Nucleon spin structure in a relativistic constituent quark model

The spin structure of the nucleon is analyzed using a relativistic constituent quark model in light-front formulation. We investigate, in particular, relativistic effects on the axial vector coupling constants. Electromagnetic and axial form factors are constructed in terms of quark form factors that reflect the possible non-trivial structure of the constituent quarks. We study the influence of flavour mixing effects on axial constants and discuss the extent to which such effects can renormalize the singlet axial constant g _A ⁰ from its SU(6) quark model value.     

Axial exchange currents and nucleon spin

We calculate the axial couplings g_A⁸(0) and g_A⁰(0) related to the spin of the nucleon in a constituent quark model. In addition to the standard one-body axial currents, the model includes two-body axial exchange currents. The latter are necessary to satisfy the Partial Conservation of Axial Current (PCAC) condition. For both axial couplings we find significant corrections to the standard quark model prediction. Exchange currents reduce the valence quark contribution to the nucleon spin and afford an interpretation of the missing nucleon spin as orbital angular momentum carried by nonvalence quark degrees of freedom.     

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.     

Hyperon beta-decay and axial charges of the lambda in view of strongly distorted baryon wave-functions

Within the collective coordinate approach to chiral soliton models we suggest that breaking of SU(3) flavor symmetry mainly resides in the baryon wave-functions while the charge operators maintain a symmetric structure. Sizable symmetry breaking in the wave-functions is required to reproduce the observed spacing in the spectrum of the  baryons. The matrix elements of the flavor symmetric charge operators nevertheless yield g_A/g_V ratios for hyperon beta-decay which agree with the empirical data approximately as well as the successful F&D parameterization of the Cabibbo scheme. Demanding the strangeness component in the nucleon to vanish in the two flavor limit of the model, determines the structure of the singlet axial charge operator and yields the various quark flavor components of the axial charge of the Λ-hyperon. The suggested picture gains support from calculations in a realistic model using pion and vector meson degrees of freedom to build up the soliton.     

The Reid93 Potential Triton in the Unitary Pole Approximation

The Reid93 potential provides a representation of the nucleon–nucleon (NN) scattering data that rivals that of a partial wave analysis. We present here a unitary pole approximation (UPA) for this contemporary NN potential that provides a rank one separable potential for which the wave function of the deuteron (³S₁-³D₁) and singlet anti-bound (¹S₀) state are exactly those of the original potential. Our motivation is to use this UPA potential to investigate the sensitivity of the electric dipole moment for the deuteron and ³H and ³He to the ground state nuclear wave function. We compare the Reid93 results with those for the original Reid (Reid68) potential to illustrate the accuracy of the bound state properties.     

The Singlet Axial Vector Coupling in the Effective Meson Baryon Lagrangian

The Goldberger-Treiman (GT) relation in the singlet channel, being consistent with the EMC experimental results, can be manifested in an extended a model in which the chiral symmetry in the singlet channel is realized in the parity doublet model by assuming that the excited nucleon state S₁₁ N(1535) is the parity partner of the nucleon state. The model gives a natural explanation of the smallness of the singlet axial vector coupling g_A⁰ without the necessity to assume a large strange sea contribution, and is unique in explaining the decay rate of N(1535) → N_η as well.     

The role of the axial anomaly in measuring spin-dependent parton distributions

It is shown that forward matrix elements of j₅^μ, the flavor singlet axial vector current, do not merely measure the helicity carried by quarks and antiquarks but also include a spin-dependent gluonic component due to the anomaly. In perturbation theory the exact value of the gluonic component depends on the infrared regulator, and we argue that computing off-shell matrix elements with zero-mass quarks gives the proper method of regulation to exhibit the chiral properties of the theory. We suggest measuring two-jet production in deep inelastic scattering off polarized targets as a means of determining the spin-dependent gluonic component of j₅^μ.     

EMC and polarized EMC effects in nuclei

We determine nuclear structure functions and quark distributions for ⁷Li, ¹¹B, ¹⁵N and ²⁷Al. For the nucleon bound state we solve the covariant quark–diquark equations in a confining Nambu–Jona-Lasinio model, which yields excellent results for the free nucleon structure functions. The nucleus is described using a relativistic shell model, including mean scalar and vector fields that couple to the quarks in the nucleon. The nuclear structure functions are then obtained as a convolution of the structure function of the bound nucleon with the light-cone nucleon distributions. We find that we are readily able to reproduce the EMC effect in finite nuclei and confirm earlier nuclear matter studies that found a large polarized EMC effect.     

