International Journal of Modern Physics A

Since LEPS collaboration reported the first evidence of Θ⁺ pentaquark in early 2003, eleven other experimental groups have confirmed this exotic state while many other groups did not see any signal. If this state is further established by future high statistical experiments, its discovery shall be one of the most important events in hadron physics for the past three decades. This exotic baryon with such a low mass and so narrow a width imposes a big challenge to hadron theorists. Up to now, there have appeared more than two hundred theoretical papers trying to interpret this charming state. I will review some important theoretical developments on pentaquarks based on my biased personal views.

A recently developed model for the QCD analytic invariant charge is compared with quenched lattice simulation data on the static quark–antiquark potential. By employing this strong running coupling one is able to obtain the confining quark–antiquark potential in the framework of the one-gluon exchange model. To achieve this objective a technique for evaluating the integrals of a required form is developed. Special attention is paid here to removing the divergences encountered the calculations. All this enables one to examine the asymptotic behavior of the potential at both small and large distances with high accuracy. An explicit expression for the quark–antiquark potential, which interpolates between these asymptotics, and satisfies the concavity condition, is proposed. The derived potential coincides with the perturbative results at small distances, and it is in a good agreement with the lattice data in the nonperturbative physically-relevant region. An estimation of the parameter Λ_QCD is obtained for the case of pure gluodynamics. It is found to be consistent with all the previous estimations of Λ_QCD in the framework of approach in hand.

Recently, Giusto and Halpern reported the open-string description of a certain basic class of untwisted open WZW strings, including their associated noncommutative geometry and open-string KZ equations. In this paper, we combine this development with results from the theory of current-algebraic orbifolds to find the open-string description of a corresponding basic class of twisted open WZW strings, which begin and end on different WZW branes. The basic class of twisted open WZW strings is in 1-to-1 correspondence with the twisted sectors of all closed-string WZW orbifolds, and moreover, the basic class can be decomposed into a large collection of open-string WZW orbifolds. At the classical level, these open-string orbifolds exhibit new twisted noncommutative geometries, and we also find the relevant twisted open-string KZ equations which describe these orbifolds at the quantum level. In a related development, we also formulate the closed-string description (in terms of twisted boundary states) of the general twisted open WZW string.

We apply the Cornwall–Jackiw–Tomboulis (CJT) formalism to the scalar λφ⁴ theory in canonical-noncommutative space–time. We construct the CJT effective potential and the gap equation for general values of the noncommutative parameter θ_μν. We observe that under the hypothesis of translational invariance, which is assumed in the effective potential construction, differently from the commutative case (θ_μν=0), the renormalizability of the gap equation is incompatible with the renormalizability of the effective potential. We argue that our result, is consistent with previous studies, suggesting that a uniform ordered phase would be inconsistent with the infrared structure of canonical noncommutative theories.

We review the analytic results for the phase shifts δ_l(k) in nonrelativistic scattering from a spherical well. The conditions for the existence of resonances are established in terms of time-delays. Resonances are shown to exist for p-waves (and higher angular momenta) but not for s-waves. These resonances occur when the potential is not quite strong enough to support a bound p-wave of zero energy. We then examine relativistic scattering by spherical wells and barriers in the Dirac equation. In contrast to the nonrelativistic situation, s-waves are now seen to possess resonances in scattering from both wells and barriers. When s-wave resonances occur for scattering from a well, the potential is not quite strong enough to support a zero momentum s-wave solution at E=m. Resonances resulting from scattering from a barrier can be explained in terms of the "crossing" theorem linking s-wave scattering from barriers to p-wave scattering from wells. A numerical procedure to extract phase shifts for general short range potentials is introduced and illustrated by considering relativistic scattering from a Gaussian potential well and barrier.

Atmospheric diffusion of high energy cosmic rays is studied analytically and the obtained integral electromagnetic fluxes are compared with the data measured by emulsion chamber detectors at mountain altitudes. We find a good consistency between them when the average nucleon inelasticity coefficient is varying between 0.50 and 0.65.

We show that the least energy conditions in the gauged nonlinear sigma model with Chern–Simons term lead to exact soliton-like solutions which look like domain walls. In fact, they are string-like solutions on the 2D plane. We will derive and discuss the corresponding solutions, and compute their energy and charge per unit length. The spin of the solutions is shown to vanish.