Occam's razor in quark mass matrices

Abstract

On the standpoint of Occam's Razor approach, we consider the minimum number of parameters in the quark mass matrices needed for the successful CKM mixing and CP violation. We impose three zeros in the down-quark mass matrix with taking the diagonal up-quark mass matrix to reduce the number of free parameters. The three zeros are maximal zeros in order to have a CP violating phase in the quark mass matrix. Then, there remain six real parameters and one CP violating phase, which is the minimal number to reproduce the observed data of the down-quark masses and the CKM parameters. The twenty textures with three zeros are examined. Among them, the thirteen textures are viable for the down-quark mass matrix. As a representative of these textures, we discuss a texture M (1) d in details. By using the experimental data on sin 2β, θ 13 and θ 23 together with the observed quark masses, the Cabibbo angle is predicted to be close to the experimental data. It is found that this surprising result remains unchanged in all other viable textures. We also investigate the correlations among |V ub /V cb |, sin 2β and J CP . For all textures, the maximal value of the ratio |V ub /V cb | is 0.09, which is smaller than the upper-bound of the experimental data, 0.094. We hope that this prediction will be tested in future experiments.

Edge of a cliff

“…We assume that the charged lepton mass matrix takes a diagonal base, while the right-handed Majorana neutrino mass matrix is also diagonal and we consider nine patterns of the four zero textures for the Dirac neutrinos mass matrices [7,8], as the same choice as the form of the mass matrices in ref. [1]. We numerically analyze the left-handed Majorana neutrino mass matrices for nine patterns of the Dirac neutrino mass matrices and we find two interesting patterns where both normal and inverted neutrino mass hierarchies can be realized.…”

“…Hereafter, we adopt non-vanishing (3, 3), (2,3), and (1, 2) elements in the Dirac mass matrix and det M D = 0 in order to reproduce all non-zero neutrino masses, as adopted in ref. [1]. Tanimoto and Yanagida considered non-vanishing (3, 3), (2,3), and (1, 2) elements to obtain two nonvanishing mixing angles θ 12 and θ 23 in the quark sector [1].…”

“…[1]. Tanimoto and Yanagida considered non-vanishing (3, 3), (2,3), and (1, 2) elements to obtain two nonvanishing mixing angles θ 12 and θ 23 in the quark sector [1]. We respect their criterion of non-zero input entries and also adopt the same non-zero entries in the neutrino Dirac mass matrix.…”

“…Recently, Tanimoto and Yanagida applied a Scholastic idea of William of Ockham, "Entities should not be multiplied unnecessarily. ", i.e., the Occam's razor, to mass matrices in the SM [1]. The Occam's razor approach is proposed and investigated originally in the quark sector, where Tanimoto and Yanagida assumed the scheme for a minimum set of free parameters in the quark mass matrices in order to realize the successful quark masses, Cabbibo-Kobayashi-Maskawa (CKM) mixing, and CP violation, simultaneously.…”

Sign of CP violating phase in quarks and leptons

“…One of authors and Yanagida proposed quark mass matrices in the standpoint of "Occam's Razor" approach [8] 2 , where the minimum number of parameters was taken for the successful CKM mixing angles and CP violation without assuming the symmetric or Hermitian mass matrix of down-type quarks. Three zeros were imposed in the down-type quark mass matrix, and the up-type quark mass matrix was assumed to be diagonal.…”