Proton Spin Problem Research Articles

Symmetry of Dirac two-oscillator system, gauge-invariance, and Landau problem

Role of gauge symmetry in the proton spin problem has intricate and unresolved aspects. One of the interesting approaches to gain physical insights is to explore the Landau problem in this context. A detailed study using the group theoretic method to understand the Landau problem establishes the significance of the gauge transformation intimately related with the space translation symmetry. An important implication of this result is that the E(2)-like Wigner’s little group for massless particles could throw more light on the question of gauge symmetry in QED and QCD. A generalized Landau-Zeeman Hamiltonian is proposed in which Dirac two-oscillator system and the symmetry of the group SO(3,2) become important. It is argued that nontrivial topology of pure gauge field holds promise to resolve the unsettled questions.

Proton spin structure at small-x

We generalize the Bartels-Ermolaev-Ryskin approach for the g1 structure function at small-x[1,2] to determine the small-x asymptotic behavior of the orbital angular momentum distributions in QCD. We present an exact analytical solution of the evolution equation in the double logarithmic approximation and discuss its implications for the proton spin problem.

Proton spin: A topological invariant

Proton spin problem is given a new perspective with the proposition that spin is a topological invariant represented by a de Rham 3-period. The idea is developed generalizing Finkelstein–Rubinstein theory for Skyrmions/kinks to topological defects, and using non-Abelian de Rham theorems. Two kinds of de Rham theorems are discussed applicable to matrix-valued differential forms, and traces. Physical and mathematical interpretations of de Rham periods are presented. It is suggested that Wilson lines and loop operators probe the local properties of the topology, and spin as a topological invariant in pDIS measurements could appear with any value from 0 to [Formula: see text], i.e. proton spin decomposition has no meaning in this approach.

Nonperturbative parton distributions and the proton spin problem

The Lorentz contracted form of the static wave functions is used to calculate the valence parton distributions for mesons and baryons, boosting the rest frame solutions of the path integral Hamiltonian. It is argued that nonperturbative parton densities are due to excitedmultigluon baryon states. A simplemodel is proposed for these states ensuring realistic behavior of valence and sea quarks and gluon parton densities at Q2 = 10 (GeV/c)2. Applying the same model to the proton spin problem one obtains Σ3 = 0.18 for the same Q2.

Gluonic structure of the constituent quark

Based on both the constituent quark picture and the instanton model for QCD vacuum, we calculate the unpolarized and polarized gluon distributions in the constituent quark and in the nucleon. Our approach consists of the two main steps. At the first step, we calculate the gluon distributions inside the constituent quark generated by the perturbative quark-gluon interaction, the non-perturbative quark-gluon interaction, and the non-perturbative quark-gluon-pion anomalous chromomagnetic interaction. The non-perturbative interactions are related to the existence of the instantons, strong topological fluctuations of gluon fields, in the QCD vacuum. At the second step, the convolution model is applied to derive the gluon distributions in the nucleon. A very important role of the pion field in producing the unpolarized and the polarized gluon distributions in the hadrons is discovered. We discuss a possible solution of the proton spin problem.

Octet spin fractions and the proton spin problem.

The relatively small fraction of the spin of the proton carried by its quarks presents a major challenge to our understanding of the strong interaction. Traditional efforts to explore this problem have involved new and imaginative experiments and QCD based studies of the nucleon. We propose a new approach to the problem that exploits recent advances in lattice QCD. In particular, we extract values for the spin carried by the quarks in other members of the baryon octet in order to see whether the suppression observed for the proton is a general property or depends significantly on the baryon structure. We compare these results with the values for the spin fractions calculated within a model that includes the effects of confinement, relativity, gluon exchange currents, and the meson cloud required by chiral symmetry, finding a very satisfactory level of agreement given the precision currently attainable.

