abstract

We review the analysis of polarized structure function data using perturbative QCD at NLO. We use the most recent experimental data to obtain updated results for polarized parton distributions, first moments and the strong coupling. We also discuss several theoretical issues involved in this analysis and in the interpretation of its results. Finally, we compare our results with other similar analyses in the recent literature.

abstract

We will give an outline of the computation of the QCD corrections to the spin structure function \(g_1(x,Q^2)\) and the spin fragmentation function \(g_1^{H}(x,Q^2)\) which are measured in deep inelastic electron-proton scattering and in electron-positron annihilation respectively. In particular we show how to deal with the \(\gamma _5\)-matrix and the Levi–Civita tensor, appearing in the amplitudes of the parton subprocesses, when the method of \(N\)-dimensional regularization is used.

abstract

We discuss the NLO evolution of quark transversity densities and of the parton distribution function for linearly polarized gluons in a linearly polarized hadron. A supersymmetric relation between the NLO evolution kernels for transversity and for linear polarization is found. We also study the implications of NLO evolution for Soffer’s inequality and the prospects of measuring transversity densities in polarized Drell–Yan at RHIC.

abstract

Theoretical expectations concerning small \(x\) behaviour of the spin dependent structure function \(g_1\) are summarised. This includes discussion of the Regge pole model predictions and of the double \(\ln ^2(1/x)\) effects implied by perturbative QCD. The quantitative implementation of the latter is described within the unified scheme incorporating both Altarelli–Parisi evolution and the double \(\ln ^2(1/x)\) resummation. The double \(\ln ^2(1/x)\) effects are found to be important in the region of \(x\) which can possibly be probed at HERA. Predictions for the polarized gluon distribution \({\mit \Delta } G(x,Q^2)\) at low \(x\) are also given.

abstract

We investigate coherence effects in the deuteron spin structure functions \(g_1^d\) and \(b_1\). In the kinematic domain of current fixed target experiments we observe that shadowing effects in \(g_1^d\) are approximately twice as large as for the unpolarized structure function \(F_2^d\). Furthermore, we find that \(b_1\) is large at \(x\lt 0.1\) and receives dominant contributions from coherent double scattering.

abstract

In this talk I want to illustrate the many possibilities for studying the structure of hadrons in hard scattering processes by giving a number of examples involving increasing complexity in the demands for particle polarization, particle identification or polarimetry. In particular the single spin asymmetries will be discussed. The measurements discussed in this talk are restricted to lepton-hadron scattering, but can be found in various other hard processes such as Drell–Yan scattering or \(e^+e^-\)-annihilation.

abstract

We present an analysis of leading order QCD amplitudes for hard exclusive leptoproduction of mesons in terms of double/nonforward parton distribution functions. Using a model for quark and gluon double distributions we derive explicit expressions for hard exclusive \(\pi ^0\), \(\eta \), neutral and charged \(\rho \) meson production amplitudes.

abstract

The concept of the QCD structure of electron is presented. Advantages of the electron structure function over that of the photon are demonstrated in the electron induced processes. At very high momenta probabilistic interpretation can be preserved despite strong \(\gamma \)-\(Z\) interference.

abstract

In the light of recent HERA data, we analyze the connection between \(F_2\) at low \(x\) and diffractive production within a Generalized Vector Dominance picture.

abstract

Experimental results of deep inelastic scattering of polarized leptons from polarized target nucleons are reviewed. Accurate values of the spin dependent structure function \(g_1(x)\) were obtained in experiments covering a large kinematic range. The combination of all experimental results confirms the validity of the Bjorken sum rule.

abstract

The study of the spin structure of the nucleon is the primary goal of the HERMES experiment. In 1995, the first year of the experiment, the neutron structure function \(g_1^n\) was measured using a polarised \(^3\)He target. Additionally, semi-inclusive hadron and pion asymmetries were extracted from \(^3\)He. In 1996/97 a polarised hydrogen target was employed and preliminary results of the inclusive asymmetry as well as semi-inclusive hadron and pion asymmetries are presented. Preliminary results from the HERMES unpolarised physics program are shown including the valence quark distribution ratio \(d_{\rm v}(x)/u_{\rm v}(x)\), the flavour asymmetry of the light quark sea, measurements of fragmentation functions and the decay angular distributions of \(\rho ^0\) mesons produced in exclusive deep inelastic electro-production.

abstract

We present a Next-to-Leading (NLO) QCD analysis of the presently available world data on the spin structure function \(g_1\), including the data on \(g_1^p\) taken by the SMC in 1996. The fit result is used to determine \(g_1^p\) at a constant \(Q^2\) and such the first moment \({\mit \Gamma }_1^p=\int \limits g_{1}^{p}(x)dx\). Its value is found to depend on the approach used to describe the behaviour of \(g_{1}^{\rm p}\) at low-\(x\). Independent of the approach we find that the Ellis–Jaffe sum rule is violated while the validity of the Bjorken sum rule is confirmed.

