GDH 2002

Foreword.

CONTENTS.

The formulation of the Gerasimov-Drell-Hearn sum rule is revisited, showing its connection with other sum rules occurring in electron scattering and discussing the problem of its saturation, both from the theoretical and experimental point of view. The generalization to other nuclear targets is also reported.

The idea of quark-hadron duality is developed and applied to integral sum rules for the photoexcitation of meson resonances. Some applications of the presented approach in the light and heavy quark sectors are made, and the role of the scalar diquark cluster degrees of freedom in the radiative formation of light scalar mesons is discussed.

A brief summary of the theoretical and experimental knowledge of the spin structure of the proton is presented. The helicity distributions of quark and gluons are discussed, together with their related sum rules. The transversity distribution is also introduced with possible strategies for its measurement. Novel spin dependent and k_⊥ unintegrated distribution and fragmentation functions are discussed, in connection with a new and rich phenomenology of transverse single spin asymmetries.

Recent developments of the unitary isobar model MAID are discussed and evaluations of the GDH sum rule and the forward spin polarizability γ₀ are presented for protons and neutrons. Compared to previous studies the situation on the neutron has theoretically improved but for both nucleons a deviation from the sum rule of about 10 – 15% still exists. This is mainly due to the uncertain situation at higher energies for W ≫ 2 GeV.

Even at moderate energy machines, there is a regime where hard pion electroproduction proceeds by a perturbatively calculable process. The process, we claim, is not the leading twist fragmentation one but rather a higher twist process that produces kinematically isolated pions. Semiexclusive data may teach us more about parton distribution functions of the target and the pion distribution amplitude. In addition, there is a connection to generalized parton distribution calculations of exclusive processes in that the perturbative kernel is the same.

We discuss how generalized parton distributions (GPDs) enter in a variety of hard exclusive processes such as deeply virtual Compton scattering (DVCS) and hard meson electroproduction reactions on the nucleon. We discuss the links between GPDs and elastic nucleon form factors as well as the information contained in the second moment of (generalized) parton distributions. We subsequently show some key observables which are sensitive to the various hadron structure aspects of the GPDs, and discuss their experimental status.

Phenomenological parameterizations of proton and neutron polarized structure functions, and , are developed for x ≳ 0.02 using deep inelastic data up to ~ 50 (GeV/c)² as well as available experimental results on photo- and electro-production of nucleon resonances. The generalized Drell-Hearn-Gerasimov sum rules are predicted from low to high values of Q² and compared with proton and neutron data. Furthermore, the main results of the power correction analysis carried out on the Q²-behavior of the polarized proton Nachtmann moments, evaluated using our parameterization of , are briefly summarized.

I briefly discuss recent work on the topic of the spin structure of the nucleon at low energies which has appeared since the previous GDH conference in 2000.

We outline a computation of a simple moment of parton distribution functions on the lattice, the average momentum of a twist-2, non-singlet operator in a pion. We demonstrate that such a calculation is feasible on the lattice, keeping the effects of the continuum limit and of a non-perturbative renormalization completely under control. We discuss the remaining open uncertainties, i.e. the chiral limit and the quenched approximation. Both these uncertainties will be overcome in the next years such that lattice computations will be able to give precise values for a number of moments like the one discussed in this contribution.

The phenomenology of transversity and of some related observables is briefly reviewed.

The GDH sum rule was tested experimentally in the photon energy range from 200 MeV to 3 GeV. Circularly polarized photons were produced at the electron accelerators MAMI and ELSA. 4π detectors around the frozen spin target measured the reaction products which permitted the determination of the helicity dependent photoabsorption cross section.

For the first time absorption of circularly polarized photons on longitudinally polarized nucleons was measured. The main goal was to perform an experimental check of the Gerasimov-Drell-Hearn sum rule. In addition the helicity dependence of single and double pion production channels up to 800 MeV was also measured. Preliminary results for this second item are presented.

The study of neutron spin structure in Hall A using a polarized ³He target is discussed. Included are recent measurements on the extended GDH integral, the Q² evolution of the spin structure functions, and the polarization asymmetry at large x. Also included is a discussion of upcoming experiments including a measurement of the electric form factor of the neutron at high Q².

