Different approaches to calculate the K±→π±π0e+e−K^{\pm}\to \pi^{\pm}\pi^0e^+e^- decay width

The rare $K^\pm\to\pi^\pm\pi^0 e^+e^-$ decay, currently under analysis by the NA48/2 Collaboration, is considered. We have performed two theoretical approaches to calculate the differential decay width -- in the kaon rest frame, where we use Cabibbo-Maksimovicz variables, and in the center-of-mass system of the lepton pair. The latter essentially simplifies the computations. A comparison between the two approaches has been performed. We have also found the dependencies of the differential decay rate as a function of the virtual photon and dipion system massesComment: 10 pages,5 figure

New Perturbation Theory for Nonstationary Anharmonic Oscillator

The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency in external field is used. Based on some intrinsic properties of unperturbed wave function the variational-iterational method is proposed, that make it possible to correct both the amplitude and the phase of wave function. As an application the first order correction are proposed both for wave function and S-matrix elements for asymmetric perturbation potential of type $V(x,\tau)=\alpha (\tau)x^3+\beta (\tau)x^4.$ The transition amplitude ''ground state - ground state'' $W_{00}(\lambda ;\rho)$ is analyzed in detail depending on perturbation parameter $\lambda$ (including strong coupling region $$ $\sim 1$) and one-dimensional refraction coefficient $\rho$.Comment: LaTeX, 13 page

Enhancement of low-mass dileptons in ultraperipheral collisions

It is shown that production of low-mass $e^+e^-$-pairs in ultraperipheral nuclear collisions is enhanced due to the Sommerfeld-Gamow-Sakharov (SGS) factor. This effect is especially strong near the threshold of creation of unbound $e^+e^-$-pairs with low masses in the two-photon fusion. Coulomb attraction of the non-relativistic components of such pairs may lead to the increased intensity of 511 keV photons. It can be recorded at the NICA collider and has some astrophysical implications. The analogous effect can be observed at LHC in dilepton production.Comment: 10 p., 3 Fig

The electromagnetic effects in Ke4K_{e4} decay

The final state interaction of pions in $K_{e4}$ decay allows one to obtain the value of the isospin and angular momentum zero $\pi\pi$ scattering length $a_0^0$.We take into account the electromagnetic interaction of pions and isospin symmetry breaking effects caused by different masses of neutral and charged pions and estimate the impact of these effects on the procedure of scattering length extraction from $K_{e4}$ decay.Comment: 8 pages,1 figur