International Journal of Modern Physics A

The Composition Algebra-based Methodology (CAM) [B. Wolk, Pap. Phys. 9, 090002 (2017); Phys. Scr. 94, 025301 (2019); Adv. Appl. Clifford Algebras 27, 3225 (2017); J. Appl. Math. Phys. 6, 1537 (2018); Phys. Scr. 94, 105301 (2019), Adv. Appl. Clifford Algebras 30, 4 (2020)], which provides a new model for generating the interactions of the Standard Model, is geometrically modeled for the electromagnetic and weak interactions on the parallelizable sphere operator fiber bundle $B_n=(T𝕄,S^n\to {\mathcal{𝒮}}^n,SO(n+1),\pi )$ consisting of base space, the tangent bundle $T𝕄$ of space–time $𝕄$, projection operator $\pi$, the parallelizable spheres $S^n=\{S^1,S^3\}$ conceived as operator fibers $S^n\to {\mathcal{𝒮}}^n$ attaching to and operating on $T_p𝕄$ $\forall p\in 𝕄$ as $p$ varies over $𝕄$, and as structure group, the norm-preserving symmetry group $SO(n+1)$ for each of the division algebras which is simultaneously the isometry group of the associated unit sphere. The massless electroweak $SU{(2)}_L\otimes U{(1)}_Y$ Lagrangian is shown to arise from $B_{3\otimes 1}$’s generation of a local coupling operation on sections of Dirac spinor and Clifford algebra bundles over $𝕄$. Importantly, CAM is shown to be a new genre of gauge theory which subsumes Yang–Mills Standard Model gauge theory. Local gauge symmetry is shown to be at its core a geometric phenomenon inherent to CAM gauge theory. Lastly, the higher-dimensional, topological architecture which generates CAM from within a unified eleven $(1,10)$-dimensional geometro-topological structure is introduced.

We show that the current quark mass should vanish to be consistent with the QCD color confinement: a bag model leads us to Heun’s equation, which requests that not only the energy but also the string tension should be quantized. This is due to the presence of higher-order singularity which requests higher regularity condition demanding that parameters of the theory should be related to one another. As a result, the Hadron spectrum is consistent with the Regge trajectory only when quark mass vanishes. Therefore, in this model, the chiral symmetry is a consequence of the confinement.

In this paper, we study the phenomenological implications of enforcing one texture zero on the inverse matrix of the neutrino mass matrix $M_{\nu }^{\mathrm{\text{TM}}}$ that can lead to the trimaximal mixing. It is found that the condition of $M_{12}^{-1}=0$, $M_{13}^{-1}=0$, $M_{22}^{-1}=0$, $M_{23}^{-1}=0$ or $M_{33}^{-1}=0$ can hold in the case of normal neutrino mass ordering, while the condition of $M_{11}^{-1}=0$, $M_{12}^{-1}=0$, $M_{13}^{-1}=0$, $M_{22}^{-1}=0$ or $M_{33}^{-1}=0$ can hold in the case of inverted neutrino mass ordering, where $M_{ij}^{-1}$ (for $i$, $j=1,2,3$) denotes the $ij$ entry of the inverse matrix of $M_{\nu }^{\mathrm{\text{TM}}}$. The ranges of the absolute neutrino mass scale and three CP phases for these cases to hold are studied in some detail. The implications of these cases for the effective neutrino mass $M_{ee}^{}$ which controls the rates of the neutrino-less double beta decay processes are also given.

In this paper, we introduce an explicit $P$-wave to construct three-quark currents to study the $P$-wave ${\mathrm{\Omega }}_b$ states with the full QCD sum rules. The predicted masses have a hierarchy if the same parameters are chosen and favor assigning the ${\mathrm{\Omega }}_b(6316)$, ${\mathrm{\Omega }}_b(6330)$, ${\mathrm{\Omega }}_b(6340)$ and ${\mathrm{\Omega }}_b(6350)$ to be the $P$-wave ${\mathrm{\Omega }}_b$ states with the $J^P={\frac{3}{2}}^{-}$, ${\frac{1}{2}}^{-}$, ${\frac{5}{2}}^{-}$ and ${\frac{3}{2}}^{-}$, respectively.

In this work we consider the scale-covariant formalism proposed by Canuto et al.,${}^{1,2}$ in order to map different eras of the universe. This technique considers a scale gauge function that can be adjusted by using different arguments like Dirac’s large numbers hypothesis or a restriction on the particle production rate. A Chaplygin constituent shows to be a consistent idea to establish a mapping between an old decelerated–accelerated universe ruled by Einstein equations and an early universe, where a new equation of state appears together with a modified general relativity theory and a de Sitter universe then emerges. These properties are a direct consequence of the use of the scale-covariant formalism. Besides, a new discussion and remarks are presented related to the well-known barotropic constituent case.

A phenomenological study of the two-photon reaction within the discrete BFKL approach is performed. We estimate the BFKL amplitude in terms of a discrete set of eigenfunctions and use the HERA $F_2^p$ data to constrain the free parameters of the model. As a consequence, we derive a parameter free prediction of the energy dependence of the total $\gamma \gamma$ cross-section and the Bjorken-$x$ dependence of the photon structure function. We demonstrate that the LEP data is quite well described by the discrete BFKL approach and that experimental data from the future $e^{+}{e}^{-}$ colliders can be useful to constrain the description of the QCD dynamics at high energies.