Quark Orbital Angular Momentum

Generalized parton distributions provide information on the distribution of quarks in impact parameter space. For transversely polarized nucleons, these impact parameter distributions are transversely distorted and this deviation from axial symmetry leads on average to a net transverse force from the spectators on the active quark in a DIS experiment. This force when acting along the whole trajectory of the active quark leads to transverse single-spin asymmetries. For a longitudinally polarized nucleon target, the transverse force implies a torque acting on the quark orbital angular momentum (OAM). The resulting change in OAM as the quark leaves the target equals the difference between the Jaffe–Manohar and Ji OAMs.     

On nuclear dependence of direct photon production

We have calculated the impact on theA dependence of direct photon production at large transverse momenta (p _T ) of models that were used successfully to explain the EMC effect. We find that, for energies andp _T 's typical of present direct photon measurements, the change in the photon yield due to nuclear modification of parton distributions can be expected to be about 15–20% on Fe. The effect is quite sensitive to the gluon distribution. In particular, for the models used in our calculations, theA dependence is affected more by the gluon distribution than by the quark distributions.     

The Magnetic Mass of Transverse Gluon, the B-Meson Weak Decay Vertex and the Triality Symmetry of Octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass m _mag becomes approximately equal to T _c at ${T=T_c\sim 1.14\Lambda_{\overline{MS}} \sim 260}$ MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.     

A study of the polarized (next-to-leading order) parton distributions from quark models

We perform a next-to-leading order study of polarized parton distributions as predicted by quark models. The approach allows a detailed investigation of the anomalous contributions as well as angular momentum effects of the partons. Higher-order effects are large in the region 0.01 ⩽ x ⩽ 0.2, where also the introduction of gluon polarization at the hadronic scale plays a crucial role.     

Recent results from COMPASS spin program

COMPASS is a fixed target experiment at CERN’s Super-Proton-Synchrotron. Part of its physics program is dedicated to the spin structure of the nucleon, which it studies with a polarized muon beam and polarized targets. An overview of its recent results along this line is given. In particular, the first results of our 2011 longitudinally polarized proton run, a report on our progress towards the extraction of the gluon polarization, ΔG, at NLO and an update on our measurements of transverse spin and k _T -dependent processes, from our 2010 transversely polarized proton data, and of hadron multiplicities.     

Spin-dependent processes involving a real photon

We calculate the helicity difference quark and gluon distributions in a polarized real photon using the Altarelli-Parisi equations. The corresponding helicity difference fragmentation functions to produce a real photon are dealt with in the same way. Both sets of results are presented in the form of simple parametrizations and the former used to investigate spin-spin asymmetries in the photoproduction of two high transverse momentum jets. These asymmetries are classed as “four jet” or “three jet” depending on whether any photon fragments are present in the final state along the beam axis. We find that the four-jet asymmetry should provide an experimental test for the presence of the anomalous polarized photon structure function while the three-jet asymmetry should provide new information about the spin structure of a polarized proton and in particular its gluon component.     

On Gravitational Form Factors and Transverse Spin Sum Rule

Using the light front wave functions of the scalar quark–diquark model for nucleon predicted by the soft-wall AdS/QCD, we calculate the flavor dependent gravitational form factors. We evaluate the matrix element of Pauli–Lubanski operator in this model and show that the intrinsic spin sum rule involves the higher twist form factor \({\bar{C}}\). The longitudinal momentum densities in the transverse impact parameter space are also discussed for both unpolarized and transversely polarized nucleons.     

Transverse spin structure of the nucleon from lattice-QCD simulations

We present the first calculation in lattice QCD of the lowest two moments of transverse spin densities of quarks in the nucleon. They encode correlations between quark spin and orbital angular momentum. Our dynamical simulations are based on two flavors of clover-improved Wilson fermions and Wilson gluons. We find significant contributions from certain quark helicity flip generalized parton distributions, leading to strongly distorted densities of transversely polarized quarks in the nucleon. In particular, based on our results and recent arguments by Burkardt [Phys. Rev. D 72, 094020 (2005)], we predict that the Boer-Mulders function h(1/1), describing correlations of transverse quark spin and intrinsic transverse momentum of quarks, is large and negative for both up and down quarks.     

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering

Recent measurements from the HERMES and SMC Collaborations show a remarkably large azimuthal single-spin asymmetries A_UL and A_UT of the proton in semi-inclusive pion leptoproduction γ^*(q)p→πX. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton–proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q² at fixed x_bj. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p=±1/2 to the same final-state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L^z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution δq(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.     

Baryon spectrum and the forces between quarks

We study the effect of confinement on gluon bremsstrahlung. A natural infrared cutoff emerges both at small gluon momenta and at small angles. If the confinement potential is of the linear “string” type, the cutoff is controlled by the tension parameter and is thus about 1GeV for the transverse momentum of a hard gluon relative to its parent quark. We propose that this confinement effect may remove the necessity for introducing ad hoc cutoffs by a large “intrinsic partonp _T ” in phenomenological applications of perturbative QCD.     

Spin densities in the transverse plane and generalized transversity distributions

We show how generalized quark distributions in the nucleon describe the density of polarized quarks in the impact parameter plane, both for longitudinal and transverse polarization of the quark and the nucleon. This density representation entails positivity bounds including chiral-odd distributions, which tighten the known bounds in the chiral-even sector. Using the quark equations of motion, we derive relations between the moments of chiral-odd generalized parton distributions of twist two and twist three. We exhibit the analogy between polarized quark distributions in impact parameter space and transverse momentum dependent distribution functions.Received: 25 April 2005, Published online: 27 July 2005     

Gluon jet in deep inelastic muon scattering

We study the quark and gluon final state in deep inelastic μ-scattering. For a hadron observed at sufficiently large angleθ _h with respect to the virtual photon direction, and sufficiently large energy fractionz _h , this final state dominates the cross-section. Moreover, at the same time, most events in this regime are due to the fragmentation of the quark. In such cases the position of the gluon in phase space is determined, the quark acting as a trigger for gluon jet detection. We demonstrate that in the rest frame of the final quark and gluon, the gluon is energetic and well separated from quark and target fragments. We study the boost from the lab to this frame, and give expressions for the most probable boost in terms ofθ _h andz _h . This study should lead to a convenient visualization of the gluon jet.     

