International Journal of Modern Physics A

These notes provide a self-contained introduction to Lie algebroids, Lie-Rinehart algebras and their universal envelopes. This review is motivated by the speculation that higher-spin gauge symmetries should admit a natural formulation as enveloping algebras of Lie algebroids since rigid higher-spin algebras are enveloping algebras of Lie algebras. Nevertheless, the material covered here may be of general interest to anyone interested in the description of gauge symmetries, connections and covariant derivatives, in terms of Lie algebroids. In order to be self-contained, a concise introduction to the algebraic characterization of vector bundles as projective modules over the algebra of functions on the base manifold is provided.

The framed standard model (FSM), constructed to explain the empirical mass and mixing patterns (including CP phases) of quarks and leptons, in which it has done quite well, gives otherwise the same result as the standard model (SM) in almost all areas in particle physics where the SM has been successfully applied, except for a few specified deviations such as the $W$ mass and the $g-2$ of muons, that is, just where experiment is showing departures from what SM predicts. It predicts further the existence of a hidden sector of particles some of which may function as dark matter. In this paper, we first note that the above results involve, surprisingly, the FSM undergoing a vacuum transition (VTR1) at a scale of around 17MeV, where the vacuum expectation values of the colour framons (framed vectors promoted into fields) which are all nonzero above that scale acquire some vanishing components below it. This implies that the metric pertaining to these vanishing components would vanish also. Important consequences should then ensue, but these occur mostly in the unknown hidden sector where empirical confirmation is hard at present to come by, but they give small reflections in the standard sector, some of which may have already been seen. However, one notes that if, going off at a tangent, one imagines colour to be embedded, Kaluza–Klein (KK) fashion, into a higher-dimensional space–time, then this VTR1 would cause 2 of the compactified dimensions to collapse. This might mean then that when the universe cooled to the corresponding temperature of $10^{11}$ K when it was about $10^{-3}$ s old, this VTR1 collapse would cause the three spatial dimensions of the universe to expand to compensate. The resultant expansion is estimated, using FSM parameters previously determined from particle physics, to be capable, when extrapolated backwards in time, of bringing the present universe back inside the then horizon, solving thus formally the horizon problem. Besides, VTR1 being a global phenomenon in the FSM, it would switch on and off automatically and simultaneously over all space, thus requiring seemingly no additional strategy for a graceful exit. However, this scenario has not been checked for consistency with other properties of the universe and is to be taken thus not as a candidate solution of the horizon problem but only as an observation from particle physics which might be of interest to cosmologists and experts in the early universe. For particle physicists also, it might serve as an indicator for how relevant this VTR1 can be, even if the KK assumption is not made.

We study the thermodynamic properties of black holes in dRGT massive gravity theory using Duan’s $\varphi -$ mapping topological current theory. The topological features and the corresponding thermodynamic stability conditions for neutral and charged cases are discussed. A neutral black hole in four dimensions has a topological number 0, sharing the same topological class of $D\ge 6$ Gauss–Bonnet–AdS black hole. We show that the charged black hole in four-dimensional massive gravity has the same topological structure as the AdS-RN black hole. Further, we have extended the calculations to higher dimensions. Our calculations strengthen the conjecture that the addition of higher interaction terms to Einstein–Hilbert action does not alter the topological number of black holes in four space–time dimensions. However, in higher-dimensional massive gravity, the topological number indeed depends on the black hole parameters.

Bi-scalar CFT from $\gamma$ deformed ${𝒩}=4$ SYM describes the fishnet theory which is integrable in the planar limit. The holographic dual of the planar model is the fishchain model. The derivation of the weak–strong duality from the first principle was presented in a recent paper (“The Holographic Fishchain” arXiv:1903.10508). In this paper, we extend the investigation to the tri-scalar CFT which arises from the large twist limit of ABJM theory. We show that it becomes tri-scalar fishnet theory in planar limit and the dual theory is the holographic bi-fishchain model.

