Quark Orbital Angular Momentum Research Articles

WHAT WE KNOW AND DON'T KNOW ABOUT THE ORIGIN OF THE SPIN OF THE PROTON

The origin of the spin of the proton is one of the most fundamental questions in modern hadron physics. Although tremendous progress has been made since the discovery of the "spin crisis" brought the issue to the fore, much remains to be understood. We carefully review what is known and, especially in the case of lattice QCD, what is not known. We also explain the importance of QCD inspired models in providing a physical picture of proton structure and the connection between those models and what is measured experimentally and on the lattice. We specifically apply these ideas to the issue of quark orbital angular momentum in the proton. We show that the Myhrer–Thomas resolution of the proton spin crisis is remarkably consistent with modern information from lattice QCD.

Transverse momentum dependent distribution functions in the bag model

Leading and subleading twist transverse momentum dependent parton distribution functions (TMDs) are studied in a quark model framework provided by the bag model. A complete set of relations among different TMDs is derived, and the question is discussed how model-(in)dependent such relations are. A connection of the pretzelosity distribution and quark orbital angular momentum is derived. Numerical results are presented, and applications for phenomenology discussed. In particular, it is shown that in the valence-x region the bag model supports a Gaussian Ansatz for the transverse momentum dependence of TMDs.

Five-quark components in baryons

Evidence has been accumulating for the existence of significant intrinsic non-perturbative five-quark components in various baryons. The inclusion of the five-quark components gives a natural explanation of the excess of d ¯ over u ¯ , significant quark orbital angular momentum in the proton, the problematic mass and decay pattern of the lowest 1 / 2 − baryon nonet, etc.. A breathing mode of q q q ↔ q q q q q ¯ is suggested for the lowest 1 / 2 − baryon octet. Evidence of a predicted member of the new scheme, Σ ∗ ( 1 / 2 − ) around 1380 MeV, is introduced.

Magnetic moments of octet baryons, angular momenta of quarks, and sea antiquark polarizations

One can determine antiquark polarizations in proton using the information from deep inelastic scattering, $\beta$ decays of baryons, orbital angular momenta of quarks, as well as their integrated magnetic distributions. The last quantities were determined previously by us performing a fit to magnetic moments of baryon octet. However, because of the SU(3) symmetry our results depend on two parameters. The quantity $\Gamma_{V}$, measured recently in a COMPASS experiment, gives the relation between these parameters. We can fix the last unknown parameter using the ratio of up and down quark magnetic moments which one can get from the fit to radiative vector meson decays. We calculate antiquark polarizations with the orbital momenta of valence quarks that follow from lattice calculations. The value of difference for up and down antiquark polarizations obtained in our calculations is consistent with the result obtained in a HERMES experiment.

Hard exclusive reactions and generalized parton distributions at HERMES

The concept of generalized parton distributions is discussed and applied to hard exclusive reactions at the HERMES experiment at DESY. Recent results on hard exclusive meson production and in particular on deeply virtual Compton scattering are presented. For the first time, information about the orbital angular momentum of quarks in the nucleon can be extracted from experiment. Using a new detector for recoil particles, HERMES will be able to give even more complete results in future.

H1T⊥and quark orbital angular momentum

We calculate the pretzelosity distribution (${h}_{1T}^{\ensuremath{\perp}}$), which is one of the eight leading twist transverse momentum dependent parton distributions (TMDs), in the light-cone formalism. We find that this quantity has a simple relation with the quark orbital angular momentum distribution, thus it may provide a new possibility to access the quark orbital angular momentum inside the nucleon. The pretzelosity distribution can manifest itself through the $\mathrm{sin}(3{\ensuremath{\phi}}_{h}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry in semi-inclusive deep inelastic scattering process. We calculate the $\mathrm{sin}(3{\ensuremath{\phi}}_{h}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry at HERMES, COMPASS, and JLab kinematics and present our prediction on different targets including the proton, deuteron, and neutron targets. Inclusion of transverse momentum cut in data analysis could significantly enhance the $\mathrm{sin}(3{\ensuremath{\phi}}_{h}\ensuremath{-}{\ensuremath{\phi}}_{S})$ asymmetry for future measurements.

