arXiv subjects
Publications and source records attributed to H. Sawanaka.
Realistic quark masses and mixing angles are obtained applying the successful $A_4$ family symmetry for leptons, motivated by the quark-lepton assignments of SU(5). The $A_4$ symmetry is suitable to give tri-bimaximal neutrino mixing matrix which is consistent with current experimental data. We study new scenario for the quark sector with the $A_4$ symmetry.
We present a new method to introduce rotationally invariant terms in staggered fermions which is based on an $SO(2D)$ Clifford algebra formulation, where $D$ means the number of space-time dimensions. We have four candidates for improved mass terms that can split the degenerate mass of staggered fermions. Among them, we analyze three types of combinations and find only one case that can identify with the light single Dirac mode.
We present analyses of the sixty hybrid textures of neutrino mass matrix, which have an equality of matrix elements and one zero. These textures are possibly derived in the models with discrete flavor symmetry. Only six textures among sixty ones are excluded by the present experimental data. Since there are many textures which give similar predictions, the textures are classified based on the numerical results. The neutrinoless double beta decay is also examined in these textures. Our results suggest that there remain still rich structures of the neutrino mass matrix in the phenomenological point of view.
We investigate exact symmetries of a staggered fermion in D dimensions. The Dirac operator is reformulated by SO(2D) Clifford algebra. The chiral symmetry, rotational invariance and parity symmetries are clarified in any dimension. Local scalar and pseudo-scalar modes are definitely determined, in which we find non-standard modes. The relation to Ichimatsu-patterned lattice approach is discussed.
We present a lattice theory with an exact fermionic symmetry, which mixes the link and the fermionic variables. The staggered fermionic variables may be reconstructed into a Majorana fermion in the continuum limit. The gauge action has a novel structure. Though it is the ordinary plaquette action, two different couplings are assigned in the ``Ichimatsu pattern'' or the checkered pattern. In the naive continuum limit, the fermionic symmetry survives as a continuum (or an $O(a^0)$) symmetry. The transformation of the fermion is proportional to the field strength multiplied by the difference of the two gauge couplings in this limit. This work is an extension of our recently proposed cell model toward the realization of supersymmetric Yang-Mills theory on lattice.
We present the lattice models with exact fermionic symmetries relating fermions and link variables. The plaquettes are distributed in an Ichimatsu pattern (chequered). We explain this peculiar structure allows us to have a translation in the algebra of the fermionic symmetries.
We proposed an `Ichimatsu'-decomposed lattice gauge theory with fermionic symmetries. The vacuum structures of the gauge sector with two coupling constants ($β_p,β_c$) are investigated for 3-dimensional Z$_2$ and 4-dimensional SU(2) cases using mean-field approximation and numerical simulation. We found two phases on the ($β_p,β_c$) phase diagram for 3-dim. Z$_2$ case, while the diagram is a single phase for the latter.
We present a new lattice super Yang-Mills theory and its SUSY transformation. After our formulation of the model in a fundamental lattice, it is extended to the whole lattice with a substructure of modulo 2.