Systematic error analysis in the absolute hydrogen gas jet polarimeter at RHIC

The Polarized Atomic Hydrogen Gas Jet Target polarimeter (HJET) is operated at the Relativistic Heavy Ion Collider (RHIC) since 2004 to measure the absolute polarization of each colliding proton beam. Polarimeter detectors and data acquisition were upgraded in 2015 to increase the solid angle, energy range, and to improve the energy and time resolution. These upgrades along with an improved beam intensity and polarization allowed us to greatly reduce the statistical and systematic errors for the proton polarization measurements in RHIC Runs 15 ($E_\text{beam}\!=\!100~\text{GeV}$) and 17 ($255~\text{GeV}$). For a typical 8 hour RHIC store, the measured proton beam average polarization was about $P_\text{beam}\!\sim\!55\pm2.0_\text{stat}\pm0.3_\text{syst}\%$. The elastic $\mathit{pp}$ analyzing power, $A_\text{N}(t)\!\sim\!0.04$, was determined with a precision of about $|\delta A_\text{N}(t)|\!\sim\!0.0002$ in the momentum transfer squared range $0.001\!<\!-t\!<\!0.020\,\text{GeV}^2$. In this paper we present a detailed systematic error analysis of the polarization measurements at HJET. Perspectives of using the HJET based absolute polarimeters in the future Electron Ion Collider (EIC) will be also discussed.