Effect of interaction with neutrons in matter on flavor conversion of super-light sterile neutrino with active neutrino

A super-light sterile neutrino was proposed to explain the absence of the expected upturn of the survival probability of low energy solar boron neutrinos. This is because this super-light sterile neutrino can oscillate efficiently with electron neutrino through a MSW resonance happened in Sun. One may naturally expect that a similar resonance should happen for neutrinos propagating in Earth matter. We study the flavor conversion of this super-light sterile neutrino with active neutrinos in Earth matter. We find that the scenario of the super-light sterile neutrino can easily pass through possible constraints from experiments which can test the Earth matter effect in oscillation of neutrinos. Interestinlgy, we find that this is because the naively expected resonant conversion disappears or is significantly suppressed due to the presence of a potential $V_n$ which arises from neutral current interaction of neutrino with neutrons in matter. In contrast, the neutron number density in the Sun is negligible and the effect of $V_n$ is effectively switched off. This enables the MSW resonance in Sun needed in oscillation of the super-light sterile neutrino with solar electron neutrinos. It's interesting to note that it is the different situation in the Sun and in the Earth that makes $V_n$ effectively turned off and turned on respectively. This observation makes the scenario of the super-light sterile neutrino quite interesting.Comment: 22 pages, 10 figure

Exact Cosmological Solutions of f(R)f(R) Theories via Hojman Symmetry

Nowadays, $f(R)$ theory has been one of the leading modified gravity theories to explain the current accelerated expansion of the universe, without invoking dark energy. It is of interest to find the exact cosmological solutions of $f(R)$ theories. Besides other methods, symmetry has been proved as a powerful tool to find exact solutions. On the other hand, symmetry might hint the deep physical structure of a theory, and hence considering symmetry is also well motivated. As is well known, Noether symmetry has been extensively used in physics. Recently, the so-called Hojman symmetry was also considered in the literature. Hojman symmetry directly deals with the equations of motion, rather than Lagrangian or Hamiltonian, unlike Noether symmetry. In this work, we consider Hojman symmetry in $f(R)$ theories in both the metric and Palatini formalisms, and find the corresponding exact cosmological solutions of $f(R)$ theories via Hojman symmetry. There exist some new solutions significantly different from the ones obtained by using Noether symmetry in $f(R)$ theories. To our knowledge, they also have not been found previously in the literature. This work confirms that Hojman symmetry can bring new features to cosmology and gravity theories.Comment: 16 pages, revtex4; v2: discussions added, Nucl. Phys. B in press; v3: published version. arXiv admin note: text overlap with arXiv:1505.0754