abstract

The RHIC facility at BNL will be operating soon, part of the year, as a polarized proton-proton collider. This will allow the undertaking of a vast spin physics programme, mainly by the two large detectors PHENIX and STAR. We review some theoretical aspects of this research programme which will allow, firstly to improve our present knowledge on polarized quark, gluon and sea distributions in a nucleon, secondly to perform novel QCD spin tests and finally, perhaps, to uncover some new physics.

abstract

The COMPASS experiment at CERN will directly access polarization of gluons in the nucleon in the region \(x_g \gt 0.02\). It will use a polarized muon beam of 100 GeV and 200 GeV and longitudinally polarized hydrogen (NH\(_3\)) and deuterium (\(^6\)LiD) targets. The gluon polarization will be determined from the measurements of charmed meson production and from the production of correlated, hight-p\(_t\) hadron pairs \(h^+h^-\) which tag the photon-gluon fusion reaction. In one year of data taking, the gluon polarization will be determined with a precision \(\delta (\Delta G/G) \sim 0.15\) and \(0.05\) using the first and the second measurement, respectively.

abstract

The operation of HERA with polarized proton and electron beams will allow to study a wide variety of observables in polarized electron–proton collisions at \(\sqrt s=300\) GeV. The physics prospects of this project have been elaborated in detail in a dedicated working group, whose results we summarize in this paper. We show that several important and often unique measurements in spin physics could be made at HERA. These include measurements of the polarized structure function \(g_1(x,Q^2)\) at low \(x\), a direct determination of the polarized gluon distribution \(\Delta G(x,Q^2)\) for the region \(0.002\lt x\lt 0.2\) from polarized di–jet rates and hadrons with high \(p_t\), polarized quark distributions from weak structure functions and semi-inclusive asymmetries, parton distributions in the polarized photon and information on the helicity structure of possible new physics at large \(Q^2\). Additionally, a program of polarized proton–proton scattering is proposed, using the high energy polarised proton beam on a polarized fixed target. In all, HERA could make a significant contribution to our understanding of spin effects in high energy collisions and to the spin structure of the nucleon.

abstract

There is a brief review of the history of polarized proton beams and the unexpected and still unexplained large transverse spin effects found in high energy proton spin experiments at the ZGS, AGS and Fermilab. Next there is a detailed discussion of Siberian snakes and some of their tests at the IUCF Cooler Ring. Finally there is a report on the use of Siberian snakes in some possible high energy polarized proton beams at RHIC, HERA and Fermilab.

abstract

Tau lepton production and decay to hadronic final states offer the unique possibility for studying low energy hadron dynamics and the weak couplings of the \(\tau \) at the same time. Eventually one may even be sensitive to signals of physics beyond the Standard Model, like deviations from the \(V-A\) structure of the charged currents, or even discover CP violation. Tau polarization and the polarization of the decay products may be crucial for these investigations.

abstract

A short introduction into the jet handedness and the handedness correlation is given. Its experimental status in \(Z^0\to q\bar q \to 2\ jets\) decay using the DELPHI 91-95 data is considered. For the longitudinal jet handedness correlation a puzzling effect was confirmed. The sign of the correlation is opposite to that predicted by the Standard Model, assuming factorization of \(q\) and \(\bar {q}\) fragmentation process. The hypothesis on the influence to the effect of a vacuum chromo-magnetic field was tried to check experimentally.

abstract

Spin alignment of inclusive vector mesons and longitudinal polarization of \({\mit \Lambda }\) hyperons have been measured in a sample of 4.3 million hadronic \(Z^0\) decays from the OPAL experiment at LEP. Leading, light vector mesons have been found to populate preferentially the helicity-zero state, a result which has no firm theoretical explanation. The values of off-diagonal elements of the helicity density matrix are in agreement with a theory based on the standard model with coherent fragmentation. The longitudinal polarization of the \({\mit \Lambda }\) is well described by a model in which the constituent strange quark carries all of the hyperon spin.

abstract

The Standard Model predicts that at LEP at the \(Z^0\) pole \(b\) quarks are produced with a high (\(\approx -0.94\)) longitudinal polarization. According to the HQET predictions substantial part of it should be transferred to the ground baryonic state \({\mit \Lambda }_b\). The polarization is experimentally accessible by measuring the charged lepton and neutrino energy spectra from the \({\mit \Lambda }_b\) semileptonic decays. From the data sample of \(\approx 3\) million hadronic \(Z^0\) decays collected by DELPHI in the years 1993–1995 \(271\pm 22\) \({\mit \Lambda }_b\) semileptonic decay candidates are selected using \({\mit \Lambda }^0\)-lepton correlations giving rise to the polarization value of \(P_{{\mit \Lambda }_b} = -0.48_{-0.27}^{+0.35}({\rm stat.}) _{-0.13}^{+0.15}({\rm syst.})\).

abstract

In the infinite mass limit for a heavy quark its spin decouples from the QCD dynamics, which leads to the heavy-quark spin symmetry. After a short discussion of spin symmetry some applications are considered.

abstract

Recently the one-loop perturbative QCD correction to the longitudinal polarization of tau lepton in semileptonic \(B\) decays has been found. Its smallness suggests that the higher order perturbative corrections are generally insignificant as far as the polarization is concerned. Prompted by the experimental need, I give here the polarization with respect to the \(W\) boson direction in Born approximation.

