Understanding the proton spin “puzzle” with a new “minimal” quark model

We investigate the spin structure of the nucleon in an extended Jaffe-Lipkin quark model. In addition to the conventional 3q structure, different (3q)(Q ) admixtures in the nucleon wave function are also taken into account. The contributions to the nucleon spin from various components of the nucleon wave function are discussed. The effect due to the Melosh-Wigner rotation is also studied. It is shown that the Jaffe-Lipkin term is only important when antiquarks are negatively polarized. We arrive at a new “minimal” quark model, which is close to the naive quark model, in order to understand the proton spin “puzzle”. Received: 4 November 2000 / Accepted: 23 October 2001     

A new forward spectrometer for PHENIX

In the last decade PHENIX has accessed via longitudinal double spin asymmetries the gluon helicity inside the proton, started probing flavor dependent valence and sea quark helicity distributions and started to explore the proton transverse spin structure. A major upgrade is planned for the next decade that will provide an increased acceptance and additional tracking and electromagnetic plus hadronic calorimetry in the forward region. Here, the layout of the new forward detector system will be discussed, together with the new insights in the proton spin structure that the new forward PHENIX spectrometer will provide.     

The Q<Superscript>2</Superscript> dependence of polarized and unpolarized proton structure functions in the relativistic quark exchange framework

In this article we intend to discuss the evolution of polarized and unpolarized structure functions in the (x,Q²) plane. We analyze the proton data on the spin dependence asymmetry A₁(x,Q²), by making the dynamical assumption that at low resolution energies, the hadrons consist only of valence quarks and the scaling violation of F₂(x,Q²) at low x comes only from the gluons density. While the sea quark and the gluon distributions are calculated using the inverse Mellin technique and the various moments of the valence quarks, the valence quark distribution itself is obtained from the relativistic quark-exchange model. A comparison is made with the corresponding available experimental data. Finally in agreement with the data, it is demonstrated that there is no significant Q²-dependence of asymmetry A₁(x,Q²) for x ranging 0.014 ≤ x ≤ 0.25. Received: 11 September 1999 / Revised version: 8 December 1999     

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.     

QCD analysis of DIS and SIDIS data with two alternative methods

The global fit analysis of all published data on DIS and semi-inclusive DIS (SIDIS) asymmetries is performed in the next to leading (NLO) QCD order. The respective parameterization on polarized PDFs is constructed. The especial attention is paid to the impact of novel SIDIS data on the polarized distributions of light sea and strange quarks as well as on the polarized gluon distributions. The first moments of these distributions entering the nucleon spin are found to be surprisingly small quantities. The alternative direct (free of any fitting procedure) method of NLO QCD analysis is elaborated. Method is especially important for analysis of SIDIS data because it allows to avoid the problems arising in the conventional fitting procedure: functional arbitrariness at initial scale and ambiguities in the error band calculation. Within the alternative method the central values and uncertainties of the measured asymmetries directly propagate to the central values and uncertainties of the polarized PDFs we are interested in. The method is applied to all existing SIDIS data on pion production for an estimation in NLO QCD of the valence and sea quark contributions to the proton spin. As a result one arrives at the conclusion that, contrary to the valence contributions, the sea contributions to the proton spin are compatible with zero within the errors.     

Thick skin in neutron/proton-rich sodium isotopes

Nucleon (both neutron and proton) density distributions of the chain of sodium isotopes are calculated using a semi-phenomenological model of nuclear density which incorporates correctly the asymptotic behaviour and the behaviour near the centre. The experimental charge root-mean-square radii and the single neutron and proton separation energies, required as input, are used. The calculated interaction cross-sections using these densities in the Glauber model agree well with the experiment. The calculated neutron rms radii r _n and the nuclear skin thickness ( r _n - r _p) closely agree with the corresponding experimental values and also are consistent with the Relativistic Hartree-Bogoliubov (RHB) calculations. Received: 24 April 2001 / Accepted: 28 June 2001     

Spin physics at COMPASS

Results for the spin structure of the nucleon from the COMPASS data taking periods 2002 to 2004 are presented. The quark contribution to the nucleon spin, following from a QCD fit to the new data, turns out to be significantly larger than it was derived from the previous world data. The new data favour, on the other side, a comparatively small gluon polarisation in the range x _g ≈ 0.1. In the data taken with the deuteron target polarised transversely the related asymmetries are found to be small on the level of accuracy reached so far, indicating a cancellation of the proton and neutron contributions. This is in agreement, for both the Collins and the Sivers asymmetry, with recent theoretical calculations. Also, a step towards the understanding of angular-momentum contributions with COMPASS is taken by the evaluation of asymmetries in exclusive vector meson production.     

