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Abstract 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$$5\sigma $$ $5\sigma$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$$5\sigma $$ $5\sigma$C.L. is possible for more than 60% of the actual values of the CP-violating phase,$$\delta _{CP}.$$ ${\delta }_{\mathrm{CP}}.$Moreover, we will measure$$\delta _{CP}$$ ${\delta }_{\mathrm{CP}}$with a precision ranging from 20$$^{\circ },$$ $_{}^{\circ },$in the case of maximal CP violation, to 6$$^{\circ },$$ $_{}^{\circ },$in the case of CP conservation. We aim to achieve a 0.5% resolution on the$$\Delta m^2_{32}$$ $\Delta m_{32}^2$parameter, and a resolution between 3% and 0.5% on the$$\sin ^2\theta _{23}$$ ${sin}^2{\theta }_{23}$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. 

A bstract The NA62 experiment at CERN targets the measurement of the ultra-rare $$ {K}^{+}\to {\pi}^{+}\nu \overline{\nu} $$ K + → π + ν ν ¯ decay, and carries out a broad physics programme that includes probes for symmetry violations and searches for exotic particles. Data were collected in 2016–2018 using a multi-level trigger system, which is described highlighting performance studies based on 2018 data. 

A bstract A sample of 2 . 8 × 10 4 K + → π + μ + μ − candidates with negligible background was collected by the NA62 experiment at the CERN SPS in 2017–2018. The model-independent branching fraction is measured to be (9 . 15 ± 0 . 08) × 10 − 8 , a factor three more precise than previous measurements. The decay form factor is presented as a function of the squared dimuon mass. A measurement of the form factor parameters and their uncertainties is performed using a description based on Chiral Perturbation Theory at $$ \mathcal{O} $$ O ( p 6 ). 

A bstract The NA62 experiment reports the branching ratio measurement $$ \mathrm{BR}\left({K}^{+}\to {\pi}^{+}\nu \overline{\nu}\right)=\left({10.6}_{-3.4}^{+4.0}\left|{}_{\mathrm{stat}}\right.\pm {0.9}_{\mathrm{syst}}\right)\times {10}^{-11} $$ BR K + → π + ν ν ¯ = 10.6 − 3.4 + 4.0 stat ± 0.9 syst × 10 − 11 at 68% CL, based on the observation of 20 signal candidates with an expected background of 7.0 events from the total data sample collected at the CERN SPS during 2016–2018. This provides evidence for the very rare K + → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ decay, observed with a significance of 3.4 σ . The experiment achieves a single event sensitivity of (0 . 839 ± 0 . 054) × 10 − 11 , corresponding to 10.0 events assuming the Standard Model branching ratio of (8 . 4 ± 1 . 0) × 10 − 11 . This measurement is also used to set limits on BR( K + → π + X ), where X is a scalar or pseudo-scalar particle. Details are given of the analysis of the 2018 data sample, which corresponds to about 80% of the total data sample. 

A bstract A search for the K + → π + X decay, where X is a long-lived feebly interacting particle, is performed through an interpretation of the K + → $$ {\pi}^{+}\nu \overline{\nu} $$ π + ν ν ¯ analysis of data collected in 2017 by the NA62 experiment at CERN. Two ranges of X masses, 0–110 MeV /c 2 and 154–260 MeV /c 2 , and lifetimes above 100 ps are considered. The limits set on the branching ratio, BR( K + → π + X ), are competitive with previously reported searches in the first mass range, and improve on current limits in the second mass range by more than an order of magnitude. 

A bstract The NA62 experiment at the CERN SPS reports a study of a sample of 4 × 10 9 tagged π 0 mesons from K + → π + π 0 ( γ ), searching for the decay of the π 0 to invisible particles. No signal is observed in excess of the expected background fluctuations. An upper limit of 4 . 4 × 10 − 9 is set on the branching ratio at 90% confidence level, improving on previous results by a factor of 60. This result can also be interpreted as a model- independent upper limit on the branching ratio for the decay K + → π + X , where X is a particle escaping detection with mass in the range 0.110–0.155 GeV /c 2 and rest lifetime greater than 100 ps. Model-dependent upper limits are obtained assuming X to be an axion-like particle with dominant fermion couplings or a dark scalar mixing with the Standard Model Higgs boson.