to the light-front wavefunctions of hadrons in physical space-time, thus providing a relativistic description of hadrons in QCD at the amplitude level. In particular, we show that there is an exact correspondence between the fifth-dimensional coordinate of AdS space z and a specific impact variable ζ which measures the separation of the quark and gluonic constituents within the hadron in ordinary space-time. New relativistic light-front equations in ordinary space-time can then be derived which reproduce the results obtained using the 5-dimensional theory. The effective light-front equations possess elegant algebraic structures and integrability properties. This connection between the AdS and the light-front representations allows one to compute the analytic form of the frame-independent light-front wavefunctions, the fundamental entities which encode hadron properties and allow the computation of decay constants, form factors, deeply virtual Compton scattering, exclusive heavy hadron decays and other exclusive scattering amplitudes. As specific examples we compute the pion coupling constant f_π and study the behavior of the pion form factor F_π(q²) in the space and time-like regions. We also determine the Dirac nucleon form factors and in the space-like region.

We review key predictions of the description of the long range structure of the nucleon in terms of a pion cloud. We explain how this, together with other aspects of nucleon structure, such as the relativistic motion of the valence quarks and the one-gluon-exchange hyperfine interaction, provides a natural explanation of the proton spin crisis.

I discuss the relation between inclusive and exclusive dynamics suggested by Bloom-Gilman duality. Duality implies the simultaneous applicability of two distinct limits, the standard DIS limit of hard inclusive processes taken at fixed x_B and a limit where the hadronic mass is held fixed. I review experimental evidence for the relevance of the fixed mass limit in inclusive processes at high x_F. Semi-local duality suggests that inclusive and exclusive processes occur on the same target Fock states. DIS scaling then implies that the Fock states contributing to hard exclusive processes have a large transverse size, i.e., that the hard scattering occurs off a single parton which carries a large fraction of the hadron momentum.

We outline the twist-two analysis of deeply virtual Compton scattering within the conformal partial wave expansion of the amplitude, represented as a Mellin–Barnes integral. The complete next-to-leading order results, including evolution, are obtained in the and a conformal factorization scheme. Within the latter, exploiting conformal symmetry, the radiative corrections are evaluated up to next-to-next-to-leading order. Using a new proposed parameterization for GPDs, we study the convergence of perturbation theory and demonstrate that our formalism is suitable for a fitting procedure of DVCS observables.

Several examples for the role of orbital angular momentum and spin-orbit correlations in hadron structure are discussed.

We consider pion electroproduction on a proton target close to threshold for Q² in the region 1 – 10 GeV². The momentum transfer dependence of the S-wave multipoles at threshold, E₀₊ and L₀₊, is calculated using light-cone sum rules.

I review history of the color transparency (CT) which started with discovery of the J/ψ meson, discovery of high energy CT phenomena and the recent progress in the investigations of CT at intermediate energies.

In contrast with common non-relativistic lore, the usual Sachs form factors are not the Fourier transforms of charge or magnetization densities. Instead, the two-dimensional Fourier transform of the electromagnetic F₁ form factor is the charge charge density of partons in the transverse plane. An analysis of the available data for neutron form factors leads to the result that the neutron charge density is negative at the center, and that the square of the transverse charge radius is positive. This contrasts with many expectations. Additionally, the use of measured proton form factors leads to the result that the proton's central d quark charge density is larger than that of the u quark by about 30%. The proton (neutron) charge density has a long range positively (negatively) charged component indicative of a pion cloud.

We summarise applications of Dyson-Schwinger equations to the theory and phenomenology of hadrons. Some exact results for pseudoscalar mesons are highlighted with details relating to the U_A(1) problem. We describe inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass. We recapitulate upon studies of nucleon electromagnetic form factors, providing a comparison of the ln-weighted ratios of Pauli and Dirac form factors for the neutron and proton.

Lattice results on the N to Δ electromagnetic, axial-vector and pseudoscalar form factors are evaluated using dynamical staggered sea quarks and domain wall valence quarks for pion masses in the range of 580-350 MeV, as well as, dynamical and quenched Wilson fermions for similar pion masses.

