International Journal of Modern Physics A

This paper contains a review of the main results of a search of regularities in collective variables properties in multiparticle dynamics, regularities which can be considered as manifestations of the original simplicity suggested by QCD. The method is based on a continuous dialog between experiment and theory. The paper follows the development of this research line, from its beginnings in the 1970's to the current state of the art, discussing how it produced both sound interpretations of the most relevant experimental facts and intriguing perspectives for new physics signals in the TeV energy domain.

We explore the geometry of superconformal moduli of the NSR superstring theory in order to construct the consistent sigma-model for NSR strings, free of picture-changing complications. The sigma-model generating functional is constructed by the integration over the bosonic and fermionic moduli, corresponding to insertions of the vertex operators in scattering amplitudes. While the integration over the supermoduli leads to the standard picture-changing insertions, the integration over the bosonic moduli results in the appearance of picture-changing operators for the b-c fermionic ghosts with the ghost number -1. Important example of the b-c ghost pictures involves the vertex operators in integrated and unintegrated forms. We obtain the BRST-invariant expressions for the b-c picture-changing operators for open and closed strings and study some of their properties. We also show that the superconformal moduli spaces of the NSR theory contain the global singularities, leading to the phenomenon of ghost-matter mixing and the appearance of nonperturbative D-brane creation operators.

We derive the master function governing the component action of the four-dimensional nonanticommutative (NAC) and fully N = 2 supersymmetric gauge field theory with a nonsimple gauge group U(2) = SU(2) × U(1). The new NAC master function is a nontrivial generalization of the known master functions in the NAC, N = 2 supersymmetric gauge theories with the U(1) and SU(2) gauge groups. We use a Lorentz-singlet NAC-deformation parameter and an N = 2 supersymmetric star (Moyal) product, which do not break any of the fundamental symmetries of the undeformed N = 2 gauge theory. The scalar potential in the NAC-deformed theory is calculated. We also propose the non-Abelian BPS-type equations in the case of the NAC-deformed N = 2 gauge theory with the SU(2) gauge group, and comment on the SU(3) case too. The NAC-deformed field theories can be thought of as the effective (nonperturbative) N = 2 gauge field theories in a certain (scalar only) N = 2 supergravity background.

We present bound state masses of the self-conjugate and non-self-conjugate mesons in the context of the Schrödinger equation taking into account the relativistic kinematics and the quark spins. We apply the usual interaction by adding the spin dependent correction. The hyperfine splittings for the 2S charmonium and 1S bottomonium are calculated. The pseudoscalar and vector decay constants of the B_c meson and the unperturbed radial wave function at the origin are also calculated. We have obtained a local equation with a complete relativistic corrections to a class of three attractive static interaction potentials of the general form V(r) = -Ar^-β+κr^β+V₀, with β = 1, 1/2, 3/4 which can also be decomposed into scalar and vector parts in the form V_V(r) = -Ar^-β+(1-∊)κr^β and V_S(r) = ∊κr^β+V₀; where 0≤∊≤1. The energy eigenvalues are carried out up to the third order approximation using the shifted large-N-expansion technique.

A proposal towards a microscopic understanding of the Bekenstein–Hawking entropy for D = 4 space–times is made. Euclidean D-branes wrapping the event horizon's boundary play an important role. After assuming a discretization of the Euclidean D-brane worldvolume, motivated by the worldvolume uncertainty relation, we count chainlike excitations on the worldvolume of specific dual Euclidean brane pairs. It is shown that one can thus reproduce the D = 4 Bekenstein–Hawking entropy and its logarithmic correction.

We apply the quantum Hamilton–Jacobi formalism, naturally defined in the complex domain, to complex Hamiltonians, characterized by discrete parity and time reversal (PT) symmetries and obtain their eigenvalues and eigenfunctions. Examples of both quasi-exactly and exactly solvable potentials are analyzed and the subtle differences, in the singularity structures of their quantum momentum functions, are pointed out. The role of the PT symmetry in the complex domain is also illustrated.

We report the results of the first computation related to the study of the spectator effects in the rare decay mode B→Kγγ within the framework of Standard Model. It is found that the account of these effects results in the enhancement factor for the short-distance reducible contribution to the branching ratio.

We investigate a dynamical mechanism to generate fermion mass in the Randall–Sundrum background. We consider four-fermion interaction models where the fermion field propagates in an extra-dimension, i.e. the bulk four-fermion interaction model. It is assumed that two types of fermions with opposite parity exist in the bulk. We show that electroweak-scale mass is dynamically generated for a specific fermion–antifermion condensation, even if all the scale parameters in the Lagrangian are set to the Planck scale.

The massless field of spin 1 is defined on the eight-dimensional configuration space; this space is a direct product of Minkowski space and of a two-dimensional complex sphere. Field equations for the spin-one field are derived from a Dirac-like Lagrangian separately for the translation group and Lorentz group parts. It is shown that a Dirac form of Maxwell equations (the so-called Majorana–Oppenheimer formulation of electrodynamics) follows directly from the field equations of translation group part. The photon field is realized via Biedenharn type functions on the Poincaré group. This allows us to consider both Dirac and Maxwell fields on an equal footing, as the functions on the Poincaré group.

A simple phenomenological potential model is suggested to describe the interaction between the constituent quarks of meson systems. Taking the spin-dependence terms in consideration modifies some previous potential models. The resonance masses and the leptonic decay widths of , , , , and mesons are calculated using the nonrelativistic wave equation. A comparison between the present calculations and the available experimental results are given.