Addressing the missing matter problem in galaxies through a new fundamental gravitational radius

We demonstrate that the existence of a Noether symmetry in $f(R)$ theories of gravity gives rise to a further gravitational radius, besides the standard Schwarzschild one, determining the dynamics at galactic scales. By this feature, it is possible to explain the baryonic Tully-Fisher relation and the rotation curve of gas-rich galaxies without the dark matter hypothesis.Comment: 9 pages, 2 figures, to be published in JCA

Recovering the fundamental plane of galaxies by f(R)f(R) gravity

The fundamental plane (FP) of galaxies can be recovered in the framework of $f(R)$ gravity avoiding the issues related to dark matter to fit the observations. In particular, the power-law version $f(R)\propto R^n$, resulting from the existence of Noether symmetries for $f(R)$, is sufficient to implement the approach. In fact, relations between the FP parameters and the corrected Newtonian potential, coming from $R^n$, can be found and justified from a physical point of view. Specifically, we analyze the velocity distribution of elliptical galaxies and obtain that $r_c$, the scale-length depending on the gravitational system properties, is proportional to $r_e$, the galaxy effective radius. This fact points out that the gravitational corrections induced by $f(R)$ can lead photometry and dynamics of the system. Furthermore, the main byproduct of such an approach is that gravity could work in different ways depending on the scales of self-gravitating systems.Comment: 18 pages, 3 tables, 8 figures. Accepted for publication in Phys. Dark Univers

Constraining Extended Gravity Models by S2 star orbits around the Galactic Centre

We investigate the possibility to explain theoretically the observed deviations of S2 star orbit around the Galactic Centre using gravitational potentials derived from modified gravity models in absence of dark matter. To this aim, an analytic fourth-order theory of gravity, non-minimally coupled with a massive scalar field is considered. Specifically, the interaction term is given by analytic functions $f(R)$ and $f(R,\phi)$ where $R$ is the Ricci scalar and $\phi$ is a scalar field whose meaning can be related to further gravitational degrees of freedom. We simulate the orbit of S2 star around the Galactic Centre in $f(R)$ (Yukawa-like) and $f(R,\phi)$ (Sanders-like) gravity potentials and compare it with NTT/VLT observations. Our simulations result in strong constraints on the range of gravity interaction. In the case of analytic functions $f(R)$, we are not able to obtain reliable constraints on the derivative constants $f_1$ and $f_2$, because the current observations of S2 star indicated that they may be highly mutually correlated. In the case of analytic functions $f(R,\phi)$, we are able to obtain reliable constraints on the derivative constants $f_0$, $f_R$, $f_{RR}$, $f_{\phi}$, $f_{\phi\phi}$ and $f_{\phi R}$. The approach we are proposing seems to be sufficiently reliable to constrain the modified gravity models from stellar orbits around Galactic Centre.Comment: 9 pages, 6 figure to appear in Phys. Rev.

Masses of constituent quarks confined in open bottom hadrons

We apply color-spin and flavor-spin quark-quark interactions to the meson and baryon constituent quarks, and calculate constituent quark masses, as well as the coupling constants of these interactions. The main goal of this paper was to determine constituent quark masses from light and open bottom hadron masses, using the fitting method we have developed and clustering of hadron groups. We use color-spin Fermi-Breit (FB) and flavor-spin Glozman-Riska (GR) hyperfine interaction (HFI) to determine constituent quark masses (especially $b$ quark mass). Another aim was to discern between the FB and GR HFI because our previous findings had indicated that both interactions were satisfactory. Our improved fitting procedure of constituent quark masses showed that on average color-spin (Fermi-Breit) hyperfine interaction yields better fits. The method also shows the way how the constituent quark masses and the strength of the interaction constants appear in different hadron environments.Comment: 15 pages, 6 tables, 1 figure. Accepted for publication in Mod. Phys. Lett.