We present the results of calculations analyzing nucleon Compton scattering to lowest order using perturbative QCD (PQCD) methods. Our recent agreement of theoretical predictions with the results of Brooks and Dixon in 2000 is a significant progress in the PQCD investigation of nucleon real Compton scattering (RCS) process at high momentum transfer. We discuss our extension of RCS calculation to the case of incoming virtual photon and a possible link to the generalized parton distribution (GPD) approach.

Seven years of experimental efforts at Jefferson Lab on Deeply Virtual Compton Scattering yielded very significant results such as a strong indication for the handbag dominance (i.e. scaling) even et low energy, the first comparisons to models and a large data sample to constrain their free parameters and even a first model-dependent extraction of the total angular momentum carried by quarks. These proceedings try to summarize the information collected so far without going into details, and in a semi-chronological fashion.

Hard exclusive reactions are the tool to learn about generalized parton distributions, which provide a more complete parametrization of the nucleon than the ordinary parton distribution functions. Recent measurements by the HERMES collaboration of the exclusive production of photons, i.e., Deeply-Virtual Compton Scattering, are summarized and compared to model calculations, focusing on the measurements and model comparisons relevant to the extraction of quark orbital angular momentum and on the measurements on heavy nuclei.

The beam spin asymmetries of the reaction in the Bjorken regime were measured over a wide kinematical domain using the CLAS detector and a new lead-tungstate calorimeter. Through the interference of the Bethe-Heitler process with Deeply Virtual Compton Scattering, those asymmetries provide constraints for the nucleon Generalized Parton Distributions models. The observed shapes are in agreement with twist-2 dominance predictions.

Deeply Virtual Compton Scattering off the neutron has been investigated in the Hall A at Jefferson Laboratory. This experiment provides, through the measurement of the helicity-dependent cross section at Q²=1.9 GeV² and x_B=0.36, a linear combination of generalized parton distributions particularly sensitive to E, the least constrained GPD.

Two DVCS experiments off the proton have been recently approved to run in Hall A at JLab to measure electro-production of photon and π⁰ absolute cross-sections in the deep inelastic regime. They will exploit the successful experimental technique as well as build on the physics outcomes of the previous generation of DVCS experiments in Hall A. The new experiments will run both before and after the CEBAF upgrade.

An overview is given about the capabilities provided by the JLab 12 GeV Upgrade to measure deeply virtual exclusive processes with high statistics and covering a large kinematics range in the parameters that are needed to allow reconstruction of a spatial image of the nucleon's quark structure. The measurements planned with CLAS12 will cross section asymmetries with polarized beams and with longitudinally and transversely polarized proton targets in the constrained kinematics x = ±ξ. In addition, unpolarized DVCS cross sections, and doubly polarized beam target asymmetries will be measured as well. In this talk only the beam and target asymmetries will be discussed.

Inclusive DIS with unpolarized beam exhibits a subtle dependence on the transverse target spin, arising from the interference of one–photon and two–photon exchange amplitudes in the cross section. We argue that this observable probes mainly the quark helicity–flip amplitudes induced by the non-perturbative vacuum structure of QCD (spontaneous chiral symmetry breaking). This conjecture is based on (a) the absence of significant Sudakov suppression of the helicity–flip process if soft gluon emission in the quark subprocess is limited by the chiral symmetry–breaking scale ; (b) the expectation that the quark helicity–conserving twist–3 contribution is small. The normal target spin asymmetry is estimated to be of the order 10⁻⁴ in the kinematics of the planned Jefferson Lab Hall A experiment.

No abstract received.

We discuss the interpretation of the ep → epρ⁰ process in terms of, on the one hand, Generalized Parton Distributions and, on the other hand, an effective hadronic model based on Regge theory.

Preliminary measurements of the Transverse Target Spin Asymmetry, A_UT(φ), for hard exclusive electro-production of ρ⁰ mesons at HERMES are presented. Information about the poorly known GPD E can be obtained through measurement of the transverse target spin asymmetry in the longitudinal cross section . Using the self-analyzing character of ρ⁰ meson decay, both and were extracted from HERMES data. The TTSA was compared with GPD model predictions.

Electroproduction of exclusive φ vector mesons has been studied with the CLAS detector at an average Q² of 2.21 GeV². The scaling exponent for the total cross section as was determined to be n = 1.97 ± 0.84, consistent with the Vector Dominance Model prediction of n=2. The data are consistent with the assumption of s-channel helicity conservation (SCHC). Under this assumption we determine the ratio of longitudinal to transverse cross sections to be R = 0.86 ±0.24.