Leading chiral contributions to the spin structure of the proton

The leading chiral contributions to the quark and gluon components of the proton spin are calculated using heavy-baryon chiral perturbation theory. Similar calculations are done for the moments of the generalized parton distributions relevant to the quark and gluon angular momentum densities. These results provide useful insight into the role of pions in the spin structure of the nucleon and can serve as a guide for extrapolating lattice QCD calculations at large quark masses to the chiral limit.     

Diffraction at HERA, Color Opacity and Nuclear Shadowing in DIS off nuclei

The QCD factorization theorem for diffractive processes in DIS is used to derive formulae for the leading twist contribution to the nuclear shadowing of parton distributions in the low thickness limit (due to the coherent projectile (photon) interactions with two nucleons). Based on the current analyzes of diffraction at HERA we find that the average strength of the interactions which govern diffraction in the gluon sector at x≤ 10⁻³, Q ₀= 2 GeV is ∼50mb. This is three times larger than in the quark sector and suggests that applicability of DGLAP approximation requires significantly larger Q ₀ in the gluon sector. We use this information on diffraction to estimate the higher order shadowing terms due to the photon interactions with N≥ 3 nucleons which are important for the scattering of heavy nuclei and to calculate nuclear shadowing and Q ² dependence of gluon densities. For the heavy nuclei the amount of the gluon shadowing: G _A(x,Q ₀ ²) /AG _N(x,Q ₀ ²)_{|x ≤ 10−3}∼ 0.25–0.4 is sensitive to the probability of the small size configurations within wave function of the gluon “partonometer” at the Q ₀ scale. At this scale for A∼ 200 the nonperturbative contribution to the gluon density is reduced by a factor of 4–5 at x≤ 10⁻³ unmasking PQCD physics in the gluon distribution of heavy nuclei. We point out that the shadowing of this magnitude would strongly modify the first stage of the heavy ion collisions at the LHC energies, and also would lead to large color opacity effects in eA collisions at HERA energies. In particular, the leading twist contribution to the cross section of the coherent J/ψ production off A≥ 12 nuclei at s ⁻²≥ 70 GeV is strongly reduced as compared to the naive color transparency expectations. The Gribov black body limit for F _2A(x,Q ²) is extended to the case of the gluon distributions in nuclei and shown to be relevant for the HERA kinematics of eA collisions. Properties of the final states are also briefly discussed. Received: 12 March 1999     

Transport theory for a scalar quark & gluon model

A model for scalar quarks and gluons that successfully gives rise to a ln s behavior in high-energy qq scattering and which contains a non-trivial three-gluon vertex is used to study collision theory with the following aspects: i) A three-body interaction simulating QCD is present and ii) particle production and annihilation occur naturally. In this paper, the collision term in the model is examined in detail in the quasiparticle approximation. The construction of cross-sections in which self-energy terms are ordered according to a coupling constant expansion is undertaken. It is shown explicitly which terms of second order are required to obtain the scattering amplitudes that are two body in nature. Additional ordering in the number of colors shows that quark loop diagrams are suppressed and gluon production or scattering processes dominate. It is also shown that a consistent calculation of the scattering graphs at the two-loop level also simultaneously yields terms that renormalize one-loop level graphs. This can then be extended to arbitrary m↦n processes. We examine the constraint equation briefly, discussing the appearance of a width. The issue of pinch singularities is also addressed, and examples of the elimination of such singularities in equilibrium are given explicitly. Received: 7 November 2001 / Accepted: 12 June 2001     

Study of parton spin-dependent distributions in hard proton-proton collisions through measurement of handedness

Polarization of partons emitted in hard scattering of an unpolarized proton beam from a polarized hydrogen target can be found through a measurement of jet handedness. Two definitions of handedness are suggested with zero and essentially nonzero contributions of gluon jets. A sensitivity of the handedness to the valence, sea quark and gluon distributions is considered. Handedness properties under the charge conjugation and flavorSU (2) transformations are investigated. An option to study the spin-dependent parton distributions in hard scattering of the unpolarized HERA proton beam from the polarized internal hydrogen target is discussed.     

