This paper presents the expected sensitivity to the neutrino oscillation parameters of the Hyper-Kamiokande long-baseline program. The Hyper-Kamiokande experiment, currently under construction in Japan, will measure the oscillations of accelerator-produced neutrinos with thousands of selected events per sample: this corresponds to an increase of statistics of a factor 25–100 with respect to recent results from the currently-running long-baseline neutrino oscillation experiment in Japan, T2K. In the most favorable scenario we will achieve the discovery of Charge-Parity (CP) violation in neutrino oscillation at $$5\sigma $$ 5 σ C.L. in less than 3 years. With 10 years of data-taking, and assuming a neutrino : antineutrino beam running ratio of 1:3, a CP violation discovery at $$5\sigma $$ 5 σ C.L. is possible for more than 60% of the actual values of the CP-violating phase, $$\delta _{CP}.$$ δ CP . Moreover, we will measure $$\delta _{CP}$$ δ CP with a precision ranging from 20 $$^{\circ },$$ ∘ , in the case of maximal CP violation, to 6 $$^{\circ },$$ ∘ , in the case of CP conservation. We aim to achieve a 0.5% resolution on the $$\Delta m^2_{32}$$ Δ m 32 2 parameter, and a resolution between 3% and 0.5% on the $$\sin ^2\theta _{23}$$ sin 2 θ 23 parameter, depending on its true value. These results are obtained by extending the analysis methods of T2K with dedicated tuning to take into account the Hyper-Kamiokande design: the larger far detector, the more powerful beam, the upgraded near detector ND280, and the planned additional Intermediate Water Cherenkov Detector.

Imposing a family symmetry on the Standard Model in order to reduce the number of its free parameters, due to the Schur’s Lemma, requires an explicit breaking of this symmetry. To avoid the need for this symmetry to break, additional Higgs doublets can be introduced. In such an extension of the Standard Model, we investigate family symmetries of the Yukawa Lagrangian. We find that adding a second Higgs doublet (2HDM) does not help, at least for finite subgroups of the $U\left(3\right)$ group up to the order of 1025.

Limits on parameters describing physics beyond the Standard Model are presented. The most general Lorentz invariant effective Hamiltonian at the quark-lepton level involving vector, scalar and tensor operators has been used. The fits have been done using the most precise and up to date experimental data for correlation coefficients measured in free neutron beta decay as well as the Fierz term measured in superallowed Fermi decays.

In the frame of two Higgs doublet model we try to explain the lepton masses and mixing matrix elements assuming that neutrinos are Dirac particles. Discrete family symmetry groups, which are subgroups of U(3) up to the 1025 order are considered. Like in the one Higgs Standard Model, we found that discrete family symmetries do not give satisfactory answer for this basic questions in the flavour problem.

Limits from neutron beta decay on parameters describing physics beyond the Standard Model are presented. New Physics is described by the most general Lorentz invariant effective Hamiltonian involving vector, scalar and tensor operators and Standard Model fields only. Two-parameter fits to the decay parameters measured in free neutron beta decay have been done, in some cases indicating rather big dependence of the results on g_A/g_V ratio of nucleon form factors at zero four-momentum transfer.