Following a previous detailed study of unpolarized generalized parton distribution functions in the non-singlet sector, and at zero values of the skewness variable, ζ, we propose a physically motivated parametrization that is valid at ζ ≠ 0. Our method makes use of information from the nucleon form factor data, from deep inelastuc scattering parton distribution functions, and from lattice results on the Mellin moments of generalized parton distributions. It provides, therefore, a step towards a model independent extraction of generalized distributions from the data, alternative to the mathematical ansatz of double distributions. Comparisons with recent experimental data on the proton are shown.

We discuss the prospects for probing Generalized Parton Distributions (GPDs) via exclusive production of a high–mass system (H = heavy quarkonium, di-photon, di-jet, Higgs boson) in diffractive pp scattering, pp → p+H+p. In such processes the interplay of hard and soft interactions gives rise to a diffraction pattern in the final–state proton transverse momenta, which is sensitive to the transverse spatial distribution of partons in the colliding protons. We comment on the plans for diffractive pp measurements at RHIC and LHC. Such studies could complement future measurements of GPDs in hard exclusive ep scattering (JLab, COMPASS, EIC).

We discuss the role of t-channel Regge trajectories in the Bjorken limit of Deeply Virtual Compton Scattering (DVCS). We show that in the limit of high energy and small t, the natural interpretation of DVCS is in terms of photon scattering off the meson cloud of the nucleon rather than in terms of scattering off the partons inside the bare nucleon.

We discus recent developments in theory of high energy two-body break-up reactions of few-nucleon systems. The characteristics of these reactions are such that the hard two-body quasielastic subprocess can be clearly separated from the accompanying soft subprocesses. We discuss in details the hard rescattering model (HRM) in which hard photodisintegration develops in two stages. At first, photon knocks-out an energetic quark which rescatters subsequently with a quark of the other nucleon. The latter provides a mechanism of sharing the initial high momentum of the photon by the outgoing two nucleons. Within HRM we discuss hard break-up reactions involving ²D and ³He targets. Another development of HRM is the prediction of new helicity selection mechanism for hard two-body reactions, which was apparently confirmed in the recent JLab experiment.

In this article, I review what has been learned about the underlying mechanisms of deuteron photodisintegration, mostly above the resonance region, and the prospects for improving our understanding of high-energy photodisintegration through proton-proton photodisintegration in ³He.

A review of measurements of the elastic form factors of the deuteron and the isotopes of helium is presented. The existing data are compared to selected theoretical calculations. Recent JLab measurements, currently in the analysis phase, of the helium form factors at large momentum transfers are described. Plans for future JLab measurements are also summarized.

The data base for the form factors of the nucleon obtained from elastic ep scattering is discussed, as well as some the recent developments in their calculation.

The analysis of the JLab proton polarization data on the ratio μ_pG_Ep(Q²)/G_Mp(Q²), together with all other existing nucleon form factor data, by the unitary and analytic model of nucleon electromagnetic structure reveals them to be consistent with all known nucleon form factor properties. Moreover, it implicates surprising non-dipole behavior of the proton electric form factor in the space-like region with the zero around the momentum transfer squared value Q² = 13GeV². Consequences of such G_Ep(Q²)-behavior on various physical quantities are briefly reviewed.

A method to measure the proton form factor ratio up to Q² of 15 GeV² using polarization transfer technique is described. A large detector acceptance needed for such high Q² measurements is achieved by means of a single dipole detector system to detect the recoil proton that includes a polarimeter and a hadron calorimeter, and a highly granulated electromagnetic calorimeter for the electron registration. For the proton tracking, Gas Electron Multiplier (GEM) technology is used that can sustain the high fluxes of particles due to direct view from the target. The impact of such high precision measurements on the theoretical description of the proton is briefly discussed.

The neutron elastic magnetic form factor has been extracted from quasielastic scattering from deuterium in the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab. The kinematic coverage of the measurement is continuous over a broad range, extending from below 1 (GeV/c)² to nearly 5 (GeV/c)² in four-momentum transfer squared. High precision was achieved by employing a ratio technique in which many uncertainties cancel, and by a simultaneous in-situ calibration of the neutron detection efficiency, the largest correction to the data. Neutrons were detected using electromagnetic calorimeters and time-of-flight scintillators. Data were taken at two different electron beam energies, allowing up to four semi-independent measurements of to be made. The dipole parameterization is found to provide a good description of the data for Q² > 1 (GeV/c)².