Singlet-triplet excitation ratios in Ne III, Ar III and N II under ion impact

Peculiar properties of ion-atom collision systems, in particular deviations from statistical populations of singlet and triplet levels, can be studied by optical spectroscopy. We have extended earlier studies by VUV spectroscopy of a number of collision systems at various collision energies in the 0.01-MeV/nucleon to 1-MeV/nucleon range, involving H₂ ⁺, H⁺, He⁺, He²⁺, Ne⁺, Ar⁺, and N₂ ⁺ as projectiles and Ne, Ar, and N₂ as target gases. Statistically significant deviations of the relative intensities of singlet and triplet lines from simple ratios are observed in the displaced terms of the valence shell of Ne III, corroborating and extending earlier work. For Ar III, the energy dependences of singlet-to-triplet excitation ratios are very different for different projectiles. For N II, in contrast, all observed line ratios are practically independent of the projectile energy. Received 17 November 2000 and Received in final form 31 January 2001     

Gottfried sum rule from maximum entropy method quark distributions with DGLAP evolution and with DGLAP evolution with GLR-MQ-ZRS corrections

A new method to test the valence quark distribution of nucleons obtained from the maximum entropy method using the Gottfried sum rule by performing the DGLAP equations with GLR-MQ-ZRS corrections and the original leading-order/next-to-leading-order(LO/NLO) DGLAP equations is outlined. The test relies on knowledge of the unpolarized electron–proton structure function F_2~(ep) and the electron–neutron structure function F_2~(en) and the assumption that Bjorken scaling is satisfied. In this work, the original Gottfried summation value obtained by the integrals of the structure function at different Q~2 is in accordance with the theoretical value of 1/3 under the premise of light-quark flavor symmetry of the nucleon sea, whether it results from dynamical evolution equations or from global quantum chromodynamics fits of PDFs. Finally, we present the summation value of the LO/NLO DGLAP global fits of PDFs under the premise of light-quark flavor asymmetry of the nucleon sea. According to analysis of the original Gottfried summation value with two evolution equations at different Q~2, we find that the valence quark distributions of nucleons obtained by using the maximum entropy method are effective and reliable.     

Flavor symmetry breaking and strangeness in the nucleon

We suggest that breaking of SU(3) flavor symmetry mainly resides in the baryon wave functions while the charge operators have no (or only small) explicit symmetry-breaking components. We utilize the collective coordinate approach to chiral soliton models to support this picture. In particular we compute the g _A /g _V ratios for hyperon beta-decay and the strangeness contribution to the nucleon axial current matrix elements and analyze their variation with increasing flavor symmetry breaking.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.39.Dc Skyrmions - 12.39.Fe Chiral Lagrangians - 13.30.Ce Leptonic, semileptonic, and radiative decays - 14.20.Jn HyperonsH. Weigel: Heisenberg-Fellow;     

Study of the γD → ppπ− reaction in the Δ(1236) region for well defined kinematical conditions

The γD → ppπ^? reaction cross section, in the Δ(1236) region, is measured in a counter experiment with high statistical accuracy. Particular emphasis is put on the accurate determination of the complete kinematics. For low values of the undetected nucleon momentum (p_r, ≈ 50 MeV/c), the validity of the spectator nucleon model is experimentally checked and the γn → pπ^? elementary reaction cross section is extracted and compared with other experimental data. When the recoiling nucleon momentum increases (p_r ≈ 150 MeV/c), significant departures from the spectator nucleon model are found. Presumably they are the signature of final state interaction effects.     

Final state interaction as the main mechanism of double hole creation in atomic K shells during electromagnetic nuclear decays

Large violations of the OZI-rule have been observed in pp-annihilation into ? mesons when the initial state is in triplet spin configuration. One possible explanation for this phenomenon is that this is due to a small negatively polarized ss?-component in the nucleon which has been found in polarized deep inelastic scattering of leptons. In the nonperturbative region there is little experimental information on the sign of Δs. We show by spin projection conservation arguments that if the ?-production enhancement in the p?p → ?π is due to the transfer of a ss? from the initial nucleon to the final ?, then Δs must be preferentially positive. We study polarization phenomena in the process N + N → + N+ V⁰ where V⁰ is a vector meson near threshold and we show that a comparison of the pp → pp? reaction (which is dominated by a spin triplet in the initial state, at threshold) and the np → np? (which is driven by non-interfering spin triplet and spin singlet amplitudes) would test quantitatively the ss?-driven spin triplet dominance. Finally we discuss the possibility of using the relationship between the Gerasimov-Drell-Hearn sum-rule and the integral of the spin structure function g_1p to measure the polarization of the ss?-component at low momentum transfer.     

On the polarization of the final nucleon in NC elastic \nu _\mu (\bar \nu _\mu )-N scattering

New short baseline neutrino experiments open new possibilities of high precision study of different neutrino processes. We present here results of the calculation of the polarization of final nucleon in elastic NC $\nu _\mu (\bar \nu _\mu )$ -nucleon scattering. In a numerical analysis the sensitivity to the different choices of the axial and axial strange form factors is examined. Measurements of the polarization of the final proton in elastic e-p scattering drastically changed our knowledge about the electromagnetic form factors of the proton. From measurement of the nucleon polarization in the NC elastic scattering a new additional information about the axial G _A (Q ²) and the strange axial G ^s _A (Q ²) form factors of the nucleon could be inferred.     

