The Electro-Weak Phase Transition at Colliders: Discovery Post-Mortem

We explore the capabilities of a future proton collider to probe nature electro-weak phase transition, following hypothetical discovery new scalar particle. focus on real singlet field extension Standard Model, representing most minimal, and challenging probe, framework that can enable strong first-order transition. By constructing detailed phenomenological methods for measuring mass accessible couplings particle, we find 100 TeV has potential parameter space model provide meaningful constraints empirically some necessary conditions realization first order transition conjecture additional information, including through multi-scalar processes gravitational wave detectors, are likely needed gauge cosmological This study represents crucial step towards solving inverse problem in context