In this letter,we make an attempt to embed theμ–τreflection symmetry(which predicts maximal atmospherical mixing angle and Dirac CP phase)in the Friedberg-Lee neutrino model(which employs a translational flavor sym...In this letter,we make an attempt to embed theμ–τreflection symmetry(which predicts maximal atmospherical mixing angle and Dirac CP phase)in the Friedberg-Lee neutrino model(which employs a translational flavor symmetry and keeps one neutrino mass vanishing)and study the consequences of such a combination.展开更多
Reflection symmetry properties play important roles for the stability of crystal lattices in which electrons and phonons move. Based on the reflection symmetry properties, cubic, tetragonal, orthorhombic, rhombohedral...Reflection symmetry properties play important roles for the stability of crystal lattices in which electrons and phonons move. Based on the reflection symmetry properties, cubic, tetragonal, orthorhombic, rhombohedral (trigonal) and hexagonal crystal systems are shown to have three-dimensional (3D) k-spaces for the conduction electrons (“electrons”, “holes”). The basic stability condition for a general crystal is the availability of parallel material planes. The monoclinic crystal has a 1D k-space. The triclinic has no k-vectors for electrons, whence it is a true insulator. The monoclinic (triclinic) crystal has one (three) disjoint sets of 1D phonons, which stabilizes the lattice. Phonons’ motion is highly directional;no spherical phonon distributions are generated for monoclinic and triclinic crystal systems.展开更多
In this paper,we consider a set of new symmetries in the SM:diagonal reflection symmetries Rm_(u,v)^(*),R=m_(u,v),m_(d,e)^(*)=mde with R=diag(-1,1,1).These generalized CP symmetries predict the Majorana phases to beα...In this paper,we consider a set of new symmetries in the SM:diagonal reflection symmetries Rm_(u,v)^(*),R=m_(u,v),m_(d,e)^(*)=mde with R=diag(-1,1,1).These generalized CP symmetries predict the Majorana phases to beα_(2.3)/2-0π/2.Realization of diagonal reflection symmetries implies a broken chiral U(1)po symmetry only for the first generation.The axion scale is suggested to be(θ_(u,d))~△GuT√m_(u,dm_(c,s))/v-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 ocp≈203°,and|ml|≈2.5 or 6.2[meV].In this scheme,the type-I seesaw mechanism and a given neutrino Yukawa matrix Y_(y)completely determine the structure of the right-handed neutrino mass M_(R).A u-y unification predicts the mass eigenvalues to be(M_(RI),M_(R2),M_(R3))=(O(10^(5)).O(10^(9)),O(10^(14))[Gev].展开更多
基金supported in part by the National Natural Science Foundation of China under grant Nos.11605081,12142507 and 12147214the Natural Science Foundation of Liaoning Province under grant NO.2019-ZD-0473。
文摘In this letter,we make an attempt to embed theμ–τreflection symmetry(which predicts maximal atmospherical mixing angle and Dirac CP phase)in the Friedberg-Lee neutrino model(which employs a translational flavor symmetry and keeps one neutrino mass vanishing)and study the consequences of such a combination.
文摘Reflection symmetry properties play important roles for the stability of crystal lattices in which electrons and phonons move. Based on the reflection symmetry properties, cubic, tetragonal, orthorhombic, rhombohedral (trigonal) and hexagonal crystal systems are shown to have three-dimensional (3D) k-spaces for the conduction electrons (“electrons”, “holes”). The basic stability condition for a general crystal is the availability of parallel material planes. The monoclinic crystal has a 1D k-space. The triclinic has no k-vectors for electrons, whence it is a true insulator. The monoclinic (triclinic) crystal has one (three) disjoint sets of 1D phonons, which stabilizes the lattice. Phonons’ motion is highly directional;no spherical phonon distributions are generated for monoclinic and triclinic crystal systems.
基金JSPS Grants-in-Aid for Scientific Research(P18H01210,20K 14459)MEXT KAKENHI(UP18H05543)。
文摘In this paper,we consider a set of new symmetries in the SM:diagonal reflection symmetries Rm_(u,v)^(*),R=m_(u,v),m_(d,e)^(*)=mde with R=diag(-1,1,1).These generalized CP symmetries predict the Majorana phases to beα_(2.3)/2-0π/2.Realization of diagonal reflection symmetries implies a broken chiral U(1)po symmetry only for the first generation.The axion scale is suggested to be(θ_(u,d))~△GuT√m_(u,dm_(c,s))/v-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 ocp≈203°,and|ml|≈2.5 or 6.2[meV].In this scheme,the type-I seesaw mechanism and a given neutrino Yukawa matrix Y_(y)completely determine the structure of the right-handed neutrino mass M_(R).A u-y unification predicts the mass eigenvalues to be(M_(RI),M_(R2),M_(R3))=(O(10^(5)).O(10^(9)),O(10^(14))[Gev].
基金supported by the EIPHI Graduate School(Grant No.ANR-17-EURE-0002)the U.S.National Science Foundation(Grant Nos.DMR-1823800,CMMI-2131760 and CMMI-1930873).
