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.

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.

How to interpret a discovery or null result of the 0ν2β0\nu 2\beta decay

The Majorana nature of massive neutrinos will be crucially probed in the next-generation experiments of the neutrinoless double-beta ($0\nu 2\beta$) decay. The effective mass term of this process, $\langle m\rangle^{}_{ee}$, may be contaminated by new physics. So how to interpret a discovery or null result of the $0\nu 2\beta$ decay in the foreseeable future is highly nontrivial. In this paper we introduce a novel three-dimensional description of $|\langle m\rangle_{ee}^{}|$, which allows us to see its sensitivity to the lightest neutrino mass and two Majorana phases in a transparent way. We take a look at to what extent the free parameters of $|\langle m\rangle_{ee}^{}|$ can be well constrained provided a signal of the $0\nu 2\beta$ decay is observed someday. To fully explore lepton number violation, all the six effective Majorana mass terms $\langle m\rangle_{\alpha\beta}^{}$ (for $\alpha, \beta = e, \mu, \tau$) are calculated and their lower bounds are illustrated with the two-dimensional contour figures. The effect of possible new physics on the $0\nu 2\beta$ decay is also discussed in a model-independent way. We find that the result of $|\langle m\rangle_{ee}^{}|$ in the normal (or inverted) neutrino mass ordering case modified by the new physics effect may somewhat mimic that in the inverted (or normal) mass ordering case in the standard three-flavor scheme. Hence a proper interpretation of a discovery or null result of the $0\nu 2\beta$ decay may demand extra information from some other measurements.Comment: 13 pages, 6 figures, Figures and references update