Polarized Structure Functions Research Articles

Spin-dependent structure functions of the photon

The implications of the positivity constraint on the presently unknown polarized structure function of the photon, g 1 γ ( x, Q 2), are studied in detail. In particular the non-trivial consequences of this constraint, | g 1 γ ( x, Q 2)|⩽ F 1 γ ( x, Q 2), in the next-to-leading order analysis of g 1 γ are pointed out by employing appropriate (DIS) factorization schemes related to g 1 γ and F 1 γ (rather than to F 2 γ ).

Do we expect light flavor sea-quark asymmetry also for the spin-dependent distribution functions of the nucleon?

After taking account of the scale dependence by means of the standard DGLAP evolution equation, the theoretical predictions of the chiral quark soliton model for the unpolarized and longitudinally polarized structure functions of the nucleon are compared with the recent high energy data. The theory is shown to explain all the qualitative features of the experiments, including the NMC data for $F_2^p (x) - F_2^n (x)$, $F_2^n (x) / F_2^p (x)$, the Hermes and NuSea data for $\bar{d}(x) - \bar{u}(x)$, the EMC and SMC data for $g_1^p(x)$, $g_1^n(x)$ and $g_1^d(x)$. Among others, flavor asymmetry of the longitudinally polarized sea-quark distributions is a remarkable prediction of this model, i.e., it predicts that $\Delta \bar{d}(x) - \Delta \bar{u}(x) = C x^{\alpha} [ \bar{d}(x) - \bar{u}(x)]$ with a sizable negative coefficient $C \simeq -2.0$ (and $\alpha \simeq 0.12$) in qualitative consistency with the recent semi-phenomenological analysis by Morii and Yamanishi.

Twist - 3 polarized structure functions

We review the nucleon's twist-3 polarized structure functions from the viewpoint of gauge invariant, nonlocal light-cone operators in QCD. We discuss a systematic treatment of the polarized structure functions and the corresponding parton distribution functions. We emphasize unique features of higher twist distributions, and the role of the QCD equations of motion to derive their anomalous dimensions for Q 2-evolution.

Nucleon structure functions in a chiral soliton model

The computation of nucleon structure functions within the Nambu-Jona-Lasinio chiral soliton model is outlined. After some technical remarks on the issue of regularization numerical results for the both unpolarized and polarized structure functions are presented. The generalization to flavor SU(3) is sketched.

Renormalization of twist-three operators and integrable lattice models

We address the problem of solution of the QCD three-particle evolution equations which govern the Q2-dependence of the chiral-even quark–gluon–quark and three-gluon correlators contributing to a number of asymmetries at leading order and the transversely polarized structure function g2(xBj). The quark–gluon–quark case is completely integrable in multicolour limit and corresponds to a spin chain with non-periodic boundary conditions, while the pure gluonic sector contains, apart from a piece in the Hamiltonian equivalent to XXX Heisenberg magnet of spin s=−32, a non-integrable addendum which can be treated perturbatively for a bulk of the spectrum except for a few lowest energy levels. We construct a quasiclassical expansion with respect to the total conformal spin of the system and describe fairly well the energy spectra of quark–gluon–quark and three-gluon systems.

Twist-3 contribution tohLin the instanton vacuum

We show that the instanton model of the QCD vacuum indicates the parametric smallness of the twist-3 contributions to the polarized structure function ${h}_{L}.$ This smallness is related to the diluteness of the QCD instanton vacuum.

Polarized structure functions of the nucleon in the resonance region

We present predictions for the spin structure functions of the proton in the framework of a unitary isobar model for one-pion photo- and electroproduction. Our results are compared with recent experimental data from SLAC. The first moments of the calculated structure functions fullfil the Gerasimov-Drell-Hearn and Burkhardt-Cottingham sum rules within an error of typically 5–10%.

Nucleon mass corrections to spin dependent structure functions and relations between their twist-3 contributions

The nucleon mass corrections are calculated to all polarized structure functions for neutral and charged current deep inelastic scattering in lowest order in the coupling constant. The impact of the target mass corrections on the general relations between the twist-2 and twist-3 parts of the structure functions is studied and three new relations between the twist-3 contributions are derived. The size of nucleon mass corrections for the g 1 and g 2 structure functions are estimated.

Twist-4 corrections to polarized structure functions in the flavor singlet sector

We summarize findings of infrared renormalon calculations to model twist-4 corrections to the polarized structure function g 1( x, Q 2).

Future physics with polarised protons at HERA

We discuss the option of having polarised protons in the HERA ep -collider at DESY. We give an overview of the physics potential, with special emphasis on the polarised structure function g i p and the polarised gluon density G(x) of the proton.

Target mass corrections for polarized structure functions and new sum rules

The target mass corrections are calculated for all structure functions of neutral and charged current deep inelastic scattering in lowest order in the coupling constant. Representations of the correction to the twist-2 and twist-3 contributions are derived both in Mellin- n and x-space. The impact of the target mass corrections on the general relations between the twist-2 and twist-3 parts of the structure functions is studied and three new relations between the twist-3 contributions are derived.

