First measurements of vector boson scattering in W$^\pm$W$^{\pm}$ and WZ production in all-leptonic final states at $\sqrt{s}$ = 13.6 TeV

The production cross sections of W$^\pm$W$^{\pm}$ and WZ boson pairs in association with two jets in proton-proton collisions are measured at $\sqrt{s}$ = 13.6 TeV. The data sample corresponds to an integrated luminosity of 171 fb$^{-1}$, collected with the CMS detector during 2022$-$2024. The measurements are performed in the leptonic decay modes: W$^{\pm}$Z $\to$ $\ell^\pm\nu\ell^{\prime\pm}\ell^{\prime\mp}$ and W$^\pm$W$^{\pm}$ $\to$ $\ell^\pm\nu\ell^{\prime\pm}\nu$, where $\ell, \ell'$ = e or $\mu$. The electroweak productions of W$^\pm$W$^{\pm}$ and WZ bosons are each observed with a significance greater than five standard deviations from the background-only hypothesis. Differential fiducial cross sections as functions of several observables are also measured.