QCD at lowQ 2—A correspondence relation for moments of structure functions

The precocious validity of QCD predictions in deep inelastic lepton nucleon scattering ande ⁺ e ^? annihilation is interpreted as a signal for an underlying “correspondence principle” relating perturbative and nonperturbative physics on theQ ² average. Correspondence relations for nonsinglet moments of deep inelastic structure functions are formulated, discussed and successfully tested against experiment. The relations provide an independent determination of the QCD ?-parameter from lowQ ² data in perfect agreement with results from largeQ ² analyses.     

QCD cascade model in deep inelastic scattering

We develop a new QCD cascade model for jets in deep inelastic scattering. We use the light-like axial gauge whose gauge vector is parallel to momentum of the initial parton so that only final partons cascade. Due to this feature we can generate events for any given virtualityQ ² andx _B =Q ²/2Pq.     

Equivalence of the “Wilson expansion” and a generalized parton model

For a target made with constituents which interact via an asymptotically free theory, it is possible to define some parton densities in the deep inelastic region and at any order of the running coupling constant. These densities depend only on the structure of the target and their Q² dependence is governed by master equations. At first order the result of Altarelli and Parisi is recovered. The scattering of any current off the target is described by a convolution of these parton densities with some charge densities, depending on the couplings of the current to the partons. All those results are equivalent to those of the Wilson operator formalism. Some explicit examples are given.     

The reaction238U +238U at 7.42MeV/u

One-particle-inclusive measurements have been performed for the charge, kinetic energy and angular distributions of reaction products from²³⁸U +²³⁸U at 1 766MeV (7.42MeV/u) incident energy. The deep inelastic products exhibit features similar to those seen in reactions induced by medium heavy nuclei: increasing particle transfer is observed with increasing energy damping, the angular distributions are peaked near the grazing angle, they broaden significantly with increasing energy loss and/or charge transfer. The dominant reaction mechanism, however, is found to be sequential fission of one or both primary reaction products. The reconstructed primaryZ- andQ-value distributions show more particle transfer at a given energy loss than in other systems, i.e. the diffusion process seems to proceed colder in this system. This is confirmed by relatively large cross sections for surviving deep inelastic reaction products belowZ=92. A direct search forα-decay or fission of superheavy nuclei being produced in a deep inelastic reaction and being implanted in a surface barrier detector resulted in an upper cross section limit of 2 ×10^?32cm².     

Possible contribution of low-l waves to the deep inelastic collisions of 32S with 27Al

The deep inelastic reactions of ³²S with ²⁷A1 have been studied at incident energies of 152.6 and 175 MeV by measuring inclusive fragment distributions, fragment-fragment and fragment-light particle coincidences. The observed Q-value distributions of the primary deep inelastic process range down to large negative Q-values as predicted by time-dependent Hartree-Fock calculations in the presence of low partial waves. No distinct low-l window for deep inelastic reactions can, however, be inferred from the data.     

Spin structure of the nucleon—status and recent results

After the initial discovery of the so-called “spin crisis in the parton model” in the 1980s, a large set of polarization data in deep inelastic lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More recently, new high precision data at large x and in the resonance region have come from experiments at Jefferson Lab. These data, in combination with the earlier ones, allow us to study in detail the polarized parton densities, the Q² dependence of various moments of spin structure functions, the duality between deep inelastic and resonance data, and the nucleon structure in the valence quark region. Together with complementary data from HERMES, RHIC and COMPASS, we can put new limits on the flavor decomposition and the gluon contribution to the nucleon spin. In this report, we provide an overview of our present knowledge of the nucleon spin structure and give an outlook on future experiments. We focus in particular on the spin structure functions g₁ and g₂ of the nucleon and their moments.     

Structure functions and parton distributions

We review recent developments in the determination of parton densities from deep inelastic and related data. We show how the asymmetries observed in theW ^± rapidity distributions and inpp/pn Drell-Yan production further constrain the partons at moderatex.     

Higher order QCD effects in inclusive annihilation and deep inelastic scattering

We present a parton model interpretation of the predictions of quantum chromodynamics in the process e⁺e^?→hadron + anything. We give thecomplete list of parameters needed for the study of the scaling violations of fragmentation functions up to the next-to-leading logarithmic approximation. This includes flavour non-singlet and flavour singlet anomalous dimensions up to order α² and coefficient functions up to order α. We also present results for the deep inelastic scattering e^?h→e^? + anything. We find that in e⁺e^? annihilation the ratio of scaling violations of second order to first order is in general bigger than the corresponding ratio for deep inelastic scattering. The Gribov-Lipatov relation is thus violated in second order. We also find that a modified Drell-Yan analytic continuation relation holds between the deep inelastic and annihilation structure functions for quarks and gluons. In x space we give detailed numerical evaluation of the QCD effects for non-singlet and singlet densities, in the space-like and time-like regions.     

Scaling violations and the gluon distribution of the nucleon

Using recent data on deep inelastic lepton-nucleon scattering an attempt is made to extract the gluon distributionG(x, Q ²=4 GeV²) from the observed scaling violations of structure functions. The accuracy of the data allows only for a rough determination of the gluon distribution. In particular it is found that a hard gluon distributionis consistent with present measurements. Implications of the hard gluon distribution for charm production in the gluon fusion model and for the perturbative contributions to σ _L /σ _T are further discussed. Finally, analytic parametrizations of the QCDx- andQ ²-dependence of quark and gluon distributions are presented facilitating further possible applications.     