Three experiments at JLAB have measured the double polarization asymmetries A_||(x, Q²) in the nucleon resonance region, using polarized electron beams incident on polarized proton and deuteron targets. The analysis for the first experiment, egla in Hall B, is nearly finished and preliminary values of the spin structure function g₁(x, Q²) and the first moment Γ₁ (x) have been extracted. The other two experiments, one in Hall B and one in Hall C are still analysing data. Some results are presented.

The MIT-Bates laboratory is uniquely suited to study polarized electron-nuclear scattering in the Δ region in the Q² range = 0.05 - 1.0 GeV². Both stored and extracted beams of high polarization are available in conjunction with polarized targets and/or recoil polarimeters. At the present the maximum beam energy delivered by the 600 Hz Linac is 1.0 GeV. We report first on recent high-precision measurements of the γ*N → Δ transition by the OOPS collaboration where for the first time a high-duty factor CW extracted electron beam and the full OOPS set-up were used. We then discuss the potential of the BLAST internal target program, where a 70 % polarized beam is used in conjunction with pure, highly polarized hydrogen, deuterium or ³He gaseous targets.

A summary of results from the HERMES experiment is presented. Inclusive and semi-inclusive asymmetries have yielded measurements of the nucleon spin structure function g₁(x) and of the flavor separated polarised parton distributions Δq(x). First indications of the size and sign of the gluon polarisation are also reported. For the exclusive measurements, results on the beam spin asymmetry in deeply virtual Compton scattering are shown, together with the first measurement of the beam charge asymmetry. A short overview of other results is also presented.

Within the GRAAL collaboration, we have constructed a Polarized HD Target Factory, implanted at IPN Orsay. The expected properties of the HD targets and the results already obtained for the polarization of HD samples and the relaxation times are given. New possibilities to perform GDH experiments on polarized proton, neutron and deuteron are now opened, by using the high circular polarization of the GRAAL backscattered photon beams and the large effective longitudinal polarization of the HD target, resulting essentially from its good dilution factors. Polarized total cross sections concerning the isovector Drell-Hearn Gerasimov Sum Rule related to the proton neutron difference, could be measured with minimum systematic uncertainties: the target containing both polarized protons and neutrons. An experimental method, taking advantage of the 4π GRAAL experimental set-up is described.

We report preliminary results of π photo-production using polarized γ beams and a polarized HD target. Four observables can be extracted simultaneously from the data, the cross section, the beam asymmetry Σ, and the double-polarization observables G and E. The latter determines the GDH sum rule integral.

Recent measurements from SLAC of the polarized nucleon structure functions g₁ and g₂ have been used to experimentally test the Bjorken, Ellis-Jaffe, Burkhardt-Cottingham, and Efremov-Leader-Teryaev sum rules. In the future, the SLAC E159 experiment will extend structure function measurements using real photons to 40 GeV, enabling a definitive test of the high energy convergence of the GDH sum rule for both proton and deuteron targets.

LEPS - a polarized high energy photon facility - has been established at SPring-8. It provides photons by means of Compton back scattering of a laser light against 8 GeV electrons in the storage ring. Physics programs currently performed in the facility are introduced. The GDH experiment is aiming at measurements of the helicity dependent total photo-absorption cross-section at the energies from 1.8 GeV to 2.8 GeV. The status of its preparation is presented.

The GDH sum rule integral for the deuteron is expected to contain a large negative contribution at energies just above photo disintegration threshold, arising from the ¹S₀ (M1) resonance state. Two indirect methods of determining this strength are presently underway at TUNL/HIγS. First, it will be shown that linearly polarized photo- disintegration data from HIγS can be used to estimate this strength. In addition, it will be shown that polarized neutron capture measurements at TUNL also provide information on the GDH integrand in this low-energy regime. The experiments presently underway will be described, and preliminary results will be presented. Finally, a brief description of plans to make a direct measurement of the GDH integrand for the deuteron using a polarized target and circularly polarized beams from HIγS will be described.

At PSI polarized scintillating targets have been operated in several particle physics experiments over extended periods of time. They proved to be very robust and reliable. Proton polarizations of more than 80%, and deuteron polarizations of 25% in fully deuterated polystyrene based scintillator have been reached in a vertical dilution refrigerator with optical access. New choices of materials and preparation procedures show potential for an improvement of the scintillation and polarization properties.