A feasibility study has been made for an experiment to greatly extend the Q²-range of precision measurements of the neutron's magnetic form factor using the existing JLab 6 GeV beam. The results are promising.

Form factors of nucleons and mesons with timelike momentum transfers are discussed. New experimental results for protons, pions, and kaons at large momentum transfers are presented, and the inadequacy of existing theoretical ideas about these is pointed out.

Polarization effects in processes are reinvestigated. The explicit form of components of the single-spin and double-spin polarization of the created nucleon N in the annihilation of of e⁺e⁻ colliding beams is presented. The sensitivity in a behavior of the single spin/or double spin polarization components of the nucleon is demonstrated graphically by using two recent formulations of the unitary and analytic model of the nucleon electromagnetic structure.

The radiative Δ → γN transition is examined at the real photon point Q² = 0 using the framework of light-cone QCD sum rules. In particular, we determine the sum rules for the transition form factors G_M(0) and R_EM up to twist 4.

A measurement of the π⁰ electroproduction cross section via the process ¹H(e, e′p)π⁰ has been made in the momentum transfer region 6.3 GeV < Q² < 7.8 GeV and for hadronic invariant masses from pion threshold up to 1.4 GeV. The information contained in the differential cross section is used to probe the Δ resonance region where transition form factors such as can be extracted. The data will be used to extract the ratio of electric quadrupole to magnetic dipole Δ excitation amplitudes, .

The differential cross section for the process p(e,e′p)η has been measured for centre-of-mass energies from threshold to 1.8 GeV, encompassing the S₁₁(1535) resonance which dominates the channel. This was at Q² = 5.7 and 7.0 (GeV/c)², the largest momentum transfer measurement of this exclusive process to date. The photocoupling amplitude for γp → S₁₁ is extracted from the data, and the possible onset of scaling in this reaction is observed.

Recent theoretical developments in the studies of two-photon exchange effects in elastic electron-proton scattering are reviewed. Two-photon exchange mechanism is considered a likely source of discrepancy between polarized and un-polarized experimental measurements of the proton electric form factor at momentum transfers of several GeV². This mechanism predicts measurable effects that are currently studied experimentally.

We construct a non-local gauge invariant Lagrangian to model the electromagnetic interaction of proton. The Lagrangian includes all allowed operators with dimension up to five. We compute the two-photon exchange contribution to elastic electron-proton scattering using this effective non-local Lagrangian. The calculation uses experimentally extracted electromagnetic form factors and depends on one unknown constant. The final result explains the difference between the form factor ratio G_E/G_M extracted by Rosenbluth at SLAC and the polarization transfer technique.

Recent polarization transfer measurements of the ratio of elastic form factors G_E/G_M on the proton are not in agreement with the results of Rosenbluth-type experiments. A two photon exchange contribution to the elastic cross section is the leading theoretical candidate to explain the discrepancy. A definitive test of this theory is the direct comparison of e⁺p and e⁻p elastic scattering. A proposed measurement of this sort using a novel mixed e⁺e⁻ lepton beam and the CEBAF Large Acceptance Spectrometer (CLAS) at Jefferson Lab is described. Preliminary results from an engineering test run showing a clear signal of elastic e⁺p and e⁻p are presented.

Experimental studies of meson form factors provide a unique and powerful tool for understanding bound quark systems due to the meson's simple valence structure. However, experiments in the space–like regime (Q² = −q² > 0) are made challenging by the lack of “free meson” targets. Recent measurements at Jefferson Lab have significantly improved the quality of measurements of the charged pion form factor up to Q² = 2.5 GeV², and future measurements will extend the database to 6 GeV².

This is a short presentation of the results for the pion-nucleon distribution amplitudes which are expressed in terms of the nucleon distribution amplitudes with the help of current algebra. Everything is considered to be at threshold.

We extend the 1/N_c meson-baryon scattering formalism to πN → multi-πN case. We first show that the leading-order large N_c processes proceed through resonant intermediate states (e.g., ρN or πΔ). We find that the pole structure of baryon resonances can be uniquely identified by their (non)appearance in ηN or mixed partial-wave πΔ final states.

