Cross section measurement of $e^+e^- \to p\bar{p}η$ and $e^+e^- \to p\bar{p}ω$ at center-of-mass energies between 3.773 GeV and 4.6 GeV

Based on $14.7~\textrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected with the BESIII detector at the BEPCII collider at 17 different center-of-mass energies between $3.7730~\textrm{GeV}$ and $4.5995~\textrm{GeV}$, Born cross sections of the two processes $e^+e^- \to p\bar{p}η$ and $e^+e^- \to p\bar{p}ω$ are measured for the first time. No indication of resonant production through a vector state $V$ is observed, and upper limits on the Born cross sections of $e^+e^- \to V \to p\bar{p}η$ and $e^+e^- \to V \to p\bar{p}ω$ at the $90\%$ confidence level are calculated for a large parameter space in resonance masses and widths. For the current world average parameters of the $ψ(4230)$ of $m=4.2187~\textrm{GeV}/c^{2}$ and $Γ=44~\textrm{MeV}$, we find upper limits on resonant production of the $p\bar{p}η$ and $p\bar{p}ω$ final states of $7.5~\textrm{pb}$ and $10.4~\textrm{pb}$ at the $90\%$ CL, respectively.