The CEBAF Large Acceptance Spectrometer is utilized for a wide ranging physics program at Jefferson Lab, including measurements of polarized structure functions and future tests of the Gerasimov-Drell-Hearn sum rule. To realize the entire extent of the program, polarized targets that can function inside the spectrometer without severely affecting its performance are necessary. In these proceedings I describe a continuously polarized solid target of protons and deuterons that operated inside CLAS for a total of ten months from 1998 to 2001. The conceptual design of a frozen spin target that will more fully exploit the 4π acceptance of CLAS is also introduced.

The polarized ³He target has been used successfully in several recent experiments investigating the spin structure of the neutron at Thomas Jefferson National Accelerator Facility (JLAB). In this note we discuss the two step polarization process of optical pumping of Rb vapor and spin exchange to the ³He nucleus, along with the independent polarimetries used to characterize the high density target cells.

The difference of the total photo absorption cross section in the helicity state 3/2 and 1/2 of the proton has been measured at the Bonn Electron Stretcher Accelerator ELSA. For this reason a polarized target basing on the frozen spin technique has been built. Since the value of the nucleon polarization and the effective density of the butanol target contribute directly to the result of the GDH-integral both quantities have to be determined with high accuracy.

The HERMES physics program includes inclusive and semi-inclusive double-polarisation measurements that allow the determination of the polarised quark distributions for each flavour of valence and sea quarks. In addition, HERMES is able to study exclusive processes like the Deeply Virtual Compton Scattering (DVCS) which allow to access the Generalised Parton Distributions (GPDs). These GPDs may provide information for the still unknown orbital angular momentum of the partons. A recoil detector will be installed around the HERMES target region in order to improve the determination of the kinematics of exclusive events by providing a direct measurement of the recoiling particle and to suppress non-exclusive background. Such a recoil system would detect more than 85 % of recoil protons from DVCS.

In the last year an upgrade of the Mainz electron accelerator MAMI has been started to reach a beam energy of 1.5GeV. Therefore a fourth stage (MAMI C), a harmonic double sided microtron (HDSM) with four normal conducting dipole magnets and two antiparallel linear accelerators is under construction. The A2-Glasgow-Mainz tagger can presently handle only electrons with an energy of 855MeV, so also here an upgrade of the existing systems is necessary to cope with the electrons from MAMI C. After the first successful round ^1,2,3 to measure helicity dependent photoabsorption cross sections in the year 1998 with a polarized proton target from Bonn and the DAPHNE detector this measurement will be continued soon with a polarized deuterium target. For future experiments, the Crystal Ball detector with its nearly 4pi acceptance, a polar and azimuthal symmetry and a high efficiency for multi photon final states will be available in Mainz. It is planned to continue the experimental program with polarized photon and polarized targets with this detector, since DAPHNE is mainly a charged particle tracking detector. Due to the fact that the Bonn Polarized Target will be needed for experiments at the Bonn accelerator ELSA at that time, it has been started to build up a polarized target for Mainz. In this talk a short overview on plans for future experiments in the A2 taggerhall will be given.

In order to detect very forward scattered particles in JLAB’s Hall A , two septum magnets will be added to the High Resolution Spectrometers (HRS) presently in the Hall. The HRS + septa system is expected to be a multipurpose tool to be utilized in many small angle physics experiments. In this contribution, technical and optical features of the two septa will be discussed with particular emphasis on their use in the low Q² GDH experiment to be performed in Hall A.

A new experimental program is about to get underway at the Mainz Microtron Facility. The experimental apparatus consists of the famous Crystal Ball detector together with TAPS as a forward wall, and a central tracker. This configuration provides a geometrical acceptance close to 4π combined with good energy and angular resolution in particular for neutral final states. In the second stage of the experiment (MAMI-C) the detector will be equipped with a frozen-spin (Bonn-type) polarized target filled with , or . This makes possible new high precision, high statistics measurements of the cross sections for the and processes at incident photon energies up to 1.5 GeV. In particular it provides a unique opportunity to investigate the GDH sum rule on a neutron target in the contributions by reactions and .

Spin structure functions provide basic information about the spin of the quark distributions inside the nucleon. Experimental understanding of the nucleon spin in the kinematic region where the three basic (“valence”) quarks dominate the nucleon wave function is still rather poor. Jefferson lab, with its high quality, high polarization continuous electron beam, and a high density polarized ³He target in experimental Hall A, provides the ideal opportunity to gather neutron spin structure data in the valence region with unprecedented precision. Two high precision neutron spin structure measurements were completed in Hall A last summer. The first experiment measured the spin asymmetry in the valence region while in second experiment higher-twist effects were studied via measurements of . Perliminary results are presented.