Interplay of Spin and Orbital Angular Momentum in the Proton

We derive the consequences of the Myhrer-Thomas explanation of the proton spin problem for the distribution of orbital angular momentum on the valence and sea quarks. After QCD evolution, these results are found to be in very good agreement with both recent lattice QCD calculations and the experimental constraints from Hermes and JLab.

A possible resolution of the proton spin problem

A number of lines of investigation into the structure of the nucleon have converged to the point where it seems possible to propose a consistent explanation of the well known proton spin problem.

X-dependence of the quark distribution functions in the χCQMconfig

Chiral constituent quark model with configuration mixing (χCQMconfig) is known to provide a satisfactory explanation of the “proton spin problem” and related issues. In order to enlarge the scope of χCQMconfig, we have attempted to phenomenologically incorporate x-dependence in the quark distribution functions. In particular, apart from calculating valence and sea quark distributions qval(x) and q(x), we have carried out a detailed analysis to estimate the sea quark asymmetries d(x)-ū(x), d(x)/ū(x) and $\frac{\overline{d}(x)-\overline{u}(x)}{u(x)-d(x)}$ as well as spin independent structure functions F2 p(x)-F2 n(x) and F2 n(x)/F2 p(x) as functions of x. We are able to achieve a satisfactory fit for all the above mentioned quantities simultaneously. The inclusion of effects due to configuration mixing have also been examined in the case F2 p(x)-F2 n(x) and F2 n(x)/F2 p(x) where the valence quark distributions dominate and it is found that it leads to considerable improvement in the results. Further, the valence quark structure has also be tested by extrapolating the predictions of our model in the limit x→1 where data is not available.

Formula omitted] as the lowest mass pseudoscalar glueball and proton spin problem

We consider the parity doublet structure observed in high hadronic excitations within the instanton model for the QCD vacuum. In the conventional approach this doubling phenomenon is treated as a manifestation of the partial restoration of chiral or U(1)A symmetry. We demonstrate that the suppression of direct instanton contribution to the masses of excited hadrons leads to the partial U(1)A symmetry restoration in hadron spectrum. The origin of X(1835) resonance observed by BES Collaboration is studied upon the doublet structure. We argue also how X(1835) be interpreted as the lowest pseudoscalar glueball state, and derive its coupling constant to proton. It turns out that this coupling is large and negative. Demonstrated is how this large coupling affects the gluonic contribution to the proton spin.

Effect of asymmetric strange–antistrange sea to the NuTeV anomaly

We calculate the strange quark and antiquark distributions of the nucleon by using the effective chiral quark model, and find that the strange–antistrange asymmetry can bring a contribution of about 60–100% to the NuTeV deviation of sin2θw from the standard value measured in other electroweak processes. The results are insensitive to different inputs. The light-flavor quark asymmetry of d¯–u¯ is also investigated and found to be consistent with the experimental measurements. Therefore the chiral quark model provides a successful picture to understand the NuTeV anomaly, as well as the light-flavor quark asymmetry and the proton spin problem in previous studies.

Neutrino Interactions in Octet Baryon Matter

Neutrino processes caused by the neutral current are studied in octet baryon matter. Previous confusion about the baryonic matrix elements of the neutral current interaction is excluded, and a correct table for them improved by consideration of the proton spin problem is presented instead.

Proton spin structure and the axial U(1) problem

We emphasise the relation between the spin structure of the proton and the axial U(1) problem. New experiments motivated by the proton spin problem which could shed light on the nature of U(1) symmetry breaking in QCD are discussed.

The spin structure of the proton and polarized collider physics

We summarise the present status of the proton spin problem and the physics possibilities for future polarized ep and pp colliders. This summary is based on the presentations and discussion sessions at the workshop “The Spin Structure of the Proton and Polarized Collider Physics” (Trento, July 23–28, 2001).

The spin structure of constituent quarks

We review the theory and present status of the proton spin problem and discuss how the spin structure of constituent quarks is manifest in polarised deep inelastic scattering.