This paper presents a method for extracting the parton distribution functions (PDFs) at small momentum fractions $x$ and at the next-to-leading order (NLO) accuracy in perturbative quantum chromodynamics. It turns out that the PDFs can be described by the “Fractal” or self-similar distributions at low $x$ below $x<0.01$. To this end, a simple parametrization for the unintegrated PDFs based on the “Fractal” approach is considered. These functions have self-similar behavior at low $x$ and $k_t^2$ for sea quarks and have self-similar behavior at low $x$ for gluon distribution. By integration from these transverse momentum distributions (TMDs), the initial input densities are obtained and the model’s free parameters are then calculated using the experimental data released by the HERA experiment. The small-$x$ experimental datasets on electron–proton ($e^{-}p$) and positron–proton ($e^{+}p$) for natural current (NC) interactions in deep inelastic scattering (DIS) processes at HERA for the range of $1.2<Q^2<500$ (GeV²) and $x<0.01$ are included in this analysis. The uncertainty estimations in this analysis are carried out using the standard “Hessian” method. Considering the overall value of ${\chi }^2∕\mathrm{\text{dof}}$ and theory-to-data comparisons, the results indicate good agreements between the experimental datasets and the theoretical predictions. A detailed comparison is also presented between the model’s predictions for the relevant small-$x$ observable and recent parametrizations for the PDFs.

The fermion flavor structure is investigated by bilinear decomposition of the mass matrix after EW symmetry breaking, and the roles of factorized matrices in flavor mixing and mass generation are explored. On a new Yukawa basis, the minimal parameterization of flavor mixing is realized containing two relative phases and two free $\mathrm{\text{SO}}{(2)}_L$ rotation angles. It is shown that flavor mixing can be addressed from four independent parameters. The validity of the flavor mixing structure is checked in both the lepton and quark sectors. Under the decomposition of flavor mixing, fermion mass matrices are reconstructed in the hierarchy limit. A flat mass matrix with all elements equal to 1 arises naturally from the requirement that homology exists between up-type and down-type fermion mass matrices. Some hints of a flat matrix and flavor breaking are also discussed.

In this paper, we investigate the thermodynamical phase transitions of the spherically symmetric AdS black hole in Horava–Lifshitz (HL) gravity for the detailed balance violation parameter $0\le {ϵ}^2\le 1$. First, by calculating the HP temperature $T_{\mathrm{\text{HP}}}$, the minimum temperature $T_{\mathrm{\text{min}}}$ and the Gibbs free energy $G$ of the AdS black hole in different values of parameter $ϵ$, we find that the HP phase transition can occur at all pressures. Comparing the HP temperature $T_{\mathrm{\text{HP}}}$ with the minimum temperature $T_{\mathrm{\text{min}}}$, we notice that the ratio of $T_{\mathrm{\text{HP}}}/T_{\mathrm{\text{min}}}$ tends to 1 when $d\to \infty$. Second, for the small–large black hole phase transition of the AdS black hole, we discover that the black hole heat capacity is divergent at the minimum temperature $T_{\mathrm{\text{min}}}$, the small–large black hole phase transition occurs at the same time. Furthermore, the black hole entropy also exists $S_{\mathrm{\text{HP}}}$ when $T=T_{\mathrm{\text{HP}}}$, and $S_{\mathrm{\text{min}}}$ when the black hole temperature has its minimum $T_{\mathrm{\text{min}}}$, we surprisingly find that the ratio of $S_{\mathrm{\text{HP}}}/S_{\mathrm{\text{min}}}$ tends to $e$ when the dimension $d\to \infty$, which provides a general relation between the Hawking–Page phase transition and the small–large black hole phase transition of the AdS black hole in the large dimension. All in all, the ratios of typical temperature and entropy of two kinds of phase transitions tend to natural constant in the large dimension limit, which may imply to understand the nature of two different phase transitions.

In this paper, we discuss bremsstrahlung induced by neutrino scattering. This process should exist since neutrinos are expected to couple to photons via magnetic dipole and transition moments. These moments are loop-induced and tiny in the Standard Model with neutrino masses but could be significantly enhanced in extended theories. As concrete example, we study the scattering of the two largest neutrino fluxes on earth, solar neutrinos and Cosmic Neutrino Background (CNB). It is tempting to consider this as a potential signature for CNB searches but it turns out that the signal is extremely small and unlikely to be observed.