The asymmetry A_|| in the deuteron has been measured by the CLAS Collaboration at JLAB in the EG1 experiment and the behaviour of the deuteron polarized structure function has been investigated in a kinematical region where baryon resonances (BR) dominate. In this talk I present the results of the measurement and the comparison with previous results obtained in different laboratories in the same kinematical region as well as in the Deep Inelastic Scattering (DIS) region. In the BR region the CLAS data show better statistics and cover the evolution of the first moment in a larger Q² interval than previous data. The comparison with the DIS data show the possible onset of duality. An improvement of the statistical precision is expected with the new data set from the EG2000 experiment presently under analysis.

JLAB experiment E94-010 has measured the spin dependent longitudinal and transverse inclusive cross sections in the Quasi-elastic and Resonance regions. This measurement allows evaluation of the extended GDH sum for both ³He and the neutron. The extended sum tests the limits of applicability of both Chiral Perturbation Theory at low Q² and higher twist expansions at large Q². At intermediate Q² our data provides a valuable benchmark in the transition region from partonic to hadronic degrees of freedom.

Nucleon spin asymmetries have been measured in the resonance region at Jefferson Lab’s Hall C using longitudinally polarized electron beam and longitudinally and transversely polarized NH₃ and ND₃ targets. The proton and deuteron spin asymmetries A₁(v, Q²) and A₂(v, Q²) will be extracted from the A_|| and A_⊥ asymmetries measured at Q² ≈ 1.3 GeV². An overview of the status of the experiment, data analysis and an outlook of what we can expect from our program will be discussed in this proceeding.

We report a measurement of the helicity asymmetry of a substantial fraction of the γp total cross section at photon energies between 2.5 and 5.3 GeV in Hall B of Jefferson Lab. The preliminary analysis uses only events with at least one charged particle between approximately 8° and 45°. Assuming that the measured asymmetry applies also to the undetected portion of the cross section, we compare our preliminary result with the results of the Regge parameterization of Bianchi and Thomas.

We report on new measurements of the separated longitudinal and transverse proton structure functions in the resonance region (1 < W² < 4 GeV²) and spanning the four-momentum transfer range 0.2 < Q² < 4.0 (GeV/c)². The experiment, E94-110, measured the unpolarized inclusive electron-proton cross section, and was performed in Hall C at JLab. Results of the analysis of the data are presented, as well as a discussion of the impact on spin asymmetry measurements in the resonance region.

Unique measurement of the proton structure function F₂ in a wide two-dimensional region of x and Q² has been reported. The accessible kinematics covers entire resonance region up to W = 2.5 GeV in the Q² interval from 0.1 to 4.5 GeV². Obtained data allowed for the first time an evaluation of moments of the structure function F₂ directly from experimental data as well as an intensive study of the Bloom-Gilman duality phenomenon.

The main features of the resonance structure of the nucleon are discussed, particular with regard to the helicity dependence of real and virtual photoabsorption. The dependence of the partial cross sections on both the resonance helicity amplitudes and the electromagnetic multipoles is outlined. The general structure of the Compton tensor is reviewed and applied to the special cases of real to real, virtual to real, and virtual to virtual Compton scattering. Recent theoretical developments in dispersion relations are presented, together with a short overview regarding static, dynamical, and generalized polarizabilities of the nucleon as well as the status of the Gerasimov-Drell-Hearn sum rule and related integrals.

We report on the recent results of the hypercentral constituent quark model^1,2. The model contains a spin independent three-quark interaction which is inspired by QCD lattice calculations and reproduces the average energy values of the SU(6) multiplets. The splittings are obtained with a residual generalized SU(6) -breaking interaction, including an isospin dependent term ². The long standing problem of the Roper resonance is absent and all the 3- and 4-star states are well reproduced. The model has also been used for predictions concerning the electromagnetic transition form factors giving a good description of the medium Q² -behaviour ^3,4. In particular the calculated S₁₁ A_½ helicity amplitude agrees very well with the recent CLAS data ⁵. Finally the ratio of the elastic form factors of the proton ⁶, calculated including kinematic relativistic corrections, exhibits a substantial decreasing with Q² in agreement with the recent TJNAF experiment ⁷.