The proton spin in the chiral bag model: Casimir contributions and Cheshire Cat Principle

The flavor singlet axial charge has been a source of study in the last years due to its relation to the so-called Proton Spin Problem. The relevant flavor singlet axial current is anomalous, i.e., its divergence contains a piece which is the celebrated U A (1) anomaly. This anomaly is intimately associated with the η′ meson, which gets its mass from it. When the gauge degrees of freedom of QCD are confined within a volume as is presently understood, the U A (1) anomaly is known to induce color anomaly leading to “leakage” of the color out of the confined volume (or bag). For consistency of the theory, this anomaly should be canceled by a boundary term. This “color boundary term” inherits part or most of the dynamics of the volume (i.e., QCD). In this paper, we exploit this mapping of the volume to the surface via the color boundary condition to perform a complete analysis of the flavor singlet axial charge in the chiral bag model using the Cheshire Cat Principle. This enables us to obtain the hitherto missing piece in the axial charge associated with the gluon Casimir energies. The result is that the flavor singlet axial charge is small independent of the confinement (bag) size ranging from the skyrmion picture to the MIT bag picture, thereby confirming the (albeit approximate) Cheshire Cat phenomenon.

Constituent quarks and g 1

We review the theory and present status of the proton spin problem with emphasis on the transition between current quarks and constituent quarks in QCD.

Color anomaly and flavor-singlet axial charge of the proton in the chiral bag: The Cheshire Cat revisited

Quantum effects inside the chiral bag induce a color anomaly which requires a compensating surface term to prevent breakdown of color gauge invariance. We show that the presence of this surface term first discovered several years ago allows one to derive in a gauge-invariant way a chiral-bag version of the Shore-Veneziano two-component formula for the flavor-singlet axial charge of the proton. This has relevance to what is referred to as the “proton spin problem” on the one hand and to the Cheshire-Cat phenomenon in hadron structure on the other. We show that when calculated to the leading order in the color gauge coupling and for a specific color electric monopole configuration in the bag, one can obtain a striking Cheshire-Cat phenomenon with a negligibly small singlet axial charge.

STATUS OF THE PROTON SPIN PROBLEM

The proton spin problem triggered by the EMC experiment and its present status are closely examined. Recent experimental and theoretical progresses and their implications are reviewed. It is pointed out that the sign of the sea quark polarization generated perturbatively by hard gluons via the anomaly mechanism is predictable. It is negative if the gluon spin component is positive. We stress that the polarized nucleon structure function g1(x) is independent of the k⊥ factorization scheme chosen in defining the quark spin density and the hard photon–gluon scattering cross-section. Consequently, the anomalous gluon and sea quark interpretations for Γ1, the first moment of g1(x), are equivalent. It is the axial anomaly that accounts for the observed suppression of [Formula: see text].

The quark-antiquark asymmetry of the nucleon sea

Although the distributions of sea quarks and antiquarks generated by leading-twist QCD evolution through gluon splitting g → qq are necessarily CP symmetric, the distributions of nonvalence quarks and antiquarks which are intrinsic to the nucleon's bound state wavefunction need not be identical. In this paper we investigate the sea quark-antiquark asymmetries in the nucleon wavefunction which are generated by a light-cone model of energetically-favored meson-baryon fluctuations. The model predicts striking quark-antiquark asymmetries in the momentum and helicity distributions for the down and strange contributions to the proton structure function: the intrinsic d and s quarks in the proton sea are predicted to be negatively polarized, whereas the intrinsic d and s antiquarks give zero contributions to the proton spin. Such a picture is supported by experimental phenomena related to the proton spin problem and the violation of the Ellis-Jaffe sum rule. The light-cone meson-baryon fluctuation model also suggests a structured momentum distribution asymmetry for strange quarks and antiquarks which could be relevant to an outstanding conflict between two different determinations of the strange quark sea in the nucleon. The model predicts an excess of intrinsic d d pairs over u u pairs, as supported by the Gottfried sum rule violation. We also predict that the intrinsic charm and anticharm helicity and momentum distributions are not identical.