arXiv subjects

Alex E. Bernardini

Publications and source records attributed to Alex E. Bernardini.

116 records · Page 7Linked to original sources

arXiv2006

The charmonium and bottomonium mass spectroscopy with a simple approximaton of the kinetic term

In this paper we propose a particular description of meson spectroscopy, with emphasis in heavy bound states like charmonia and bottomonia, after working on the main aspects of the construction of an effective potential model. We use the prerogatives from ``soft QCD'' to determine the effective potential terms, establishing the asymptotic Coulomb term from one gluon exchange approximation. At the same time, a linear confinement term is introduced in agreement with QCD and phenomenological prescription. The main aspect of this work is the simplification in the calculation, consequence of a precise and simplified description of the kinetic term of the Hamiltonian. With this proposition we perform the calculations of mass spectroscopy for charmonium and bottomonium mesons and we discuss the real physical possibilities of developing a generalized potential model, its possible advantages relative to experimental parameterization and complexity in numerical calculations.

hep-ph↗

arXiv2006

Chirality Dynamics for a fermionic particle non-minimally coupling with an external magnetic field

We proceed with the construction of normalizable Dirac wave packets for treating chiral oscillations in the presence of an external magnetic field. Both chirality and helicity quantum numbers correspond to variables of fundamental importance in the study of chiral interactions, in particular, in the context of neutrino physics. In order to clarify a subtle aspect in the confront of such concepts which, for massive particles, represent different physical quantities, we are specifically interested in quantifying chiral oscillations for a {\em fermionic} Dirac-{\em type} particle (neutrino) non-minimally coupling with an external magnetic field {\boldmath$B$} by solving the correspondent interacting Hamiltonian (Dirac) equation. The viability of the intermediate wave packet treatment becomes clear when we assume {\boldmath$B$} orthogonal/parallel to the direction of the propagating particle.

hep-th↗

arXiv2006

Flavor coupled with chiral oscillations in the presence of an external magnetic field

By reporting to the Dirac wave-packet prescription where it is formally assumed the {\em fermionic} nature of the particles, we shall demonstrate that chiral oscillations implicitly aggregated to the interference between positive and negative frequency components of mass-eigenstate wave-packets introduce some small modifications to the standard neutrino flavor conversion formula. Assuming the correspondent spinorial solutions of a ``modified'' Dirac equation, we are specifically interested in quantifying flavor coupled with chiral oscillations for a {\em fermionic} Dirac-{\em type} particle (neutrino) non-minimally coupling with an external magnetic field {\boldmath$B$}. The viability of the intermediate wave-packet treatment becomes clear when we assume {\boldmath$B$} orthogonal/parallel to the direction of the propagating particle.

hep-th↗

arXiv2006

Additional time-dependent phase in the flavor-conversion formulas

In the framework of intermediate wave-packets for treating flavor oscillations, we quantify the modifications which appear when we assume a strictly peaked momentum distribution and consider the second-order corrections in a power series expansion of the energy. By following a sequence of analytic approximations, we point out that an extra time-dependent phase is merely the residue of second-order corrections. Such phase effects are usually ignored in the relativistic wave-packet treatment, but they do not vanish non-relativistically and can introduce some small modifications to the oscillation pattern even in the ultra-relativistic limit.

hep-th↗

arXiv2005

The stationary phase condition applicability to the study of tunnel effect

Some recent theoretical studies have tended to employ analytically-continuous {\em gaussian}, or infinite-bandwidth step pulses to examine tunneling process. The stationary phase method is often employed to this aim. However, {\em gaussian} functions do not have a well-defined front, such that their speed of propagation becomes ambiguous. Also, infinite bandwidth signals cannot propagate through any real physical medium (whose transfer function is therefore finite) without pulse distortion, which also leads to ambiguities in determining propagation velocity during the tunneling process. In this manuscript, we appoint some incompatibilities with the application of the method of stationary phase in deriving tunneling times which, eventually, can ruin the {\em superluminal} interpretation of transition times.

quant-ph↗

arXiv2005

Flavor and chiral oscillations with Dirac wave packets

We report about recent results on Dirac wave packets in the treatment of neutrino flavor oscillation where the initial localization of a spinor state implies an interference between positive and negative energy components of mass-eigenstate wave packets. A satisfactory description of fermionic particles requires the use of the Dirac equation as evolution equation for the mass-eigenstates. In this context, a new flavor conversion formula can be obtained when the effects of chiral oscillation are taken into account. Our study leads to the conclusion that the fermionic nature of the particles, where chiral oscillations and the interference between positive and negative frequency components of mass-eigenstate wave packets are implicitly assumed, modifies the standard oscillation probability. Nevertheless, for ultra-relativistic particles and sharply peaked momentum distributions, we can analytically demonstrate that these modifications introduce correction factors proportional to (m12/p0) square which are practically un-detectable by any experimental analysis

hep-ph↗

arXiv2004

Dirac Spinors and Flavor Oscillations

In the standard treatment of particle oscillations the mass eigenstates are implicitly assumed to be scalars and, consequently, the spinorial form of neutrino wave functions is not included in the calculations. To analyze this additional effect, we discuss the oscillation probability formula obtained by using the Dirac equation as evolution equation for the neutrino mass eigenstates. The initial localization of the spinor state also implies an interference between positive and negative energy components of mass eigenstate wave packets which modifies the standard oscillation probability.

hep-ph↗

arXiv2004

An Analytic Approach to the Wave Packet Formalism in Oscillation Phenomena

We introduce an approximation scheme to perform an analytic study of the oscillation phenomena in a pedagogical and comprehensive way. By using Gaussian wave packets, we show that the oscillation is bounded by a time-dependent vanishing function which characterizes the slippage between the mass-eigenstate wave packets. We also demonstrate that the wave packet spreading represents a secondary effect which plays a significant role only in the non-relativistic limit. In our analysis, we note the presence of a new time-dependent phase and calculate how this additional term modifies the oscillating character of the flavor conversion formula. Finally, by considering Box and Sine wave packets we study how the choice of different functions to describe the particle localization changes the oscillation probability.

hep-ph↗