Abstract: Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of a hypothetical dark matter. In fact, the behavior of the rotation curves shows the existence of a constant velocity region, near the baryonic matter distribution, followed by a quick decay at large distances. In this work, we consider the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained within the framework of the recently proposed hybrid metric-Palatini gravitational theory. The latter is constructed by modifying the metric Einstein-Hilbert action with an f(R) term in the Palatini formalism. It was shown that the theory unifies local constraints and the late-time cosmic acceleration, even if the scalar field is very light. In the intermediate galactic scale, we show explicitly that in the hybrid metric-Palatini model the tangential velocity can be explicitly obtained as a function of the scalar field of the equivalent scalar-tensor description. The model predictions are compared model with a small sample of rotation curves of low surface brightness galaxies, respectively, and a good agreement between the theoretical rotation Curves and the observational data is found. The possibility of constraining the form of the scalar field and the parameters of the model by using the stellar velocity dispersions is also analyzed. Furthermore, the Doppler velocity shifts are also obtained in terms of the scalar field. All the physical and geometrical quantities and the numerical parameters in the hybrid metric-Palatini model can be expressed in terms of observable/measurable parameters, such as the tangential velocity, the baryonic mass of the galaxy, the Doppler frequency shifts, and the stellar dispersion velocity, respectively. Therefore, the obtained results open the possibility of testing the hybrid metric-Palatini gravitational models at the galactic or extra-galactic scale by using direct astronomical and astrophysical observations.

Abstract: The study of the relation between Lie algebras and groups, and especially the derivation of new algebras from them, is a problem of great interest in mathematics and physics, because finding a new Lie group from an already known one also means that a new physical theory can be obtained from a known one. One of the procedures that allow us to do so is called expansion of Lie algebras, and has been recently used in different physical applications-particularly in gauge theories of gravity. Here we report on further developments of this method, required to understand in a deeper way their consequences in physical theories. We have found theorems related to the preservation of some properties of the algebras under expansions that can be used as criteria and, more specifically, as necessary conditions to know if two arbitrary Lie algebras can be related by some expansion mechanism. Formal aspects, such as the Cartan decomposition of the expanded algebras, are also discussed. Finally, an instructive example that allows us to check explicitly all our theoretical results is also provided.

Abstract: We study an approximate version of the Schwinger-Dyson equation that controls the nonperturbative behavior of the ghost-gluon vertex in the Landau gauge. In particular, we focus on the form factor that enters in the dynamical equation for the ghost dressing function, in the same gauge, and derive its integral equation, in the “one-loop dressed” approximation. We consider two special kinematic configurations, which simplify the momentum dependence of the unknown quantity; in particular, we study the soft gluon case and the well-known Taylor limit. When coupled with the Schwinger-Dyson equation of the ghost dressing function, the contribution of this form factor provides considerable support to the relevant integral kernel. As a consequence, the solution of this coupled system of integral equations furnishes a ghost dressing function that reproduces the standard lattice results rather accurately, without the need to artificially increase the value of the gauge coupling.

Abstract: The K hindrance to the gamma decay is studied in the warm rotating W-174 nucleus, focusing on the weakening of the selection rules of the K quantum number with increasing excitation energy. W-174 was populated by the fusion reaction of Ti-50 (at 217 MeV) on a Te-128 target, and its gamma decay was detected by the AGATA Demonstrator array coupled to a BaF2 multiplicity filter at Laboratori Nazionali di Legnaro of INFN. A fluctuation analysis of gamma coincidence matrices gives a similar number of low-K and high-K discrete excited bands. The results are compared to simulations of the gamma-decay flow based on a microscopic cranked shell model at finite temperature in which the K mixing is governed by the interplay of Coriolis force with the residual interaction. Agreement between simulations and experiment is obtained only by hindering the E1 decay between low-K and high-K bands by an amount compatible with that determined by spectroscopic studies of K isomers in the same mass region, with a similar trend with excitation energy. The work indicates that K mixing due to temperature effects may play a leading role for the entire body of discrete excited bands, which probes the onset region of K weakening.

Abstract: We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major improvement compared to the analysis presented in Aguilar et al. [Phys. Rev. D 86, 014032 (2012)], where the behavior of the gluon propagator in the deep infrared was estimated through numerical extrapolation. The resulting nonlinear system is then treated numerically, yielding unique solutions for the modified gluon mass and the quenched gluon propagator, which fully confirms the picture put forth recently in several continuum and lattice studies. In particular, an infrared finite gluon propagator emerges, whose saturation point is considerably suppressed, due to a corresponding increase in the value of the gluon mass. This characteristic feature becomes more pronounced as the number of active quark families increases, and can be deduced from the infrared structure of the kernel entering in the gluon mass equation.