International Journal of Modern Physics A

We review in a pedagogical way the method of differential equations for the evaluation of D-dimensionally regulated Feynman integrals. After dealing with the general features of the technique, we discuss its application in the context of one- and two-loop corrections to the photon propagator in QED, by computing the Vacuum Polarization tensor exactly in D. Finally, we treat two cases of less trivial differential equations, respectively associated to a two-loop three-point, and a four-loop two-point integral. These two examples are the playgrounds for showing more technical aspects about: Laurent expansion of the differential equations in D (around D = 4); the choice of the boundary conditions; and the link among differential and difference equations for Feynman integrals.

Proceeding from optical analogy we propose a new physical interpretation of unitarity saturation leading to antishadowing as a reflective scattering. This interpretation of antishadowing is related to the nonperturbative aspects of strong interactions and follows from the specific property of the unitarity saturation when elastic S-matrix S(s, b)|_{b = 0} → -1 at s→∞. The analogy with Berry phase and experimental consequences of the proposed interpretation as reflective scattering at the LHC and in the cosmic rays studies are discussed.

The Nariai black hole, whose two horizons are lying close to each other, is an extreme and important case in the research of black hole. In this paper we study the evolution of a massless scalar field scattered around in 5D Schwarzschild–de Sitter black string space. Using the method shown by Brevik and Simonsen (2001) we solve the scalar field equation as a boundary value problem, where real boundary condition is employed. Then with convenient replacement of the 5D continuous potential by square barrier, the reflection and transmission coefficients (R, T) are obtained. At last, we also compare the coefficients with the usual 4D counterpart.

We explore a knot model of the elementary particles that is compatible with electroweak physics. The knots are quantized and their kinematic states are labeled by , irreducible representations of SU_q(2), where j = N/2, m = w/2, m′ = (r+1)/2 and (N, w, r) designate respectively the number of crossings, the writhe, and the rotation of the knot. The knot quantum numbers (N, w, r) are related to the standard isotopic spin quantum numbers (t, t₃, t₀) by (t = N/6, t₃ = -w/6, t₀ = -(r+1)/6), where t₀ is the hypercharge. In this model the elementary fermions are low lying states of the quantum trefoil (N = 3) and the gauge bosons are ditrefoils (N = 6). The fermionic knots interact by the emission and absorption of bosonic knots.

We present a new approach to finding multipartite entangled state representation by decomposing normally ordered Gaussian-form operator in completeness relation, the technique of integration within an ordered product (IWOP) of operators is essential in this searching.

We discuss renormalization of propagator of interacting Rarita–Schwinger field. Spin-3/2 contribution after renormalization takes usual resonance form. For nonleading spin-1/2 terms we found procedure, which guarantees absence of poles in energy plane. The obtained renormalized propagator has one free parameter and is a straight generalization of the famous free propagator of Moldauer and Case. Application of this propagator for production of Δ⁺⁺(1232) in π⁺ p →π⁺p leads to good description of total cross-section and to reasonable agreement with results of partial wave analysis.

Sea quark distributions in the NLO approximation, based on the phenomenological valon model or constituent quark model are analyzed. We use the parametrized inverse Mellin transform technique to perform a direct fit with available experimental data and obtain the unknown parameters of the distributions. We try to extend the calculation to the NLO approximation for the singlet and nonsinglet cases in DIS phenomena. We do also the same calculation for electron–positron annihilation. The resulting sea distributions are effectively independent of the process used. The approach of complete RG improvement (CORGI) is employed and the results are compared with the standard approach of perturbative QCD in the scheme with a physical scale. The comparisons with data are in good agreement. As is expected, the results in the CORGI approach indicate a better agreement to the data than the NLO calculation in the standard approach.