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.