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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 general search is presented for supersymmetric particles (sparticles) in scenarios featuring compressed mass spectra using proton-proton collisions at a center-of-mass energy of 13 TeV, recorded with the CMS detector at the LHC. The analyzed data sample corresponds to an integrated luminosity of $138{\mathrm{fb}}^{-1}$. A wide range of potential sparticle signatures are targeted, including pair production of electroweakinos, sleptons, and top squarks. The search focuses on events with a high transverse momentum system from initial-state-radiation jets recoiling against a potential sparticle system with significant missing transverse momentum. Events are categorized based on their lepton multiplicity, jet multiplicity, number of $b$-tagged jets, and kinematic variables sensitive to the sparticle masses and mass splittings. The sensitivity extends to higher parent sparticle masses than previously probed at the LHC for production of pairs of electroweakinos, sleptons, and top squarks with mass spectra featuring small mass splittings (compressed mass spectra). The observed results demonstrate agreement with the predictions of the background-only model. Lower mass limits are set at 95% confidence level on production of pairs of electroweakinos, sleptons, and top squarks that extend to 325, 275, and 780 GeV, respectively, for the most favorable compressed mass regime cases. 

We present work on design and reconstruction methods for sampling electromagnetic calorimeters with emphasis on highly granular designs. We use the clustered logarithmically weighted center-of-gravity estimator (lwk-means) for initial benchmarking of position resolution. We find that the θ and φ resolution for high energy photons in Si-W designs improves when increasing both sampling frequency and sampling thickness. Augmenting only one is found to have mixed results. We find that lwk-means is unable to effectively use calorimeter transverse cell sizes smaller than 2 mm. New reconstruction methods for highly granular designs are developed. We find that methods that only measure the initial particle shower and disregard the remaining shower can take advantage of cell sizes down to at least 10 µm, significantly outperforming the benchmark method. Of these, the best method and design is the initial particle shower “single hit” method using the calorimeter design with the highest sampling frequency and sampling fraction. 

Our recent work has shown that a novel much higher granularity forward calorimetry concept can enable much more detailed and precise reconstruction than the baseline designs based on LEP luminometers, along with the capability of electron/positron/photon separation. This new calorimeter concept is designed primarily to maximize the acceptance for e⁺e⁻→ γγ as an alternative luminosity process, where it serves to define the inner edge of the acceptance (there is no outer edge, as the complete detector is used in the measurement), while continuing to provide the standard luminosity measurement from small-angle Bhabha scattering (SABS). It will also serve as a general forward electromagnetic calorimeter helping ensure hermeticity and detecting individual electrons, positrons, and photons. In this contribution we highlight the Bhabha rejection capability in the context of the e⁺e⁻→ γγ luminosity measurement and motivate the utility of a Bhabha “mini-tracker” consisting of a few planes of upstream thin silicon detectors. This could further refine the e⁺/e⁻polar angle measurement, aid with charge measurement, improve Bhabha rejection (for γγ), and, last-but-not-least, help mitigate the beam-induced electromagnetic deflection that biases the Bhabha acceptance by providing high precision longitudinal vertex information in Bhabha events, which can be used to diagnose this effect of the beam on the final-state electron and positron.