Two-particle azimuthal and rapidity correlations in intervals of transverse momentum in π+ p-interactions at 250 GeV/c

A multi-dimensional analysis of two-particle correlations in π⁺ p-interactions at 250 GeV/c shows interesting structure. Particularly strong positive shortrange rapidity and azimuthal correlations are observed for low-p _T like sign pairs. This observation is not reproduced by models used for comparison (FRITIOF, DPM, quark gluon (multi)string model). A possible explanation is Bose-Einstein interference not included in these models.     

QCD three-jet production in large-p⊥ processes

The contribution of the hard scattering subprocess quark + quark → quark + quark + gluon to two-particle inclusive distributions at large p_⊥ is studied. It is shown to be accessible experimentally, and agrees with recent data on azimuthal distributions in the adequate kinematical region.     

The light-cone expansion and the parton model in polarized muon-production

The relation between the light-cone expansion and the QCD improved parton model formalism for polarized deep inelastic muon-production is discussed in detail. The regulator dependence of the relevant quantities is explicity studied at the two-loop level for the first moment ofg ₁ ^P . It is shown that the anomalous gluon component is well defined if the quark term is specified as a conserved quantity that does not evolve inQ ². The behaviour of the first moment ofg ₁ ^P at the threshold for heavy quark production is also discussed.     

Spin-dependent parton distributions from polarized structure function data

In the past year, polarized deep inelastic scattering experiments at CERN and SLAC have obtained structure function measurements off proton, neutron and deuteron targets at a level of precision never before achieved. The measurements can be used to test the Bjorken and Ellis-Jaffe sum rules, and also to obtain information on the parton distributions in polarized nucleons. We perform a global leading-order QCD fit to the proton deep inelastic data in order to extract the spin-dependent parton distributions. By using parametric forms which are consistent with theoretical expectations at large and smallx, we find that the quark distributions are now rather well constrained. We assume that there is no significant intrinsic polarization of the strange quark sea. The data are then consistent with a modest amount of the proton's spin carried by the gluon, although the shape of the gluon distribution is not well constrained, and several qualitatively different shapes are suggested. The spin-dependent distributions we obtain can be used as input to phenomenological studies for future polarized hadron-hadron and lepton-hadron colliders.     

Gluon bremsstrahlung production of heavy particles in neutrino and antineutrino scattering

Weak charged current production of charmed quark pairs is studied in the framework of the QCD inspired parton model. The magnitude of the cross section strongly depends on the charmed quark pair production threshold, above which the gluons are assumed to decay into either charmed particle pairs of hidden charmonium states. The normalized distributions are rather insensitive to the choice of this threshold value and the angular distribution of J/gy particles will show significant azimuthal asymmetry about the current-target axis. The sign of the asymmetry cannot be mimicked by the parton primordial transverse momentum effects and thus the process can serve a clean test of the gluon bremsstrahlung mechanism.     

Polarized coincidence electroproduction scaling laws for the final state

We study the inclusive electroproduction of single hadrons off a polarized target. Bjorken scaling laws and the hadron azimuthal distribution are derived from the quark parton model.The polarization asymmetries scale when the target spin is along the direction of the virtual photon, and (apart from one significant exception) vanish for transverse spin. These results have a simple explanation; emphasis is given both to the general mathematical formalism and to intuitive physical reasoning.Through this framework we consider other cases: quarks with anomalous magnetic moment; renormalization group effects and asymptotic freedom; production of vector mesons (whose spin state is analysed by their decay); relation to large transverse momentum hadron production; and a covariant parton model calculation. We also look into spin-0 partons and Regge singularities.All of these cases (apart from the last two) modify the pattern of conclusions. Vector meson production shows polarization enhancements in the density matrix element ?₀₊; the renormalization group approach does not lead to any significant suppressions. They are also less severe in parton models for large p_T hadrons, and are not supported by the covariantly formulated calculation. The origins of these differences are isolated and used to exemplify the sensitivity that polarized hadron electroproduction has to delicate detail that is otherwise concealed.     

Infrared Features of Unquenched Lattice Landau Gauge QCD

The running coupling and the Kugo-Ojima parameter of unquenched lattice Landau gauge are simulated and compared with the continuum theory. Although the running coupling measured by the ghost and gluon dressing function is infrared suppressed, the running coupling has a maximum of α₀ ∼ 2 − 2.5 at around q = 0.5 GeV irrespective of the fermion actions (Wilson fermions and Kogut-Susskind (KS) fermions). The Kugo-Ojima parameter c which saturated to about 0.8 in quenched simulations becomes consistent with 1 in the MILC configurations produced with the use of the Asqtad action, after averaging the dependence on polarization directions caused by the asymmetry of the lattice. The presence of the correction factor 1 + c ₁/q ² in the running coupling depends on the lattice size and the sea quark mass. In the large lattice size and small sea quark mass, c ₁ is confirmed of the order of a few GeV. The MILC configuration of a = 0.09 fm suggests also the presence of dimension-4 condensates with a sign opposite to the dimension-2 condensates. The gluon propagator, the ghost propagator, and the running coupling are compared with recent pQCD results including an anomalous dimension of fields up to the four-loop level.