Determination of the polarization in the $\vec{p}p\to pp$ reaction with WASA-at-COSY detector

The dynamics of $\eta$-meson production and the interaction of $\eta$-mesons with nucleons can be studied using the $\vec{p}p\to pp\eta$ reaction via measurements of the analyzing power $A_y$. To this end, we have performed a measurement of the $\vec{p}p\to pp\eta$ reaction using the WASA-at-COSY detector, which provides large acceptance and is $\phi$-symmetric. The experiment was carried out for beam momenta of $2026$ MeV/c and $2188$ MeV/c. In this article we present a method and results for the determination of the degree of the beam polarization.