We study the possibilities on the search of the light and weakly interacting gauge boson in the gauged L µ − L τ model. Introducing the kinetic mixing at the tree-level, the allowed parameter regions for the gauge coupling and kinetic mixing parameter are presented. Then, we analyze one photon plus missing event within the allowed region and show that search for the light gauge boson will be possible at Belle-II experiment. We also analyze neutrino trident production process in neutrino beam experiments.

We discuss the neutrino mass matrix based on the Occam's Razor approach in the framework of the seesaw mechanism. We impose four zeros in the Dirac neutrino mass matrix, which give the minimum number of parameters needed for the observed neutrino masses and lepton mixing angles, while the charged lepton mass matrix and the right-handed Majorana neutrino mass matrix are taken to be real diagonal ones. The low-energy neutrino mass matrix has only seven physical parameters. We show successful predictions for the mixing angle θ 13 and the CP violating phase δ CP with the normal mass hierarchy of neutrinos by using the experimental data on the neutrino mass squared differences, the mixing angles θ 12 and θ 23 . The most favored region of sin θ 13 is around 0.13 ∼ 0.15, which is completely consistent with the observed value. The CP violating phase δ CP is favored to be close to ±π/2. We also discuss the Majorana phases as well as the effective neutrino mass for the neutrinoless double-beta decay m ee , which is around 7 ∼ 8 meV. It is extremely remarkable that we can perform a "complete experiment" to determine the low-energy neutrino mass matrix, since we have only seven physical parameters in the neutrino mass matrix. In particular, two CP violating phases in the neutrino mass matrix are directly given by two CP violating phases at high energy. Thus, assuming the leptogenesis we can determine the sign of the cosmic baryon in the universe from the low-energy experiments for the neutrino mass matrix. *

The model of neutrino mass matrix with minimal texture is now tightly constrained by experiment so that it can yield a prediction for the phase of CP violation. This phase is predicted to lie in the range δ CP = 0.77π − 1.24π. If neutrino oscillation experiment would find the CP violation phase outside this range, this means that the minimal-texture neutrino mass matrix, the element of which is all real, fails and the neutrino mass matrix must be complex, i.e., the phase must be present that is responsible for leptogenesis.

We discuss the Dirac CP violating phase δ CP in the Froggatt-Nielsen model for a neutrino mass matrix M ν imposing a condition det[M ν ] = 0. This additional condition restricts the CP violating phase δ CP drastically. We find that the phase δ CP is predicted in the region of ±(0.4 − 2.9) radian, which is consistent with the recent T2K and NOνA data. There is a remarkable correlation between δ CP and sin 2 θ 23 . The phase δ CP converges to ∼ ±π/2 if sin 2 θ 23 is larger than 0.5. Thus, the accurate measurement of sin 2 θ 23 is important for a test of our model. The effective mass m ee for the neutrinoless double beta decay is predicted in the rage 3.3 − 4.0 meV.

The usefulness and value of Multi-step Machine Learning (ML), where a task is organized into connected sub-tasks with known intermediate inference goals, as opposed to a single large model learned end-to-end without intermediate sub-tasks, is presented. Pre-optimized ML models are connected and better performance is obtained by re-optimizing the connected one. The selection of an ML model from several small ML model candidates for each sub-task has been performed by using the idea based on Neural Architecture Search (NAS). In this paper, Differentiable Architecture Search (DARTS) and Single Path One-Shot NAS (SPOS-NAS) are tested, where the construction of loss functions is improved to keep all ML models smoothly learning. Using DARTS and SPOS-NAS as an optimization and selection as well as the connections for multi-step machine learning systems, we find that (1) such a system can quickly and successfully select highly performant model combinations, and (2) the selected models are consistent with baseline algorithms, such as grid search, and their outputs are well controlled.