Related papers: Generalized solutions of the Dirac equation, W bos…
We study the two-body decay of mesons using the covariant helicity formalism. We find that to explain the ratio of partials wave amplitudes (PWAs) of the decay, the Lagrangian must include derivative interactions in addition to contact…
We present the general expression of helicity amplitudes for generic multi-body particle decays characterised by multiple decay chains. This is achieved by addressing for the first time the issue of the matching of final particle spin…
We calculate the cross section of the inverse beta decay process, $\nu_e+n\to p+e$, in a magnetic field which is much smaller than $m_p^2/e$. Using exact solutions of the Dirac equation in a constant magnetic field, we find that the cross…
There are constructed exact solutions of the quantum-mechanical Dirac equation for a spin S=1/2 particle in the space of constant positive curvature, spherical Riemann space, in presence of an external magnetic field, analogue of the…
The Higgs boson decay into a pair of real or virtual W bosons, with one of them decaying leptonically, is predicted within the Standard Model to have the largest branching fraction of all Higgs decays that involve an isolated electron or…
Radiative corrections to the $h\rightarrow Z\gamma$ are evaluated in the one-loop approximation. The unitary gauge gauge is used. The analytic result is expressed in terms of the Passarino-Veltman functions. The calculations are applicable…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
The Foldy-Wouthuysen transformation for relativistic spin-1 particles interacting with nonuniform electric and uniform magnetic fields is performed. The Hamilton operator in the Foldy-Wouthuysen representation is determined. It agrees with…
We write down the four-dimensional fully differential decay distribution for the top quark decay $t \to Wb \to \ell \nu b$. We discuss how its eight physical parameters can be measured, either with a global fit or with the use of selected…
A generalized relativistic harmonic oscillator for spin 1/2 particles is studied. The Dirac Hamiltonian contains a scalar $S$ and a vector $V$ quadratic potentials in the radial coordinate, as well as a tensor potential $U$ linear in $r$.…
We study a fuzzy Boltzmann equation, where particles interact via delocalised collisions, in contrast to classical Boltzmann equations. We discuss the existence and uniqueness of solutions and provide a natural variational characterisation…
We calculate the decay rate of scalar and pseudoscalar Higgs bosons into a pair of gluinos, within the Minimal Supersymmetric Standard Model. In the theoretically and experimentally allowed light gluino window, $\mg \sim $ 3--5 GeV, gluino…
An analytical formula is obtained to describe the evolution of the average populations of spin components of spin-1 atomic gases. The formula is derived from the exact time-dependent solution of the Hamiltonian $H_{S}=c mathbf{S}^{2}$…
These are introductory notes on the study of the Dirac equation in curved spacetime and its relation to hidden symmetries of the dynamics. We present general results on the relation between special spacetime tensors and hidden symmetries,…
We show how the decoherence that occurs in an entangling atomic spin-light interface can be simply modeled as the dynamics of a bosonic mode. Although one seeks to control the collective spin of the atomic system in the permutationally…
We propose formulas of the nuclear beta-decay rate that are useful in a practical calculation. The decay rate is determined by the product of the lepton and hadron current densities. A widely used formula relies upon the fact that the…
The covariant spectator (or Gross) equations for the bound state of three identical spin 1/2 particles, in which two of the three interacting particles are always on shell, are developed and reduced to a form suitable for numerical…
A schematic study of the $\beta \beta 2\nu $-decay of $^{48}Ca$ is made in a shell-model approach. The emphasis is especially put on the role of the spin-orbit potential in relation with the contribution of other terms in the strong…
We propose the relativistic point particle models invariant under the bosonic counterpart of SUSY. The particles move along the world lines in four dimensional Minkowski space extended by $N$ commuting Weyl spinors. The models provide after…
In this article we study global in time (not necessarily small) solutions of the equation for the Higgs boson in the Minkowski and in the de Sitter spacetimes. We reveal some qualitative behavior of the global solutions. In particular, we…