International Journal of Modern Physics A

The workshop The Helicity Structure of the Nucleon (BNL June 5, 2006) was organized as part of the 2006 RHIC & AGS Users' Meeting to review the status of the spin problem and future directions. The presentations can be found at the workshop's website:¹. Recent data suggest small polarized glue and strangeness in the proton. Here we present a personal summary of the main results and presentations. What is new and exciting in the data, and what might this tell us about the structure of the proton?

We estimate final state interactions in the B-meson decays into two pions by the Regge model. We consider Pomeron exchange and the leading Regge trajectories that can relate intermediate particles to the final state. In some cases, most notably B→π⁰π⁰ and B→π⁺π^-, the effect is relevant and produces a better agreement between theory and experiment.

We present the case of quantal transmission through a smooth, single-piece exponential potential, V(x) = -V₀e^x/a, in contrast to the piecewise continuous potentials, as an intersecting model to demonstrate the analytic extraction of transmission (reflection) coefficient. Several other aspects of quantal transmission are also discussed in this simple and exactly solvable model.

We extend our earlier work on the possible microscopic origin of the Bekenstein–Hawking entropy to higher-dimensional space–times. The mechanism of counting chain-like states is shown to work for space–times with event horizon wrapped by a Euclidean doublet (E₁,M₁)+(E₂,M₂) of electric–magnetic dual brane pairs of type II string-theory or M-theory. Noncommutativity on the brane worldvolume enters naturally the derivation of the Bekenstein–Hawking entropy including the correct prefactor. Moreover, a logarithmic correction with prefactor 1/2 is predicted.

The perfect-fluid cosmology in the (1+d+D)-dimensional Kaluza–Klein space–times for an arbitrary barotropic equation of state p = (γ-1)ρ is quantized by using the Schutz's variational formalism. We make efforts in the mathematics to solve the problems in two cases. In the first case of the stiff fluid γ = 2 we exactly solve the Wheeler–DeWitt equation when the d space is flat. After the superposition of the solutions the wave-packet function is obtained exactly. We analyze the Bohmian trajectories of the final-stage wave-packet functions and show that the scale functions of the flat d spaces and the compact D spaces will eventually evolve into the nonzero finite values. In the second case of γ≈2, we use the approximated wave function in the Wheeler–DeWitt equation to find the analytic forms of the final-stage wave-packet functions. After analyzing the Bohmian trajectories we show that the flat d spaces will be expanding forever while the scale function of the contracting D spaces would not become zero within finite time. Our investigations indicate that the quantum effect in the quantum perfect-fluid cosmology could prevent the extra compact D spaces in the Kaluza–Klein theory from collapsing into a singularity or that the "crack-of-doom" singularity of the extra compact dimensions is made to occur at t = ∞.

The quantum Yang–Mills theory, describing a system of fields with nondual (chromoelectric g) and dual (chromomagnetic ) charges and revealing the generalized dual symmetry, is developed by analogy with the Zwanziger formalism in QED. The renormalization group equations (RGE's) for pure non-Abelian theories are analyzed for both constants, α = g²/4π and . The pure gauge theory is investigated as an example. We consider not only monopoles, but also dyons. The behavior of the total SU(3) β-function is investigated in the whole region of α≡α_s: 0≤α < ∞. It is shown that this β-function is antisymmetric under the interchange α ↔ 1/α and is given by the well-known perturbative expansion not only for α≪1, but also for α≫1. Using an idea of the Maximal Abelian Projection by 't Hooft, we have considered the formation of strings — the ANO flux tubes — in the Higgs model of scalar monopole (or dyon) fields. In this model we have constructed the behavior of the β-function in the vicinity of the point α = 1, where it acquires a zero value. Considering the phase transition points at α≈0.4 and α≈2.5, we give the explanation of the freezing of α_s. The evolution of with energy scale μ and the behavior of V_eff(μ) are investigated for both, perturbative and nonperturbative regions of QCD. It was shown that the effective potential has a minimum, ensured by the dual sector of QCD. The gluon condensate , corresponding to this minimum, is predicted: , in agreement with the well-known results.

We construct a set of noncommuting translation operators in two- and high-dimensional lattices. The algebras they close are w_∞-algebras. The construction is based on the introduction of noncommuting elementary link operators which link two neighborhood sites in the lattice. This type of operators preserve the braiding nature of exotic particles living basically in two-dimensional space.

We present a general formalism based on the framework of noncommutative geometry, suitable to the study of the standard model of electroweak interactions, as well as that of more general gauge theories. Left- and right-handed chiral fields are assigned to two different sheets of space–time (a discretized version of Kaluza–Klein theory). Scalar Higgs fields find themselves treated on the same footing as the gauge fields, resulting in spontaneous symmetry breaking in a natural and predictable way. As a first test, we apply the formalism to the Standard Model, where one can predict the Higgs mass and the top Yukawa coupling. The results obtained for this case are similar with results obtained in alternate formulations. We then study the left–right symmetric model, where we show that this framework imposes interesting constraints on the type and coefficients of terms appearing in the Higgs potential.

A generalization of A_r statistics is proposed and developed. The generalized A_r quantum statistics is completely specified by a set of Jacobson generators satisfying a set of triple algebraic relations. Fock–Hilbert representations and Bargmann–Fock realizations are derived.

The finiteness properties of the supersymmetric Yang–Mills theory are reanalyzed both in the component formulation and using superfields, in order to discuss some subtleties that emerge in the computation of gauge dependent quantities. The one-loop corrections to various Green functions of elementary fields are calculated. In the component formulation it is shown that the choice of the Wess–Zumino gauge, that is standard in supersymmetric gauge theories, introduces ultraviolet divergences in the propagators at the one-loop level. Such divergences are exactly canceled when the contributions of the fields that are put to zero in the Wess–Zumino gauge are taken into account. In the description in terms of superfields, infrared divergences are found for every choice of gauge different from the supersymmetric generalization of the Fermi–Feynman gauge. Two-, three- and four-point functions of superfields are computed and some general features of the infrared problem are discussed. We also examine the effect of the introduction of mass terms for the (anti)chiral superfields in the theory, which break supersymmetry from to . It is shown that in the mass deformed model no ultraviolet divergences appear in two-point functions. It is argued that this result can be generalized to n-point functions, supporting the proposal of a possible of use of this modified model as a supersymmetry-preserving regularization scheme for theories.

Next-to-leading order approximation of the quark helicity distributions are used in the framework of polarized valon model. The flavor-asymmetry in the light-quark sea of the nucleon can be obtained from the contributions of unbroken sea quark distributions. We employ the polarized valon model and extract the flavor-broken light sea distributions which are modeled with the help of a Pauli-blocking ansatz. Using this ansatz, we can obtain broken polarized valon distributions. From there and by employing convolution integral, broken sea quark distributions are obtainable in this framework. Our results for δu, δd, and are in good agreement with recent experimental data for polarized parton distribution from HERMES experimental group and also with GRSV model. Some information on orbital angular momentum as a main ingredient of total nucleon spin are given. The Q² evolution of this quantity, using the polarized valon model is investigated.

The interesting state X(1600) with J^PCI^G = 2⁺⁺2⁺ cannot be a conventional meson in the quark model. Using a mixed interpolating current with different color configurations, we investigate the possible existence of X(1600) in the framework of QCD finite energy sum rules. Our results indicate that both the "hidden color" and coupled channel effects may be quite important in the multiquark system. We propose several reactions to look for this state.