abstract

The possible origin of an \(X\)-boson having a mass value around 17 MeV had motivated us to investigate its interaction with leptons of QED. This new hypothetical particle can possibly be a candidate to describe the so-called fifth interaction in a new physics scenario beyond the Standard Model. The simplest \(X\)-boson model unified to the Standard Model is based on an \(\mathrm {SU}_{c}(3) \times \mathrm {SU}_{L}(2) \times \mathrm {U}_{Y}(1) \times \mathrm {U}(1)_{B-L}\) symmetry, where the group \(\mathrm {U}(1)_{B-L}\) is attached to the \(X\)-boson, with a kinetic mixing with the gauge field of \(\mathrm {U}_{Y}(1)\). The Higgs sector was revisited to generate the mass for the new boson. Thus, the mass of 17 MeV fixes a vacuum expected value scale. Thereby, we could estimate the mass of the hidden Higgs field through both the VEV-scale and the Higgs’ couplings. A model of QFT was constructed in a renormalizable \(R_{\xi }\)-gauge, and we analyze its perturbative structure. After that, the radiative correction of the \(X\)-boson propagator has been calculated at one-loop approximation to yield the Yukawa potential correction. The form factors associated with the QED-vertex correction were calculated to confirm the electron’s anomalous magnetic moment together with the computation of the interaction magnitude. The muon case was discussed. Furthermore, we have introduced a renormalization group scheme to explore the running \(X\)-boson mass and its coupling constant with the leptons of the Standard Model.

abstract

We compute the quark and gluon condensates in QCD with \(N\) colors and \(N_{\mathrm {f}}\) flavors based on the renormalization group equations and on the knowledge of a single-scale \({\mit \Lambda }\) which is directly related to \({\mit \Lambda }_{\mathrm {QCD}}\). For \(N=3\) and \(N_{\mathrm {f}}=3\), our findings are in the good range for \(0.2\,{\mathrm {GeV}}\leq {\mit \Lambda }\leq 0.36\) GeV and in excellent agreement with the results in the literature from sum rules for a value \({\mit \Lambda }_{\mathrm {QCD}}=0.28\) GeV.

abstract

We analyze algebraic structure of a relativistic semi-classical Wigner function of massive particles with spin \(\onehalf \) and show that it consistently includes information about the spin density matrix both in two-dimensional spin and four-dimensional spinor spaces. This result is subsequently used to explore various forms of equilibrium functions that differ by specific incorporation of spin potential. We argue that a scalar spin potential should be momentum dependent, while a tensor one may be a function of space-time coordinates only. This allows for the use of the tensor form in local thermodynamic relations. We furthermore show how scalar and tensor forms can be linked to each other.

abstract

We have reported a systematic shell model description of the experimental Gamow–Teller transition strength for \(^{44}\)Sc \(\rightarrow \) \(^{44}\)Ca, \(^{45}\)Ti \(\rightarrow \) \(^{45}\)Sc, \(^{48}\)Ti \(\rightarrow \) \(^{48}\)V, \(^{66}\)Co \(\rightarrow \) \(^{66}\)Ni, and \(^{66}\)Fe \(\rightarrow \) \(^{66}\)Co transitions using KB3G and GXPF1A interactions for \(fp\) model space. In order to see the importance of higher orbital for \(^{66}\)Co \(\rightarrow \) \(^{66}\)Ni and \(^{66}\)Fe \(\rightarrow \) \(^{66}\)Co transitions, we have reported the shell model results with \(fpg_{9/2}\) space using GXPF1Br+\(V_\mathrm {MU}\) interaction. We have obtained the qualitative agreement for the individual transitions, while the calculated summed transition strengths closely reproduce the observed ones.

abstract

In this study, we develop a computer code called Numerical Calculation of the Penetration Factor (NCPF) for calculation of the penetration factor in nuclear interactions. The code is valid in both low-energy thermonuclear reactions for astrophysical applications and high-energy interactions of heavy nuclei. Our validation results indicate that this code can be successfully used to determine the penetrability for calculations of the partial widths of thermonuclear reactions and the half-lives of heavy isotopes. By using the code, we evaluate the astrophysical rates of the \(^{22}\)Mg(\(\alpha ,p)^{25}\)Al reaction and the \(\alpha \)-decay half-lives of super-heavy nuclei with atomic numbers up to \(Z = 118\).

abstract

Reflection and transmission of electrons scattered by a rectangular potential step in the presence of an external magnetic field parallel to the electron beam is described with the use of the Dirac equation. It is shown that in addition to the known effects present in the so-called Klein paradox, the presence of magnetic field gives rise to electron components with reversed spin in the reflected and transmitted beams. The spin-flip scattering processes are caused by the spin–orbit interaction activated by electric field of the potential step and transverse momentum components of electron motion induced by the magnetic field. The contemporary understanding of the Klein paradox, consisting in the finite transmission even when the potential height tends to infinity, is generalized to the presence of magnetic field and spin-reversed electron beams. The spin-reversed beams are shown to occur also for electrons moving above the step. It is proposed that, accounting for the anomalous value of the electron spin \(g\)-factor related to radiation corrections, the reflection and transmission scattering from the potential step can be used as an electron spin filter.

abstract

We consider a scalar field propagating in the static region of the two-dimensional de Sitter space. This simple system is used to illustrate the advantages of hyperboloidal foliations in the analysis of quasinormal modes.