Structure functions in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons. I. General formalism

We discuss general formalism for the structure functions which can be investigated in the polarized Drell-Yan processes with spin-1/2 and spin-1 hadrons. To be specific, the formalism can be applied to the proton-deuteron Drell-Yan processes. Because of the spin-1 nature, there are new structure functions which cannot be studied in the proton-proton reactions. Imposing Hermiticity, parity conservation, and time-reversal invariance, we find that 108 structure functions exist in the Drell-Yan processes. However, the number reduces to 22 after integrating the cross section over the virtual-photon transverse momentum Q_T or after taking the limit Q_T->0. There are 11 new structure functions in addition to the 11 ones in the Drell-Yan processes of spin-1/2 hadrons. The additional structure functions are associated with the tensor structure of the spin-1 hadron, and they could be measured by quadrupole spin asymmetries. For example, the structure functions exist for "intermediate" polarization although their contributions vanish in the longitudinal and transverse polarization reactions. We show a number of spin asymmetries for extracting the polarized structure functions. The proton-deuteron reaction may be realized in the RHIC-Spin project and other future ones, and it could be a new direction of next generation high-energy spin physics.

Polarized Structure Functions in QCD

Hadron spin physics is now one of the most active fields of physics. Especially in the last ten years, great progress has been made both theoretically and experimentally that has considerably improved our knowledge of the spin structure of nucleons. We review the nucleon's polarized structure functions from the viewpoint of factorization theorems and the gauge invariant, nonlocal light-cone operators in QCD. We discuss a systematic treatment of the polarized structure functions and the corresponding parton distribution functions, which are relevant to inclusive lepto- and hadro-production. We give a detailed analysis of these spin-dependent distribution functions at the twist-2 and twist-3 level, and present various properties and relations satisfied by the parton distributions, which can be derived directly from QCD. We emphasize unique features of higher twist distributions, and the role of the QCD equations of motion to derive their sensitivity to the quark-gluon correlation and their anomalous dimensions for Q^2-evolution.

Target mass corrections to the spin-dependent structure functions

The target mass corrections are calculated for polarized structure functions of neutral and charged current interactions. The influence of such corrections to the twist-2 relations between the structure functions are discussed.

Small-x behaviour of the nonsinglet polarized structure function g2 in DLA QCD

Small-x behaviour of the nonsinglet polarized structure function g2 in DLA QCD

A study of the polarized structure function

We present estimates of possible data on spin-dependent asymmetries in inclusive scattering of high energy polarized electrons by high energy polarized protons at HERA with their statistical errors and discuss systematic errors. We show that these data will provide important information on the low-x behavior of the polarized structure function g_1, and will reduce the uncertainty in the determination of the first moment of the polarized gluon distribution Delta g(x,Q^2) obtained from the QCD analysis of g_1 in NLO. Furthermore, using asymmetries for di-jet events from a polarized HERA would substantially reduce the uncertainty in the shape of Delta g(x,Q^2). Using the information on Delta g(x,Q^2) from the di-jet analysis in conjunction with the NLO QCD analysis of g_1 will provide an accurate determination of Delta g(x,Q^2) and its first moment.

Spin physics in deep inelastic scattering: summary

The problem of our understanding of the spin structure of the nucleon has been with us since the publication of the EMC measurements of the polarized structure function of the proton in 1987. In this talk a review of the results discussed in Working Group 6 at this workshop is presented.

Polarized structure functions in a constituent quark scenario

Using a simple picture of the constituent quark as a composite system of point-like partons, we construct the polarized parton distributions by a convolution between constituent quark momentum distributions and constituent quark structure functions. Using unpolarized data to fix the parameters we achieve good agreement with the polarization experiments for the proton, while not so for the neutron. By relaxing our assumptions for the sea distributions, we define new quark functions for the polarized case, which reproduce well the proton data and are in better agreement with the neutron data. When our results are compared with similar calculations using non-composite constituent quarks the accord with the experiments of the present scheme is impressive. We conclude that, also in the polarized case, DIS data are consistent with a low energy scenario dominated by composite constituents of the nucleon.

Quark and gluon orbital angular momentum and spin in hard processes

We suggest a method of constructing gauge-invariant quark and gluon distributions that describe an abstract QCD observable and apply this method to analyze angular momentum of a hadron. In addition to the known quark and gluon polarized structure functions, we obtain gauge-invariant distributions for quark and gluon orbital angular momenta, and consider some basic properties of these distributions and their moments.

Bloom-Gilman duality in the resonance spin structure functions

We investigate the relations between the spin structure functions in the scaling and resonance regions. We examine the possible duality between the two, and draw inferences for the behavior of the asymmetry ${A}_{1}$ at large $x.$ Finally, we point out the importance of additional polarized structure function data in the resonance region for observing lingering effects of single quark interactions in a region where final state interactions are large.