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

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