Diagonal reflection symmetries and universal four-zero texture

Abstract

In this paper, we consider a set of new symmetries in the SM, {\it diagonal reflection} symmetries $R{m}_{u,\nu }^{\ast }R=m_{u,\nu },m_{d,e}^{\ast }=m_{d,e}$ with $R=$ diag $(-1,1,1)$. These generalized $CP$ symmetries predict the Majorana phases to be ${\alpha }_{2,3}/2\sim 0$ or $\pi /2$. A realization of reflection symmetries suggests a broken chiral $U(1{)}_{\mathrm{PQ}}$ symmetry and a flavored axion. The axion scale is suggested to be $⟨{\theta }_{u,d}⟩\sim {\Lambda }_{\mathrm{GUT}}\sqrt{m_{u,d}{m}_{c,s}}/v\sim 10^{12}$[GeV]. By combining the symmetries with the four-zero texture, the mass eigenvalues and mixing matrices of quarks and leptons are reproduced well. This scheme predicts the normal hierarchy, the Dirac phase ${\delta }_{CP}\simeq 203^{\circ },$ and $|m_1|\simeq 2.5$ or $6.2$[meV]. In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix $Y_{\nu }$ completely determine the structure of right-handed neutrino mass $M_R$. An $u-\nu$ unification predicts mass eigenvalues to be $(M_{R1},M_{R2},M_{R3})=(O(10^5),O(10^9),O(10^{14}))$[GeV].

19 pages, 1 table, the final version published in Chinese Physics C