Model-dependence of the single-pion contribution to the GDH, Baldin, and forward spin-polarizability sum rules is explored, using the most recent SAID multipole analysis. Results from SAID and MAID are compared.

The set of experiments forming the g8 run took place this past summer (6/04/01 – 8/13/01) in Hall B of Jefferson Lab. These experiments made use of a beam of linearly-polarized photons produced through coherent bremsstrahlung and represent the first time such a probe has been employed at Jefferson Lab. Among the several new and upgraded Hall-B beamline devices commissioned prior to the production running of g8a were the photon tagger, the coherent bremsstrahlung facility (goniometer + an instrumented collimator), a photon profiler, and the PrimEx dipole + pair spectrometer telescopes. We essentially commissioned a new beamline for photon running in Hall B. The scientific purpose of g8 is to improve the understanding of the underlying symmetry of the quark degrees of freedom in the nucleon, the nature of the parity exchange between the incident photon and the target nucleon, and the mechanism of associated strangeness production in electromagnetic reactions. With the high-quality beam of the tagged and collimated linearly-polarized photons and the nearly complete angular coverage of the Hall-B spectrometer, we seek to extract the differential cross sections and polarization observables for the photoproduction of vector mesons and kaons at photon energies ranging between 1.1 and 2.25 GeV. For the first phase of g8, i.e. g8a, we collected approximately 1.8 billion triggers for . In this paper, we report on the results of the commissioning of the beamline devices for the g8a run.

An extensive experimental program to measure the spin structure of the nucleons is underway in Hall B at Jefferson Lab using a polarized electron beam incident on polarized hydrogen and deuterium targets, consisting of frozen NH₃ and ND₃ material. Spin degrees of freedom offer the possibility to test, in an independent way, existing models of resonance electroproduction. The most accessible resonance is the Δ(1232) since it does not overlap with other states and decays strongly via π emission. The present analysis select the Δ+(1232) in the exclusive channel from data of the EG1 run period, taken in the Fall of 1998, to extract single and double spin asymmetries in a Q² range from 0.5 to 1.5 GeV²/c². Results of the asymmetries are presented as a function of the center of mass decay angles of the π⁰ and compared with the unitary isobar model MAID, the dynamic model by Sato and Lee and the effective Lagrangian theory by Davidson and Mukhopadhyay.

The polarized longitudinal-transverse structure function σ_LT′ in the reaction has been measured for the first time in the Δ(1232) resonance region for invariant mass W = 1.1 - 1.3 GeV and at four-momentum transfer Q² = 0.40 and 0.65 GeV². Data were taken at the Thomas Jefferson National Accelerator Facility with the CEBAF Large Acceptance Spectrometer (CLAS) using longitudinally polarized electrons at an energy of 1.515 GeV. This newly measured σ_LT′ provides new and unique information on the interference between resonant and non-resonant amplitudes in the Δ(1232) resonance region. The comparison to recent phenomenological calculations shows sensitivity to the description of non-resonant amplitudes and higher resonances.

In 1997/1998 an experiment was carried out at MAMI to verify the so called Gerasimov-Drell-Hearn (GDH) sum rule. This sum rule relates dynamic and static properties of the nucleon. In addition to the measurement of the helicity dependent total photoabsorption cross-sections, helicity dependencies of partial channels for Nπ, Nη and Nππ were observed and are partly published in ¹, ² and ³. Preliminary results from double-pion photoproduction for the isospin channels and are shown here.

Using a model for two pion photoproduction on the proton previously tested in total cross sections and invariant mass distributions, we evaluate here polarization observables on which recent experiments are providing new information. We evaluate cross sections for spin 1/2 and 3/2, which are measured at Mainz and play an important role in tests of the GHD sum rule.

Polarization degrees of freedom in exclusive channel of two charged pion electro production are studied in the Q² region from 0.6 to 1.3 GeV². Predictions for the contribution to the GDH integral as well as helicity components of the cross section are estimated in the framework of the phenomenological approach developed for the analysis of the two pion production data from CLAS (JLAB). Calculations show high sensitivity of the helicity difference σ_1/2 – σ_3/2 to baryon resonances with strongly different A_1/2 and A_3/2 photocouplings.

A tagged and polarized Compton backscattered photon beam is produced at the GRAAL facility in the energy range from 0.5 GeV up to 1.5 GeV. We present new very preliminary results on beam polarization asymmetry Σ for the ω photoproduction on the proton. These results confirm the relevance of resonance contributions to polarization observables.

