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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. 

A bstract We measure the branching fractions and CP asymmetries for the singly Cabibbo-suppressed decays D 0 → π + π − η , D 0 → K + K − η , and D 0 → ϕη , using 980 fb − 1 of data from the Belle experiment at the KEKB e + e − collider. We obtain $$ {\displaystyle \begin{array}{c}\mathcal{B}\left({D}^0\to {\pi}^{+}{\pi}^{-}\eta \right)=\left[1.22\pm 0.02\left(\mathrm{stat}\right)\pm 0.02\left(\mathrm{syst}\right)\pm 0.03\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-3},\\ {}\mathcal{B}\left({D}^0\to {K}^{+}{K}^{-}\eta \right)=\left[{1.80}_{-0.06}^{+0.07}\left(\mathrm{stat}\right)\pm 0.04\left(\mathrm{syst}\right)\pm 0.05\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-4},\\ {}\mathcal{B}\left({D}^0\to \phi \eta \right)=\left[1.84\pm 0.09\left(\mathrm{stat}\right)\pm 0.06\left(\mathrm{syst}\right)\pm 0.05\left({\mathcal{B}}_{\mathrm{ref}}\right)\right]\times {10}^{-4},\end{array}} $$ B D 0 → π + π − η = 1.22 ± 0.02 stat ± 0.02 syst ± 0.03 B ref × 10 − 3 , B D 0 → K + K − η = 1.80 − 0.06 + 0.07 stat ± 0.04 syst ± 0.05 B ref × 10 − 4 , B D 0 → ϕη = 1.84 ± 0.09 stat ± 0.06 syst ± 0.05 B ref × 10 − 4 , where the third uncertainty ( $$ \mathcal{B} $$ B ref ) is from the uncertainty in the branching fraction of the reference mode D 0 → K − π + η . The color-suppressed decay D 0 → ϕη is observed for the first time, with very high significance. The results for the CP asymmetries are $$ {\displaystyle \begin{array}{c}{A}_{CP}\left({D}^0\ {\pi}^{+}{\pi}^{-}\eta \right)=\left[0.9\pm 1.2\left(\mathrm{stat}\right)\pm 0.5\left(\mathrm{syst}\right)\right]\%,\\ {}{A}_{CP}\left({D}^0\to {K}^{+}{K}^{-}\eta \right)=\left[-1.4\pm 3.3\left(\mathrm{stat}\right)\pm 1.1\left(\mathrm{syst}\right)\right]\%,\\ {} ACP\ \left({D}^0\to \phi \eta \right)=\left[-1.9\pm 4.4\left(\mathrm{stat}\right)\pm 0.6\left(\mathrm{syst}\right)\right]\%.\end{array}} $$ A CP D 0 π + π − η = 0.9 ± 1.2 stat ± 0.5 syst % , A CP D 0 → K + K − η = − 1.4 ± 3.3 stat ± 1.1 syst % , ACP D 0 → ϕη = − 1.9 ± 4.4 stat ± 0.6 syst % . The results for D 0 → π + π − η are a significant improvement over previous results. The branching fraction and A CP results for D 0 → K + K − η , and the ACP result for D 0 → ϕη , are the first such measurements. No evidence for CP violation is found in any of these decays. 

A bstract We present a search for the dark photon A ′ in the B 0 → A ′ A ′ decays, where A ′ subsequently decays to e + e − , μ + μ − , and π + π − . The search is performed by analyzing 772 × 10 6 $$ B\overline{B} $$ B B ¯ events collected by the Belle detector at the KEKB e + e − energy-asymmetric collider at the ϒ(4 S ) resonance. No signal is found in the dark photon mass range 0 . 01 GeV /c 2 ≤ m A ′ ≤ 2 . 62 GeV /c 2 , and we set upper limits of the branching fraction of B 0 → A ′ A ′ at the 90% confidence level. The products of branching fractions, $$ \mathrm{\mathcal{B}}\left({B}^0\to A^{\prime }A^{\prime}\right)\times \mathrm{\mathcal{B}}{\left(A\prime \to {e}^{+}{e}^{-}\right)}^2 $$ ℬ B 0 → A ′ A ′ × ℬ A ′ → e + e − 2 and $$ \mathrm{\mathcal{B}}\left({B}^0\to A^{\prime }A^{\prime}\right)\times \mathrm{\mathcal{B}}{\left(A\prime \to {\mu}^{+}{\mu}^{-}\right)}^2 $$ ℬ B 0 → A ′ A ′ × ℬ A ′ → μ + μ − 2 , have limits of the order of 10 − 8 depending on the A ′ mass. Furthermore, considering A ′ decay rate to each pair of charged particles, the upper limits of $$ \mathrm{\mathcal{B}}\left({B}^0\to A^{\prime }A^{\prime}\right) $$ ℬ B 0 → A ′ A ′ are of the order of 10 − 8 –10 − 5 . From the upper limits of $$ \mathrm{\mathcal{B}}\left({B}^0\to A^{\prime }A^{\prime}\right) $$ ℬ B 0 → A ′ A ′ , we obtain the Higgs portal coupling for each assumed dark photon and dark Higgs mass. The Higgs portal couplings are of the order of 10 − 2 –10 − 1 at $$ {m}_{h\prime}\simeq {m}_{B^0} $$ m h ′ ≃ m B 0 ± 40 MeV /c 2 and 10 − 1 –1 at $$ {m}_{h\prime}\simeq {m}_{B^0} $$ m h ′ ≃ m B 0 ± 3 GeV /c 2 .