Constraining Non-local Gravity by S2 star orbits

Non-local theories of gravity have recently gained a lot of interest because they can suitably represent the behavior of gravitational interaction in the ultraviolet regime. Furthermore, at infrared scales, they give rise to notable cosmological effects which could be important to describe the dark energy behavior. In particular, exponential forms of the distortion function seem particularly useful for this purpose. Using Noether Symmetries, it can be shown that the only non-trivial form of the distortion function is the exponential one, which is working not only for cosmological mini-superspaces, but also in a spherically symmetric spacetime. Taking this result into account, we study the weak field approximation of this type of non-local gravity, and comparing with the orbits of S2 stars around the Galactic center (NTT/VLT data), we set constraints on the parameters of the theory. Non-local effects do not play a significant role on the orbits of S2 stars around Sgr A*, but give richer phenomenology at cosmological scales than the $\Lambda$CDM model. Also, we show that non-local gravity model gives better agreement between theory and astronomical observations than Keplerian orbits.Comment: 11 pages, 6 figures. Accepted for publication in Phys. Rev.

Donut and dynamic polarization effects in proton channeling through carbon nanotubes

We investigate the angular and spatial distributions of protons of the energy of 0.223 MeV after channeling through an (11,~9) single-wall carbon nanotube of the length of 0.2 $\mu$m. The proton incident angle is varied between 0 and 10 mrad, being close to the critical angle for channeling. We show that, as the proton incident angle increases and approaches the critical angle for channeling, a ring-like structure is developed in the angular distribution - donut effect. We demonstrate that it is the rainbow effect. When the proton incident angle is between zero and a half of the critical angle for channeling, the image force affects considerably the number and positions of the maxima of the angular and spatial distributions. However, when the proton incident angle is close to the critical angle for channeling, its influence on the angular and spatial distributions is reduced strongly. We demonstrate that the increase of the proton incident angle can lead to a significant rearrangement of the propagating protons within the nanotube. This effect may be used to locate atomic impurities in nanotubes as well as for creating nanosized proton beams to be used in materials science, biology and medicine.Comment: 17 pages, 14 figure

Dynamic polarization effects on the angular distributions of protons channeled through carbon nanotubes in dielectric media

The best level of ordering and straightening of carbon nanotube arrays is often achieved when they are grown in a dielectric matrix, so such structures present the most suitable candidates for future channeling experiments with carbon nanotubes. Consequently, we investigate here how the dynamic polarization of carbon valence electrons in the presence of various surrounding dielectric media affects the angular distributions of protons channeled through (11,~9) single-wall carbon nanotubes. Proton speeds between 3 and 10 a.u., corresponding to energies of 0.223 and 2.49 MeV, are chosen with the nanotube's length varied between 0.1 and 1 $\mu$m. We describe the repulsive interaction between a proton and the nanotube's atoms in a continuum-potential approximation based on the Doyle-Turner potential, whereas the attractive image force on a proton is calculated using a two-dimensional hydrodynamic model for the dynamic response of the nanotube valence electrons, while assigning to the surrounding medium an appropriate (frequency dependent) dielectric function. The angular distributions of channeled protons are generated using a computer simulation method which solves the proton equations of motion in the transverse plane numerically. Our analysis shows that the presence of a dielectric medium can strongly affect both the appearance and positions of maxima in the angular distributions of channeled protons.Comment: 14 pages, 11 figures, Accepted for publication in Phys. Rev.

Metastability and Transient Effects in Vortex Matter Near a Decoupling Transition

We examine metastable and transient effects both above and below the first-order decoupling line in a 3D simulation of magnetically interacting pancake vortices. We observe pronounced transient and history effects as well as supercooling and superheating between the 3D coupled, ordered and 2D decoupled, disordered phases. In the disordered supercooled state as a function of DC driving, reordering occurs through the formation of growing moving channels of the ordered phase. No channels form in the superheated region; instead the ordered state is homogeneously destroyed. When a sequence of current pulses is applied we observe memory effects. We find a ramp rate dependence of the V(I) curves on both sides of the decoupling transition. The critical current that we obtain depends on how the system is prepared.Comment: 10 pages, 15 postscript figures, version to appear in PR

Study of qqqccˉqqqc\bar{c} five quark system with three kinds of quark-quark hyperfine interaction

The low-lying energy spectra of five quark systems $uudc\bar{c}$ (I=1/2, S=0) and $udsc\bar{c}$ (I=0, S=-1) are investigated with three kinds of schematic interactions: the chromomagnetic interaction, the flavor-spin dependent interaction and the instanton-induced interaction. In all the three models, the lowest five quark state ($uudc\bar{c}$ or $udsc\bar{c}$) has an orbital angular momentum L=0 and the spin-parity $J^{P}=1/2^{-}$; the mass of the lowest $udsc\bar{c}$ state is heavier than the lowest $uudc\bar{c}$ state