Breakup corrections to spin asymmetries in the ${}^3$He beam polarization measurements with the Polarized Atomic Hydrogen Gas Jet Target

The requirements for hadron polarimetry at the future Electron Ion Collider (EIC) include measurements of the absolute helion (${}^3$He, $h$) beam polarization with systematic uncertainties better than ${\sigma }_P^{\text{syst}}\mathrm{/}P\le 1\mathrm{\%}$. Recently, it was proposed that the Polarized Atomic Hydrogen Gas Jet Target (HJET) be utilized for the precision measurement of the polarization of the $\approx 100\text{ GeV/n}$ helion beam. At the Relativistic Heavy Ion Collider, HJET serves to determine the absolute proton beam polarization with low systematic uncertainties of about ${\delta }^{\text{syst}}P\mathrm{/}P\lesssim 0.5\mathrm{\%}$. To adapt the HJET method for the EIC helion beam, the experimentally determined ratio of the beam and target (jet) spin-correlated asymmetries should be adjusted by the ratio of $p^{\uparrow }h$ and $h^{\uparrow }p$ analyzing powers. A potential problem with the suggested method is that the breakup of ${}^3$He in polarization measurements could drastically affect the analyzing power ratio. However, an analysis of the breakup corrections, presented in this paper, reveals that while these corrections can be as substantial as $\approx 4\mathrm{\%}$, the effect cancels out to a negligible level in the measured beam polarization.