arXiv subjects
Publications and source records attributed to Jun-Nan Lu.
We propose a flavour theory of leptons implementing an $A_4$ family symmetry. Our scheme provides a simple way to derive trimaximal neutrino mixing from first principles, leading to simple and testable predictions for neutrino mixing and CP violation. Dark matter mediates neutrino mass generation, as in the simplest scotogenic model.
We have studied the lepton and quark mixing patterns which can be derived from the dihedral group $D_n$ in combination with CP symmetry. The left-handed lepton and quark doublets are assigned to the direct sum of a singlet and a doublet of $D_n$. A unified description of the observed structure of the quark and lepton mixing can be achieved if the flavor group $D_n$ and CP are broken to $Z_2\times CP$ in neutrino, charged lepton, up quark and down quark sectors, and the minimal group is $D_{14}$. We also consider another scenario in which the residual symmetry of the charged lepton and up quark sector is $Z_2$ while $Z_2\times CP$ remains preserved by the neutrino and down quark mass matrices. Then $D_7$ can give the experimentally favored values of CKM and PMNS mixing matrices.
We have studied two approaches to predict quark and lepton mixing patterns from the same flavor symmetry group in combination with CP symmetry. The first approach is based on the residual symmetry $Z_2$ in the charged lepton sector and $Z_2\times CP$ in the neutrino sector. All lepton mixing angles and CP violation phases depend on three real parameters $θ_{l}$, $δ_{l}$ and $θ_ν$. This approach is extended to the quark sector, the up and down quark mass matrices are assumed to be invariant under a $Z_2$ subgroup and $Z_2\times CP$. The necessary and sufficient conditions for the equivalence of two mixing patterns are derived. The second approach has an abelian subgroup and a single CP transformation as residual symmetries of the charged lepton and neutrino sectors respectively. The lepton mixing would be determined up to a real orthogonal matrix multiplied from the right hand side. Analogously we assume that a single CP transformation is preserved by the down (or up) quark mass matrix, and the residual symmetry of the up (or down) quark sector is be an abelian subgroup. As an example, we analyze the possible mixing patterns which can be obtained from the breaking of $Δ(6n^2)$ and CP symmetries. We find $Δ(294)$ combined with CP is the smallest flavor group which can give a good fit to the experimental data of quark and lepton mixing in both approaches.
We discussed the scenario that a discrete flavor group combined with CP symmetry is broken to $Z_2\times CP$ in both neutrino and charged lepton sectors. All lepton mixing angles and CP violation phases are predicted to depend on two free parameters $θ_{l}$ and $θ_ν$ varying in the range of $[0, π)$. As an example, we comprehensively study the lepton mixing patterns which can be derived from the flavor group $Δ(6n^2)$ and CP symmetry. Three kinds of phenomenologically viable lepton mixing matrices are obtained up to row and column permutations. We further extend this approach to the quark sector. The precisely measured quark mixing angles and CP invariant can be accommodated for certain values of the free parameters $θ_{u}$ and $θ_{d}$. A simultaneous description of quark and lepton flavor mixing structures can be achieved from a common flavor group $Δ(6n^2)$ and CP, and accordingly the smallest value of the group index $n$ is $n=7$.
We suggest two alternative schemes to predict lepton mixing angles as well as $CP$ violating phases from a discrete flavor symmetry group combined with $CP$ symmetry. In the first scenario, the flavor and $CP$ symmetry is broken to the residual groups of the structure $Z_2\times CP$ in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters $θ_ν$ and $θ_{l}$. This type of breaking pattern is extended to the quark sector. In the second scheme, an abelian subgroup contained in the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant $CP$ transformation, all lepton mixing parameter are determined in terms of three free parameters $θ_{1, 2, 3}$. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters $θ_{ν, l}$ and $θ_{1, 2, 3}$ is taken into account. We have studied the lepton mixing patterns arising from the flavor group $S_4$ and $CP$ symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.
We study a second CP symmetry compatible with the $A_4$ flavor group, which interchanges the representations $\mathbf{1}'$ and $\mathbf{1}"$. We analyze the lepton mixing patterns arising from the $A_4$ and CP symmetry broken to residual subgroups $Z_3$ and $Z_2\times CP$ in the charged lepton and neutrino sectors respectively. One phenomenologically viable mixing pattern is found, and it predicts maximal atmospheric mixing angle as well as maximal Dirac CP phase, trivial Majorana phase and the correlation $\sin^2θ_{12}\cos^2θ_{13}=1/3$. We construct a concrete model based on the $A_4$ and CP symmetry, the above interesting mixing pattern is achieved, the observed charged lepton mass hierarchy is reproduced, and the reactor mixing angle $θ_{13}$ is of the correct order.