Latest HERMES results on transverse spin effects in hadron structure and formation⋆

Transverse target single-spin asymmetries in semi-inclusive deep inelastic scattering allow to study the so-called Collins and Sivers mechanisms. The first one connects the poorly known fundamental transversity distribution function, describing the transverse spin-polarization of quarks in a transversely polarized proton, to the Collins fragmentation function, describing spin-orbit correlations in the hadron formation process. The second one is sensitive to the Sivers function, which correlates the intrinsic transverse momentum of quarks with the proton’s spin orientation and is related to the orbital angular momentum of quarks. Preliminary results on azimuthal single target-spin asymmetries in semi-inclusive electro-production of pions and kaons at the HERMES experiment are presented. The full data set collected with a transversely polarized hydrogen target was analyzed providing the HERMES most precise results on the Collins and Sivers azimuthal moments.

HERMES measurement of the collins and sivers asymmetries from a transversely polarized hydrogen target

In 2005 the HERMES collaboration published first evidence for azimuthal single-spin asymmetries in semi-inclusive production of charged pions on a transversely polarised hydrogen target. The distinctive Fourier components of the measured asymmetries caused by both the Collins and the Sivers mechanisms provide signals for previously unmeasured quantities: the transversity quark distribution in conjunction with the Collins fragmentation function (Collins mechanism) and the Sivers parton distribution (Sivers mechanism). The transversity distribution will provide a detailed insight into the relativistic nature of the quarks inside the nucleon. Recent theoretical work demonstrated a relation between the Sivers function and the contribution of the orbital angular momentum of quarks within the nucleon. The results presented for charged pions have a much higher statistical significance than the published data. In addition the Collins and Sivers asymmetries for neutral pions and charged kaons are provided.

Hadron properties and Dyson–Schwinger equations

An overview of the theory and phenomenology of hadrons and QCD is provided from a Dyson–Schwinger equation viewpoint. Following a discussion of the definition and realization of light-quark confinement, the nonperturbative nature of the running mass in QCD and inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass are described. Some exact results for pseudoscalar mesons are also highlighted, with details relating to the U A ( 1 ) problem, and calculated masses of the lightest J = 0 , 1 states are discussed. Studies of nucleon properties are recapitulated upon and illustrated: through a comparison of the ln -weighted ratios of Pauli and Dirac form factors for the neutron and proton; and a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest. Comments on prospects for the future of the study of quarks in hadrons and nuclei round out the contribution.

Effect of Orbital Angular Momentum on Valence-Quark Helicity Distributions

We study the quark helicity distributions at large x in perturbative QCD, taking into account contributions from the valence Fock states of the nucleon which have nonzero orbital angular momentum. We find that the quark orbital angular momentum contributes a large logarithm to the negative helicity quark distributions in addition to its power behavior, scaling as (1-x){5}log{2}(1-x) in the limit of x-->1. Our analysis shows that the ratio of the polarized over unpolarized down quark distributions, Deltad/d, will still approach 1 in this limit. By comparing with the experimental data, we find that this ratio should cross zero at x approximately 0.75.

Nucleon electromagnetic form factors

Elastic electromagnetic nucleon form factors have long provided vital information about the structure and composition of these most basic elements of nuclear physics. The form factors are a measurable and physical manifestation of the nature of the nucleons' constituents and the dynamics that binds them together. Accurate form factor data obtained in recent years using modern experimental facilities has spurred a significant reevaluation of the nucleon and pictures of its structure; e.g., the role of quark orbital angular momentum, the scale at which perturbative QCD effects should become evident, the strangeness content, and meson-cloud effects. We provide a succinct survey of the experimental studies and theoretical interpretation of nucleon electromagnetic form factors.

Connection between the Sivers function and the anomalous magnetic moment

The same light-front wave functions of the proton are involved in both the anomalous magnetic moment of the nucleon and the Sivers function. Using the diquark model, we derive a simple relation between the anomalous magnetic moment and the Sivers function, which should hold in general with good approximation. This relation can be used to provide constraints on the Sivers single spin asymmetries from the data on anomalous magnetic moments. Moreover, the relation can be viewed as a direct connection between the quark orbital angular momentum and the Sivers function.

The HERMES Recoil Detector

The HERMES Collaboration installed a new Recoil Detector to upgrade the existing spectrometer to study hard exclusive processes which provide access to generalised parton distributions (GPDs) and hence to the orbital angular momentum of quarks. The HERMES Recoil Detector mainly consists of three components: a silicon detector surrounding the target cell inside the beam vacuum, a scintillating fibre tracker and a photon detector with three layers of tungsten and scintillator bars in three different orientations. All three detectors are located inside a solenoidal magnet which provides a 1T longitudinal magnetic field. The Recoil Detector was installed in January 2006 and data taking will last until July of 2007.

