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

We carry out a new study of quark mass matrices Mu (up-type) and Md (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 Mu and Md 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 Mu and Md are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalization-group equations

How to interpret a discovery or null result of the 0ν2β decay

The Majorana nature of massive neutrinos will be crucially probed in the next-generation experiments of the neutrinoless double-beta ( 0ν2β ) decay. The effective mass term of this process, ⟨m⟩ee , may be contaminated by new physics. So how to interpret a discovery or null result of the 0ν2β decay in the foreseeable future is highly nontrivial. In this paper we introduce a novel three-dimensional description of |⟨m⟩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 |⟨m⟩ee| can be well constrained provided a signal of the 0ν2β decay is observed someday. To fully explore lepton number violation, all the six effective Majorana mass terms ⟨m⟩αβ (for α,β=e,μ,τ ) are calculated and their lower bounds are illustrated with the two-dimensional contour figures. The effect of possible new physics on the 0ν2β decay is also discussed in a model-independent way. We find that the result of |⟨m⟩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 0ν2β decay may demand extra information from some other measurements