abstract

A model based on a nonrelativistic potential supplemented by spin dependent terms of the Breit–Fermi type is described. This model reproduces the known masses of the \(\overline {b}b\) quarkonia within \(1\)MeV and the known masses of the \(\overline {c}c\) quarkonia within \(5\)MeV. Many predictions are made, some of them, e.g. for the fine splittings of the high \(L\) states of the \(\overline {b}b\) quarkonia and of the mass spectrum of the \(\overline {b}c\) quarkonia, significantly different from previous predictions made by other authors.

abstract

We discuss the physics involved in the production and decay chain of top quarks in \(e^+e^- \to t\bar {t} \to bl^+\nu \bar {b}W^-\) near the top quark threshold. We elucidate the effects of the final-state interactions. Namely, we clarify how the evolution and decay of \(t\) in this process are affected by the chromostatic field generated by the other color charge (\(\bar {t}\) or \(\bar {b}\)) nearby. Furthermore, we propose and calculate inclusive and exclusive observables in the threshold region. The latter depends only on the decay of free polarized top quarks, and thus it can be calculated without knowledge of bound-state effects or the final-state interactions.

abstract

If all new particles are too heavy to be directly produced in the future Colliders, then the long sought New Physics (NP) could only appear in the form of new interactions, beyond those of the Standard Model (SM). Many of the processes that could be used to study these interactions, have already been discussed in the literature. Here, I first briefly discuss the list of all not yet excluded CP conserving such interactions, realized as SU(3)\(\times \)SU(2)\( \times \)U(1) gauge invariant \({\rm dim}=6\) operators affecting the Higgs and the quarks of the third family. Subsequently, I concentrate on the \(\gamma t\bar t\) and \(Zt\bar t\) vertices generated by NP, and on the possibility to study them by using various spin asymmetries accessible in \(e^-e^+ \to t \bar t\), for polarized and unpolarized beams. It is found that these asymmetries can fully determine the form of the \(\gamma t\bar t\) and \(Zt\bar t\) couplings.

abstract

Spin observables may reveal much deeper properties of non perturbative hadronic physics than unpolarized quantities. We discuss the polarization of hadrons produced in \(e^+e^-\) annihilation at LEP. We show how final state \(q \bar q\) interactions may give origin to non zero values of the off-diagonal element \(\rho ^{\,}_{1,-1}\) of the helicity density matrix of vector mesons: some predictions are given for \(K^*, \phi , D^*\) and \(B^*\) in agreement with recent OPAL data. We also discuss the relative amount of vector and pseudovector meson states and the probability of helicity zero vector states. Similar measurements in other processes are suggested.

abstract

We discuss spin effects for \(W\)-pair production and decay at LEP2 and higher energies. As an example we use observables in the \(s\bar s c \bar c\) decay channel: the two-quark/jet invariant-mass distribution and cross section, in the case when the other two may escape detection. We show, the strong interplay of spin correlations and detector cut-offs resulting in narrowly peaked distributions.

abstract

A new approach to determine the LHC luminosity is investigated. Instead of employing the proton–proton luminosity measurement, we suggest to measure directly the parton–parton luminosity. It is shown that the electron and muon pseudorapidity distributions, originating from the decay of \(W^{+}\), \(W^{-}\) and \(Z^{0}\) bosons produced at 14 TeV pp collisions (LHC), constrain the \(x\) distributions of sea and valence quarks and antiquarks in the range from \(\approx 3 \times 10^{-4}\) to \(\approx 10^{-1}\) at a \(Q^{2}\) of about \(10^{4}\) GeV\(^{2}\). Using this information one can relate the rate of \(l^{\pm }\) events to the quark and antiquark luminosity at the LHC. Furthermore, it is demonstrated that other \(q\bar {q}\) related scattering processes like \( q\bar {q} \rightarrow W^{+}W^{-}\)can then be predicted accurately. This continuum production is an important background process for the resonant signature \( H \rightarrow W^{+}W^{-} \rightarrow l^+\nu l^-\bar {\nu }\). It is shown that precise prediction of this background enhances the discovery potential for the Standard Model Higgs in the \(W^{+}W^{-}\) decay channel for 120 GeV \(\leq m_H \leq \) 500 GeV.

abstract

We study the process \(e^+ e^- \to \tilde {\chi }^0_1\tilde {\chi }^0_2\) and the subsequent decay \(\tilde {\chi }^0_2 \to \tilde {\chi }^0_1 \ell ^{+}\ell ^{-}\) with polarized beams, including the complete spin correlations of \(\tilde {\chi }^0_2\). We present numerical results for the lepton energy and angular distributions, and for the distribution of the opening angle between the leptons for \(\sqrt {s}=500\) GeV. The effects of spin correlations are important in the lepton angular distribution, especially for gaugino–like neutralinos. The opening angle distribution is particularly suitable for distinguishing between higgsino- and gaugino-like neutralinos. The polarized cross sections and lepton angular distributions are very sensitive to the mixing of the neutralinos.

abstract

We review the recent work on obtaining precise estimates of higher-order corrections in QCD and field theory.