On the four-zero texture of quark mass matrices and its stability

We carry out a new study of quark mass matrices $M^{}_{\rm u}$ (up-type) and $M^{}_{\rm d}$ (down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We identify two more specific four-zero patterns of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ with fewer free parameters, and present two toy flavor-symmetry models which can help realize such special and interesting quark flavor structures. We also show that the texture zeros of $M^{}_{\rm u}$ and $M^{}_{\rm d}$ are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalization-group equations.Comment: 33 pages, 4 figures, minor comments added, version to appear in Nucl. Phys.

Constraining f(R) gravity in solar system, cosmology and binary pulsar systems

The $f(R)$ gravity can be cast into the form of a scalar-tensor theory, and scalar degree of freedom can be suppressed in high-density regions by the chameleon mechanism. In this article, for the general $f(R)$ gravity, using a scalar-tensor representation with the chameleon mechanism, we calculate the parameterized post-Newtonian parameters $\gamma$ and $\beta$, the effective gravitational constant $G_{\rm eff}$, and the effective cosmological constant $\Lambda_{\rm eff}$. In addition, for the general $f(R)$ gravity, we also calculate the rate of orbital period decay of the binary system due to gravitational radiation. Then we apply these results to specific $f(R)$ models (Hu-Sawicki model, Tsujikawa model and Starobinsky model) and derive the constraints on the model parameters by combining the observations in solar system, cosmological scales and the binary systems.Comment: LaTex, 19 pages,1 figure, typo corrected. To appear in Physics Letters

The effective neutrino mass of neutrinoless double-beta decays: how possible to fall into a well

If massive neutrinos are the Majorana particles and have a normal mass ordering, the effective mass term $\langle m\rangle^{}_{ee}$ of a neutrinoless double-beta ($0\nu 2\beta$) decay may suffer significant cancellations among its three components and thus sink into a decline, resulting in a "well" in the three-dimensional graph of $|\langle m\rangle^{}_{ee}|$ against the smallest neutrino mass $m^{}_1$ and the relevant Majorana phase $\rho$. We present a new and complete analytical understanding of the fine issues inside such a well, and discover a novel threshold of $|\langle m\rangle^{}_{ee}|$ in terms of the neutrino masses and flavor mixing angles: $|\langle m\rangle^{}_{ee}|^{}_* = m^{}_3 \sin^2\theta^{}_{13}$ in connection with $\tan\theta^{}_{12} = \sqrt{m^{}_1/m^{}_2}$ and $\rho =\pi$. This threshold point, which links the {\it local} minimum and maximum of $|\langle m\rangle^{}_{ee}|$, can be used to signify observability or sensitivity of the future $0\nu 2\beta$-decay experiments. Given current neutrino oscillation data, the possibility of $|\langle m\rangle^{}_{ee}| < |\langle m\rangle^{}_{ee}|^{}_*$ is found to be very small.Comment: 9 pages, 3 figures, version to appear in Eur. Phys. J.