Evidence for the absence of gluon orbital angular momentum in the nucleon

The Sivers mechanism for the single-spin asymmetry in unpolarized lepton scattering from a transversely polarized nucleon is driven by the orbital angular momentum carried by its quark and gluon constituents, combined with QCD final-state interactions. Both quark and gluon mechanisms can generate such a single-spin asymmetry, though only the quark mechanism can explain the small single-spin asymmetry measured by the COMPASS collaboration on the deuteron, suggesting the gluon mechanism is small relative to the quark mechanism. We detail empirical studies through which the gluon and quark orbital angular momentum contributions, quark-flavor by quark-flavor, can be elucidated.

Generalized form factors, generalized parton distributions, and the spin contents of the nucleon

With a special intention of clarifying the underlying spin contents of the nucleon, we investigate the generalized form factors of the nucleon, which are defined as the $n$th $x$ moments of the generalized parton distribution functions, within the framework of the chiral quark soliton model. A particular emphasis is put on the pion mass dependence of final predictions, which we shall compare with the predictions of lattice QCD simulations carried out in the so-called heavy pion region around ${m}_{\ensuremath{\pi}}\ensuremath{\simeq}(700--900)\text{ }\text{ }\mathrm{MeV}$. We find that some observables are very sensitive to the variation of the pion mass. It will be argued that the negligible importance of the quark orbital angular momentum indicated by the LHPC and QCDSF lattice collaborations might be true in the unrealistic heavy pion world, but it is not necessarily the case in our real world close to the chiral limit.

Anomalous magnetic moments and quark orbital angular momentum

We derive an inequality for the distribution of quarks with nonzero orbital angular momentum, and thus demonstrate, in a model-independent way, that a nonvanishing anomalous magnetic moment requires both a nonzero size of the target as well as the presence of wave function components with quark orbital angular momentum ${L}_{z}^{q}g0$.

Light cone sum rules forγ*N→Δtransition form factors

A theoretical framework is suggested for the calculation of gamma* N -> Delta transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the ``soft'' contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The ``minus'' components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular momentum

Moments of generalized parton distribution functions and the nucleon spin contents

It is shown that, based only upon empirically and semiempirically known facts together with some reasonable theoretical postulates, we are inevitably led to a novel conclusion that the quark orbital angular momentum carries nearly half of the total nucleon spin at the low energy scale around ${Q}^{2}\ensuremath{\simeq}(600\text{ }\mathrm{MeV}{)}^{2}$. We also perform an explicit model analysis to find that the quark spin fraction $\ensuremath{\Delta}\ensuremath{\Sigma}$ is extremely sensitive to the pion mass, which may resolve the discrepancy between the observation and the prediction of the recent lattice QCD simulation carried out in the heavy pion region.

Generalized counting rule and oscillatory scaling

We studied the energy dependence of the pp elastic scattering data and the pion-photoproduction data at a ${90}^{\ifmmode^\circ\else\textdegree\fi{}}\phantom{\rule{0.3em}{0ex}}\text{c.m.}$ angle in light of the new generalized counting rule derived for exclusive processes. We show that by including the helicity-nonconserving amplitudes and their interference with the Landshoff amplitude, we are able to reproduce the energy dependence of all the pp elastic cross-section and spin-correlation $({A}_{NN})$ data available above the resonance region. The pion-photoproduction data can also be described by this approach; however, data with much finer energy spacing are needed to confirm the oscillations about the scaling behavior. This study strongly suggests an important role for helicity-nonconserving amplitudes related to the quark orbital angular momentum and for the interference of these amplitudes with the Landshoff amplitude at GeV energies.

QCD form factors and hadron helicity nonconservation

Recent data for the ratio $R(Q)= QF_{2}(Q^{2})/F_{1}(Q^{2})$ shocked the community by disobeying expectations held for 50 years. We examine the status of perturbative QCD predictions for helicity-flip form factors. Contrary to common belief, we find there is no rule of hadron helicity conservation for form factors. Instead the analysis yields an inequality that the leading power of helicity-flip processes may equal or exceed the power of helicity conserving processes. Numerical calculations support the rule, and extend the result to the regime of laboratory momentum transfer $Q^{2}$. Quark orbital angular momentum, an important feature of the helicity flip processes, may play a role in all form factors at large $Q^{2}$, depending on the quark wave functions.