Radiative decays and transition form factors of strange mesons in the relativistic constituent quark model

Motivated by the recent lattice QCD results indicating that the topological charge contribution to the flavor singlet axial vector current can be traded off by the constituent quark masses, we investigate the radiative decays of pseudoscalar (π,K, η, η′), vector (ρ,K*, ω, ?) and axial vector (A ₁) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock-state expansion of meson wavefunctions are not contaminated by the vacuum fluctuation, (2) the assignment of meson quantum numbers are given by the Melosh transformation. Except the well-known constituent quark masses of (u,d,s) quarks and the spin-averaged meson masses, the only parameter in the model is the gaussian parameter β which determines the broadness (or sharpness) of radial wavefunction. The computed decay widths and the transition form factors of ρ, ω → π(η)γ*,K* →Kγ* andA ₁ → πγ* at 0≤Q ²≤5 GeV² and π⁰(η) → γ*γ at 0≤Q ²≤3 GeV² are in a remarkably good agreement with the experimental data and the result forA ₁ ⁺ → π₊ γ* transition is quite consistent with the experiments of pion scattering on a nucleus using Primakoff effect. This model is potentially useful in the cocktail analyses of the dilepton productions in proton-proton, proton-nucleus and nucleus-nucleus collisions at SPS energies and a little above.     

Spin Dependent Quark Forces and the Spin Content of the Nucleon

The spin crisis of the nucleon is that the quark spin contribution is only a small fraction of the nucleon spin. A relativistic Dirac equation approach is followed assuming three low mass current quarks in the nucleon described by a (1/2⁺)³ configuration. If the lower component contribution to the normalization of the quark wave function is about 0.18, then the axial charge of the nucleon can be reproduced. However including the same lower component to every quark wave function is not enough to resolve the spin crisis. The net u quark spin z component is predicted as 1.0 and the net d quark spin z component is predicted as –0.25, both in disagreement with experiment. These predictions can be brought into agreement with experiment if flavor independent but spin dependent forces are assumed between the quarks. The strength of the spin dependent force found by empirically fitting the nucleon spin data is shown to be comparable to the spin dependence that can explain the -nucleon mass difference. The spin content of the ⁺ is then predicted using the interactions that reproduce the spin content of the proton.     

Direct and indirect detection of dark matter in D6 flavor symmetric model

We study fermionic dark matter in a non-supersymmetric extension of the standard model with a family symmetry based on D₆ ×[^(Z)]₂×Z₂D_{6} \times\hat{Z}_{2}\times Z_{2}. In our model, the final state of the dark matter annihilation is determined to be e ⁺ e ⁻ by the flavor symmetry, which is consistent with the PAMELA result. At first, we show that our dark matter mass should be within the range of 230 GeV–750 GeV in the WMAP analysis combined with μ→eγ constraint. Moreover, we simultaneously explain the experiments of direct and indirect detection, by simply adding a gauge and D ₆ singlet real scalar field. In the direct detection experiments, we show that the lighter dark matter mass ≃230 GeV and the lighter standard model Higgs boson ≃115 GeV are in favor of the observed bounds reported by CDMS II and XENON100. In the indirect detection experiments, we explain the positron excess reported by PAMELA through the Breit–Wigner enhancement mechanism. We also show that our model is consistent with there being no antiproton excess, as suggested by PAMELA.     

Nucleon axial and pseudoscalar form factors from the covariant Faddeev equation

We compute the axial and pseudoscalar form factors of the nucleon in the Dyson-Schwinger approach. To this end, we solve a covariant three-body Faddeev equation for the nucleon wave function and determine the matrix elements of the axialvector and pseudoscalar isotriplet currents. Our only input is a well-established and phenomenologically successful ansatz for the non-perturbative quark-gluon interaction. As a consequence of the axial Ward-Takahashi identity that is respected at the quark level, the Goldberger-Treiman relation is reproduced for all current-quark masses. We discuss the timelike pole structure of the quark-antiquark vertices that enters the nucleon matrix elements and determines the momentum dependence of the form factors. Our result for the axial charge underestimates the experimental value by 20 -25% which might be a signal of missing pion-cloud contributions. The axial and pseudoscalar form factors agree with phenomenological and lattice data in the momentum range above Q ² ~ 1...2 GeV².     

Spin structure of the nucleon—status and recent results

After the initial discovery of the so-called “spin crisis in the parton model” in the 1980s, a large set of polarization data in deep inelastic lepton-nucleon scattering was collected at labs like SLAC, DESY and CERN. More recently, new high precision data at large x and in the resonance region have come from experiments at Jefferson Lab. These data, in combination with the earlier ones, allow us to study in detail the polarized parton densities, the Q² dependence of various moments of spin structure functions, the duality between deep inelastic and resonance data, and the nucleon structure in the valence quark region. Together with complementary data from HERMES, RHIC and COMPASS, we can put new limits on the flavor decomposition and the gluon contribution to the nucleon spin. In this report, we provide an overview of our present knowledge of the nucleon spin structure and give an outlook on future experiments. We focus in particular on the spin structure functions g₁ and g₂ of the nucleon and their moments.