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. Received: 7 January 1999 / Revised version: 12 February 1999     

Viewing the proton through "color" filters

While the form factors and parton distributions provide separately the shape of the proton in coordinate and momentum spaces, a more powerful imaging of the proton structure can be obtained through phase-space distributions. Here we introduce the Wigner-type quark and gluon distributions which depict a full-3D proton at every fixed light-cone momentum, like what is seen through momentum ("color") filters. After appropriate phase-space reductions, the Wigner distributions are related to the generalized parton distributions (GPDs) and transverse-momentum dependent parton distributions, which are measurable in high-energy experiments. The new interpretation of GPDs provides a classical way to visualize the orbital motion of the quarks, which is known to be the key to the spin and magnetic moment of the proton.     

The quark condensate in relativistic nucleus-nucleus collisions

We compute the modification of the quark condensate <ˉq q> in relativistic nucleus-nucleus collisions and estimate the 4-volume, where the quark condensate is small (<ˉqq>/<ˉqq>⁰≤ 0.1–0.3) using hadron phase-space distributions obtained with the quark-gluon string model. As a function of the beam energy the 4-volume rises sharply at a beam energy E^lab/A ≃ (2–5) GeV, remains roughly constant up to beam energies ≃ 20 GeV and rises at higher energies. At low energies the reduction of the condensate is mainly due to baryons, while at higher energies the rise of the 4-volume is due to the abundant mesons produced. Based on our results we expect that moderate beam energies on the order of 10 GeV per nucleon are favourable for studying the restoration of chiral symmetry in a baryon-rich environment in nucleus-nucleus collisions. Received: 4 December 1997 / Revised version: 31 July 1998     

Thermodynamic properties of the SU(2)f chiral quark–loop soliton

We consider a chiral one-loop hedgehog soliton of the bosonized SU(2)_f Nambu & Jona-Lasinio model which is embedded in a hot medium of constituent quarks. Energy and radius of the soliton are determined in self-consistent mean-field approximation. Quasi-classical corrections to the soliton energy are derived by means of the pushing and cranking approaches. The corresponding inertial parameters are evaluated. It is shown that the inertial mass is equivalent to the total internal energy of the soliton. Corrected nucleon and δ isobar masses are calculated in dependence on temperature and density of the medium. As a result of the self-consistently determined internal structure of the soliton the scaling between constituent quark mass, soliton mass and radius is noticeably disturbed. Received: 26 September 1997     

Nucleon form factors in a relativistic quark model

Electromagnetic form factors of protons and neutrons are investigated based on a relativistic quark model with the inclusion of a pion cloud. Pseudo-scalar π-quark interaction is employed to study the coupling between the nucleon and the π. The results show the important role of the pion cloud for the neutron charge form factor. Moreover, our numerical analysis indicates a difference between the relativistic and the nonrelativistic treatments. Received: 10 March 1999 / Revised version: 14 June 1999     

Contributions of qqqq(q) components to nucleon spin structure

The spin structure of nucleons is presented in the framework of an extended quark model which in addition to the conventional qqq structure also takes into account qqqq(q) admixtures in the nucleon wave functions, where the qqqq(q) components are in colored quark cluster configurations. The axial vector weak coupling constant and spin distributions for polarized nucleons as well as spin content are obtained for the lowest positive parity qqqq(q) configurations in flavor-spin dependent interaction. In particular, the contributions of the down and strange quarks to the proton spin and the sum rule for polarized neutron are negative, in agreement with recent experiments.