We present an overview of different types of dispersion relations (DRs) for real Compton scattering, by discussing in particular fixed-t and fixed-angle DRs in both an unsubtracted and subtracted version. We apply these combined formalisms to the analysis of existing real Compton scattering data, with the aim to extract information on the proton polarizabilities with a minimum of model dependence.

At the GRAAL facility, a polarised and tagged ray beam is produced in the energy range from 500 MeV up to 1500 MeV. Preliminary results of beam polarization asymmetries for Compton scattering on the proton are presented. These very precise measurements cover the angular range 30°-150°, providing stringent constraints to theoretical models.

In addition to the E2/M1 ratio of the N → Δ transition, the electromagnetic polarizabilities and spin-polarizabilities are important structure constants of the nucleon which serve as sensitive tests of chiral perturbation theory and of models of the nucleon. Recently, these quantities have been investigated experimentally at MAMI (Mainz) by high-precision Compton scattering using hydrogen and deuterium targets, where for the latter the method of quasi-free scattering has been applied.

We calculate the spin-dependent amplitudes of virtual Compton scattering(VCS) and forward doubly virtual Compton scattering (VVCS) in HBChPT at and extract the generalized spin polarizabilities and generalized forward spin polarizabilities.

It is argued that spin is a fundamental aspect of gauge theories at short distances. As a consequence there are characteristic helicity asymmetries in hard inclusive and exclusive reactions of which a few are discussed.

We present measurements of recoil proton polarization for in and above the resonance region. These are the first data in this reaction for polarization transfer with circularly polarized photons. The results are compared to phase shift analyses and quark model calculations.

We have measured the induced polarization and the polarization transfer to the proton in the reaction for incident photon energies up to 2.4 GeV. Hadron helicity conservation predicts that these observables should vanish. The induced polarization p_y is found to vanish above 1 GeV. However, the polarization transfer C_x does not vanish above 1 GeV, inconsistent with hadron helicity conservation.

Deuteron two-body photodisintegration is analysed within the framework of the Quark-Gluon Strings Model. The model describes fairly well the recent experimental data from TJNAF in the few GeV region. Angular distributions at different γ-energies are presented and the effect of a forward-backward asymmetry is discussed. Results for polarization observables from 1.5-6 GeV are presented and compared with available data.

The physics of real photon exclusive scattering on the proton and JLab experiment E99-114 is discussed. Data on Compton form factors at s up to 11 (GeV/c)² and t up to 6.5 (GeV/c)² have been obtained. The polarization transfer parameter K_LL is found to be in fair agreement with the handbag diagram prediction. Possible additional polarization transfer measurements are outlined.

Spin physics is the main focus of the HERMES physics program. Over the last five years measurements have been performed with polarised lepton beam and polarised or unpolarised nuclear targets. In this contribution results on single-spin asymmetries in semi-inclusive hadron production from longitudinally polarized targets are presented. These results are compared with theoretical calculations which relate the azimuthal dependence of the observed asymmetries to the transversity structure function h₁(x).

The class of interference fragmentation functions, arising from interference among different hadron production channels, is reconsidered. Their symmetry properties with respect to chiral transformations allow building spin asymmetries where the quark transversity distribution can be factorized out at leading twist. For the case of two leading spinless hadrons inside the same current jet, the pair system is expanded in relative partial waves. The cross section is represented on the helicity basis of the target and the fragmenting quark, as well as on the relative orbital angular momentum of the pair. From the decay matrix being positive semi-definite, new bounds on the interference fragmentation functions can be derived. The expansion in partial waves allows to naturally incorporate in a unified formalism specific cases already studied in the literature, such as the fragmentation functions arising from the interference of two mesons in relative s and p waves, as well as the fragmentation of a spin-1 hadron.

The fragmentation of deuterons into pions emitted forward in the kinematic region forbidden for free nucleon-nucleon collisions is analyzed. It is shown that the inclusion of the non-nucleonic degrees of freedom in a deuteron results in a satisfactory description of the data for the inclusive pion spectrum and improves the description of the data about T₂₀. According to the data, T₂₀ has very small positive values, less than 0.2, which contradicts the theoretical calculations ignoring these degrees of freedom.

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Author Index.

Program of the Symposium.

List of Participants.