International Journal of Modern Physics A

We review the approach to the Standard Model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular, the bosonic spectral action and the fermionic action are discussed in detail, and how they lead to phenomenology. We also discuss the Euclidean versus Lorentz issues and how to go beyond the Standard Model in this framework.

In this paper, we study the $\bar{D}{\mathrm{\Sigma }}_c$, $\bar{D}{\mathrm{\Sigma }}_c^{\ast }$, ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c$ and ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c^{\ast }$ pentaquark molecular states with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension $13$ in a consistent way. The present calculations support assigning the $P_c(4312)$ to be the $\bar{D}{\mathrm{\Sigma }}_c$ pentaquark molecular state with $J^P={\frac{1}{2}}^{-}$, assigning the $P_c(4380)$ to be the $\bar{D}{\mathrm{\Sigma }}_c^{\ast }$ pentaquark molecular state with $J^P={\frac{3}{2}}^{-}$, assigning the $P_c(4440/4457)$ to be the ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c$ pentaquark molecular state with $J^P={\frac{3}{2}}^{-}$ or the ${\bar{D}}^{\ast }{\mathrm{\Sigma }}_c^{\ast }$ pentaquark molecular state with $J^P={\frac{5}{2}}^{-}$. Special attention is paid to the operator product expansion.

As the first topic, we propose a new parametrization of the complex Yukawa matrix in the scotogenic model. The new parametrization is compatible with the particle data group parametrization of the neutrino sector. Some analytical expressions for the neutrino masses with the new parametrization are shown. As the second topic, we consider the phenomenology of the scotogenic model with the one-zero-textures of the neutrino flavor mass matrix. One of the six patterns of the neutrino mass matrix is favorable for the real Yukawa matrix. On the other hand, for the complex Yukawa matrix, five of the six patterns are compatible with observations of the neutrino oscillations, dark matter relic abundance and branching ratio of the $\mu \to e\gamma$ process.

We consider the cosmological application of a (variant of) relatively newly proposed model¹ unifying inflation, dark energy, dark matter, and the Higgs mechanism. The model was originally defined using additional non-Riemannian measures, but it can be reformulated into effective quintessential model unifying inflation, dark energy and dark matter. Here, we demonstrate numerically that it is capable of describing the entire evolution of the Universe in a seamless way, but this requires some revision of the model setup. The main reason is that there is a strong effective friction in the model, a feature which has been neglected in the pioneer work. This improves the model potential for proper description of the evolution of the Universe, because the friction ensures a finite time inflation with dynamically maintained low-value slow-roll parameters in the realistic scenarios. In addition, the model predicts the existence of a constant scalar field in late Universe.

Propagator for spinning particle described in the Feshbach–Villars formalism is set up using fermionic coherent state path integral. The fermionization of the charge-spin symmetry is presented following the Schwinger recipe. The explicit calculations are done in the free case and magnetic interaction using the Foldy–Wouthuysen tranformation. The spectrum and wave functions are deduced.

Superheavy neutrinos can, via the seesaw model, provide a mechanism for lepton number violation. If they are combined with flavor violation as characterized by the Froggatt–Nielsen mechanism, then the phenomenology for the neutrinos in oscillation experiments, neutrinoless double beta decay, and other experiments can be described by a relatively few number of parameters. We describe the low-energy neutrino mass matrix and show that the results are consistent with currently available data.

This work expands previous efforts, within the classical theories of Special and General Relativity, to include tachyons (faster-than-light particles) along with ordinary (slower-than-light) particles at any energy. The objective here is to construct a Hamiltonian that includes both the particles and the gravitational field that they produce. We do this with a linear approximation for the Einstein field equations; and we also assume a time-independent gravitational metric implied by a static picture of the particles’ motion. The resulting formulas will allow serious modeling to test the idea that cosmic background neutrinos may be tachyons, which can produce the observed gravitational effects now ascribed to some mysterious Dark Matter.