Exploring Data-Driven Corrections for $\phi$-Meson Global Spin Alignment Measurements

Non-central heavy ion collisions generate large orbital angular momentum (OAM), providing opportunities to study spin phenomena such as the global spin alignment of vector mesons. Such studies are expected to reveal properties of the quark-gluon plasma produced in these collisions. Global spin alignment of vector mesons, such as the $\phi$-meson, can be measured by the $00^{\rm th}$ coefficient of the spin density matrix, $\rho_{00}$, via the polar angle of the decay kaon momentum in the parent rest frame with respect to the OAM direction of the collision. A deviation of $\rho_{00}$ from the isotropic value of $1/3$ indicates a finite spin alignment. The reported signal of $\rho_{00}-1/3$ is on the order of $\sim 1\%$ and therefore corrections for finite detector performance and acceptance, which are expected to be on the order of a few tenths of a percent, are important. Additional complications in the detector corrections may arise from the $\phi$-meson azimuthal anisotropy which could become intertwined with the detector efficiency. Typically, detector corrections for global spin alignment of vector mesons are performed with Monte-Carlo (MC) methods using detector simulation packages such as GEANT, however it is unclear if such methods can be trusted at the needed level of precision. In this paper, we investigate an alternative, data-driven approach in correcting for detector effects. This approach utilizes detector effects on combinatorial kaon pairs from $\phi$-meson decays that fall within the $\phi$-meson mass window, which can be obtained through statistical identification of decay kaons in real data analysis. We examine the degree of success of such a data-driven approach using toy-model MC simulations as well as its shortcomings.