Modern Physics Letters A

We review the status of recently observed positive parity charmed resonances, both in the non-strange and strange sectors. We describe the experimental findings, the main theoretical analyses and the open problems deserving further investigations.

We show that for the triple well potential with non-equivalent vacua, instantons generate for the low lying energy states a singlet and a doublet of states rather than a triplet of equal energy spacing. Our energy splitting formulas are also confirmed numerically. This splitting property is due to the presence of non-equivalent vacua. A comment on its generality to multi-well is presented.

We use the theory of YFS resummation to compute the size of the expected resummed soft radiative threshold effects in precision studies of heavy particle production at the LHC, where accuracies of 1% are desired in some processes. We find that the soft QED threshold effects are at the level of 0.3% whereas the soft QCD threshold effects enter at the level of 20% and hence both must be controlled to be on the conservative side to achieve such goals.

Exact analytic solutions are found to the Dirac equation in (2+1) dimensions for a combination of Aharonov–Bohm and Lorentz 3-vector Coulomb potentials. By means of solutions obtained the relativistic Aharonov–Bohm effect is studied for free and bound electron states.

The coupling constant of ϕ→π⁰γ decay is calculated using QCD sum rules. A comparison of our prediction on the coupling constant with the result obtained from analysis of the experimental data is performed.

We build the Z₃ invariants fusion rules associated to the (D₄,A₆) conformal algebra. This algebra is known to describe the tri-critical Potts model. The 4-point correlation functions of critical fields are developed in the bootstrap approach, and on the other hand, they are written in terms of integral representation of the conformal blocks. By comparing both expressions, one can determine the structure constants of the operator algebra.

While the usual harmonic oscillator potential gives discrete energies in the nonrelativistic case, it does not however give genuine bound states in the relativistic case if the potential is treated in the usual way. In the present article, we have obtained the eigenfunctions of the Dirac oscillator in two spatial dimensions, adapting the prescription of Moshinsky.