We report the first observation of e⁺e⁻ annihilations into hadronic states of positive C-parity, ρ⁰ρ⁰ and φρ⁰. The angular distributions support two-virtual-photon annihilation production. We also report the observations of e⁺e⁻ → φη and a preliminary result on e⁺e⁻ → ρ⁺ρ⁻.

We give a brief overview of the theoretical status of the Transition Distribution Amplitudes and discuss their experimental near future.

Initial-state and final-state interactions which are conventionally neglected in the parton model, have a profound effect in QCD hard-scattering reactions. These effects, which arise from gluon exchange between the active and spectator quarks, cause leading-twist single-spin asymmetries, diffractive deep inelastic scattering, diffractive hard hadronic reactions, and the breakdown of the Lam-Tung relation in Drell-Yan reactions. Diffractive deep inelastic scattering also leads to nuclear shadowing and non-universal antishadowing of nuclear structure functions through multiple scattering reactions in the nuclear target. Factorization-breaking effects are particularly important for hard hadron interactions since both initial-state and final-state interactions appear. Related factorization breaking effects can also appear in exclusive electroproduction reactions and in deeply virtual Compton scattering. None of the effects of initial-state and final-state interactions are incorporated in the light-front wavefunctions of the target hadron computed in isolation.

In this talk, I summarize a recent study showing that the large-x parton distributions contain important information on the quark orbital angular momentum of nucleon. This contribution could explain the conflict between the experimental data and the theory predictions for the polarized quark distributions. Future experiments at JLab shall provide further test for our predictions.

We study the transverse momentum dependent distribution functions of the up and down quarks inside the proton using the spectator model by Jakob et al. We calculate the double spin asymmetry for the setups of COMPASS, HERMES, and JLab. We investigate the differences between the spectator model and the model based on factorization ansatz.

The chiral-odd and time reversal-odd transverse momentum dependent (TMD) parton distribution , the so-called Boer-Mulders function, is calculated in the diquark spectator model for both an active up- and down-quark. In particular the signs of and are of interest as they were predicted in other works, and the result of this analysis is consistent with these predictions. Both flavors of the Boer-Mulders function contribute to observables such as the azimuthal cos(2φ) asymmetry in semi-inclusive DIS. Using the results of this analysis for and and recent calculations of the Collins fragmentation function in a similar spectator model, phenomenological predictions for the cos(2φ) asymmetry are presented. In addition, the chiral-odd but time-reversal even TMD is computed in the diquark spectator model, and is used to present predictions for the sin(2φ) single-spin asymmetry for a longitudinally polarized target in SIDIS.

We investigate the single-spin asymmetries in deep inelastic electron-proton scattering and electron-positron annihilation. We show that it is possible to measure the single-spin asymmetry in the inclusive Λ production at the present B-factories.

To study hard exclusive processes which provide access to Generalized Parton Distributions (GPDs) and hence to the orbital angular momentum of the quarks, a new Recoil Detector surrounding the internal gas target of the HERMES experiment at DESY was installed. The Recoil Detector improves the selection of exclusive events by a direct measurement of the momentum and track direction of the recoiling particle as well as by rejecting non-exclusive background. This detector is an ideal tool to combine energy and position measurements for charged particles in an intermediate momentum range of 0.1 to 1.4 GeV. The HERMES Recoil Detector consists of three main components located inside a solenoidal magnet which provides a 1 T longitudinal magnetic field: a silicon strip detector surrounding the target cell inside the vacuum, a scintillating fiber tracker and a photon detector.

The new Inner Calorimeter (IC) was developed specifically for dedicated CLAS/DVCS experiment.¹ IC consists of 424 PbWO₄ tapered crystals readout by avalanche photodiodes (APD) followed by low-noise preamplifiers. It is a high precision calorimeter with energy resolution better than 3% at 2-5 GeV and has an angle resolution of 3 to 4 mrad.

There are many potentially interesting 12 GeV-era electron experiments that require transversely polarized H or D. The high fields associated with conventional Dynamically Polarized targets lead to challenging background conditions if oriented transverse to an electron beam. Frozen-spin targets that are maintained by low holding fields could greatly mitigate such problems. There is at least indirect evidence that frozen-spin HD could be quite radiation resistant and might maintain D polarization with modest electron currents.

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