Sensitivity to longitudinal vector boson scattering and doubly charged Higgs boson production in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>±</mml:mo> </mml:msup> <mml:msup> <mml:m

We study the sensitivity to longitudinal vector boson scattering at a 27-, 50-, and 100-TeV collider using events containing two leptonically decaying same-electric-charge <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>W</a:mi> </a:math> bosons produced in association with two jets. The baseline FCC-hh detector parametrization within the framework is used under the assumption of fully efficient pileup mitigation. A tightly constrained phase space with a dijet mass greater than 2 TeV is considered in order to suppress the impact of potential instrumental backgrounds. Based on this setup, the expected sensitivity to the production of longitudinally polarized same-sign <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>W</c:mi> </c:math> boson pairs is evaluated. Additionally, expected limits are set on doubly charged Higgs bosons produced via vector boson fusion processes and decaying to same-sign <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>W</e:mi> </e:math> boson pairs.