Diagonal reflection symmetries and universal four-zero texture *

<jats:title>Abstract</jats:title> <jats:p>In this paper, we consider a set of new symmetries in the SM: <jats:italic>diagonal reflection</jats:italic> symmetries <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M1.jpg" xlink:type="simple"/> </jats:inline-formula> with <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M2.jpg" xlink:type="simple"/> </jats:inline-formula> diag <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M3.jpg" xlink:type="simple"/> </jats:inline-formula>. These generalized <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M4.jpg" xlink:type="simple"/> </jats:inline-formula> symmetries predict the Majorana phases to be <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M5.jpg" xlink:type="simple"/> </jats:inline-formula> or <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M6.jpg" xlink:type="simple"/> </jats:inline-formula>. Realization of diagonal reflection symmetries implies a broken chiral <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M7.jpg" xlink:type="simple"/> </jats:inline-formula> symmetry only for the first generation. The axion scale is suggested to be <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M8.jpg" xlink:type="simple"/> </jats:inline-formula> [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 <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M9.jpg" xlink:type="simple"/> </jats:inline-formula> and <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M10.jpg" xlink:type="simple"/> </jats:inline-formula> or <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M11.jpg" xlink:type="simple"/> </jats:inline-formula> [meV]. In this scheme, the type-I seesaw mechanism and a given neutrino Yukawa matrix <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M12.jpg" xlink:type="simple"/> </jats:inline-formula> completely determine the structure of the right-handed neutrino mass <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M13.jpg" xlink:type="simple"/> </jats:inline-formula>. A <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M14.jpg" xlink:type="simple"/> </jats:inline-formula> unification predicts the mass eigenvalues to be <jats:inline-formula> <jats:tex-math/> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpc_45_4_043103_M15.jpg" xlink:type="simple"/> </jats:inline-formula> [GeV]. </jats:p>