Smooth mass corrections to massless theories

We analyze the transition from massive to massless theories in cases in which mass singularities are present. In massless theories these singularities are absorbed into densities or fragmentation functions. We define a subtraction procedure for massive theories which is a canonical generalization of the “minimal subtraction” in massless theories. We use this procedure to calculate smooth mass corrections to the structure functionsF ₂ andG ₁ of deep inelastic scattering. In particular we show how, in our scheme, heavy quarks affect the spin of the proton.     

Hadronic colliders as probes of the proton spin structure

We perform a systematic analysis of different processes with high energy polarized proton beams: jets, direct photon, lepton pairs (Drell-Yan) andWZ production. Different sets of polarized partonic densities are used that fit EMC and SLAC polarized deep inelastic scattering data with variable amount of quark and gluon components of the proton spin. The case of the future Relativistic Heavy Ion Collider (RHIC) used as a polarized collider at a maximum energy of \(\sqrt s = 500\) GeV is analyzed in detail.     

Light particle emission in deeply inelastic collisions of 280 MeV40Ar+58Ni: Thermal equilibrium and angular momentum transfer

Protons andα-particles emitted in coincidence with a deep inelastic fragment produced in the reaction⁴⁰Ar (280 MeV)+⁵⁸Ni have been measured. From a detailed study of their in-plane angular distribution, it is shown that the bulk of the light charged particle emission can be attributed to a secondary evaporation process by the two primary deep inelastic fragments. A lowest estimate of the fragment spin (assuming total alignment perpendicular to the reaction plane) is obtained from the anisotropy of the out-of-plane angular distribution of theα-particles. For very asymmetric splitting, the heavy fragment spin estimate as obtained from theα-anisotropy measurement is consistent with the observed proton toα-particle multiplicity ratio. The results are in agreement with the hypothesis of a sticking configuration between two deformed nuclei.     

Production of149gTb in deep inelastic transfer reactions: An approach to the angular momentum of fragments

The excitation functions for deep inelastic reactions in which two to six charges are transferred from⁴⁰Ar and⁶³Cu ions to rare earth targets have been measured using activation techniques, the observed radionuclides being^{150, 151}Dy and^149gTb. From the comparison of the curves relative to^149gTb and those relative to^{150, 151}Dy, it was deduced that the low spin isomer^149gTb was produced with significant probability for low incident energies. Using data from (heavy ions,xn) reactions, it was possible to attribute this production to the deexcitation of Tb fragments formed in deep inelastic transfers with angular momenta lower than 9?. This result is in good agreement with the angular momentum calculations performed under the hypothesis that the initial angular momentum window leading to deep inelastic reactions is situated between the critical angular momentum for fusion and that corresponding to grazing collisions. As far as Cu induced reactions are concerned, both hypothesis of rolling and sticking are consistent with the experimental data. For Ar induced reactions, the results indicate that the stage of sticking is not reached when the incident energy is lower than 200 MeV. Nuclear Reactions:^{142, 145}Nd,^{144, 148}Sm,¹⁵⁴Gd(Ar,X)^{151, 150}Dy,^149gTbE=160–280 MeV; measuredσ(E).¹⁴⁴Nd,¹⁴⁸Sm,¹⁵¹Eu,¹⁵⁴Gd(Cu, X)^{151, 150}Dy,^149gTb.E=280–420 MeV measuredσ(E). Enriched targets. Deduced angular momentum of Tb fragments.     

Study of inelastic proton amplitudes for a fragmented analogue state in45Sc

The relative sign of inelastic proton-channel amplitudes has been measured for 31 resonances in⁴⁵Sc. These resonances include the fragmented 3/2^? analogue state observed atE ^p=2.62MeV in the⁴⁴Ca(p, p) and⁴⁴Ca(p, p′) reactions. The analogue fine structure is analyzed for the elastic and two inelastic channels; the Robson asymmetry is displayed clearly in the inelastic channels. The relative sign of the mixing ratio remains the same for the 15 fine structure resonances of the analogue. The mixing ratios enable the determination of the amplitude correlation of the widths in the inelastic channels. The recently introduced “off-diagonal strength function” is constructed from these data and compared with the theory of analogue state broadening.     

Nuclear gamma-transitions via the accompanying atomic excitations

The nuclearγ-transitions via excitation of the atomic electrons (electronic bridges) is considered in the framework of the strong coupling channels method. The nuclearM4 transitions from the lowest isomeric level of nuclei⁹³Nb and¹⁹³Ir in the both mechanisms of elastic and inelastic electronic bridges are investigated. The comparison between the semiclassical and selfconsistent Dirac-Hartree-Fock-Slater calculations is presented. The derived valuesκ _f of a relative probability of nuclearγ-transition via the atomic excitation (inelastic electronic bridge)κ _f(⁹³Nb)=6.9·10^?2 andκ _f(¹⁹³Ir)=1.4·10^?2 are in agreement with the experimental data.     

Quasielastic versus inelastic and deep inelastic lepton scattering in nuclei at x > 1

We have made a thorough investigation of the nuclear structure function W_2A in the region of 0.8 < x < 1.5 and Q² < 20 GeV², separating the quasielastic and inelastic plus deep inelastic contributions. The agreement with present experimental data is good giving support to the results for both channels. Predictions are made in yet unexplored regions of x and Q² to assert the weight of the quasielastic or inelastic channels. We find that at Q² < 4 GeV² the structure function is dominated by the quasielastic contributions for x < 1.5, while for values of Q² > 15 GeV² and the range of x studied the inelastic channels are over one order of magnitude bigger than the quasielastic one. The potential of the structure function at x > 1 as a source of information on nuclear correlations is stressed once more.