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Abstract In this paper we review the physics opportunities at linear$$\mathrm{e}^{+}\mathrm{e}^{-} $$ $e^{+}{e}^{-}$colliders with a special focus on high centre-of-mass energies and beam polarisation, take a fresh look at the various accelerator technologies available or under development and, for the first time, discuss how a facility first equipped with a technology that is mature today could be upgraded with technologies of tomorrow to reach much higher energies and/or luminosities. In addition, we discuss detectors, alternative collider modes, as well as opportunities for beyond-collider experiments and R&D facilities as part of a linear collider facility (LCF). The material of this paper supports all plans for$$\mathrm{e}^{+}\mathrm{e}^{-} $$ $e^{+}{e}^{-}$linear colliders and the additional opportunities they offer, independently of technology choice or proposed site, as well as R&D for advanced accelerator technologies. This joint perspective on the physics goals, early technologies and upgrade strategies has been developed by the LCVision team based on an initial discussion at LCWS2024 in Tokyo and a follow-up at the LCVision Community Event at CERN in January 2025. It heavily builds on decades of achievements of the global linear collider community, in particular in the context of CLIC and ILC. 

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. 

Abstract The landmark discovery that neutrinos have mass and can change type (or flavour) as they propagate—a process called neutrino oscillation^1–6—has opened up a rich array of theoretical and experimental questions being actively pursued today. Neutrino oscillation remains the most powerful experimental tool for addressing many of these questions, including whether neutrinos violate charge-parity (CP) symmetry, which has possible connections to the unexplained preponderance of matter over antimatter in the Universe^7–11. Oscillation measurements also probe the mass-squared differences between the different neutrino mass states (Δm²), whether there are two light states and a heavier one (normal ordering) or vice versa (inverted ordering), and the structure of neutrino mass and flavour mixing¹². Here we carry out the first joint analysis of datasets from NOvA¹³and T2K¹⁴, the two currently operating long-baseline neutrino oscillation experiments (hundreds of kilometres of neutrino travel distance), taking advantage of our complementary experimental designs and setting new constraints on several neutrino sector parameters. This analysis provides new precision on the$$\Delta {m}_{32}^{2}$$ $\Delta m_{32}^2$mass difference, finding$$2.4{3}_{-0.03}^{+0.04}\times 1{0}^{-3}\,{{\rm{eV}}}^{2}$$ $2.43_{-0.03}^{+0.04}\times 10^{-3}{\mathrm{eV}}^2$in the normal ordering and$$-2.4{8}_{-0.04}^{+0.03}\times 1{0}^{-3}\,{{\rm{eV}}}^{2}$$ $-2.48_{-0.04}^{+0.03}\times 10^{-3}{\mathrm{eV}}^2$in the inverted ordering, as well as a 3σinterval onδ_CPof [−1.38π, 0.30π] in the normal ordering and [−0.92π, −0.04π] in the inverted ordering. The data show no strong preference for either mass ordering, but notably, if inverted ordering were assumed true within the three-flavour mixing model, then our results would provide evidence of CP symmetry violation in the lepton sector. 

The Super-Kamiokande and T2K Collaborations present a joint measurement of neutrino oscillation parameters from their atmospheric and beam neutrino data. It uses a common interaction model for events overlapping in neutrino energy and correlated detector systematic uncertainties between the two datasets, which are found to be compatible. Using 3244.4 days of atmospheric data and a beam exposure of $19.7\left(16.3\right)\times {10}^{20}$protons on target in (anti)neutrino mode, the analysis finds a $1.9\sigma$exclusion of $CP$conservation (defined as $J_{CP}=0$) and a $1.2\sigma$exclusion of the inverted mass ordering. Published by the American Physical Society2025