Axion Like Particle Search at Higgs Factories

We study the potential of the future Higgs factories, including the ILC, CEPC, and FCC-ee with $\sqrt{s}$ = 240-250 GeV on discovering axion-like particles (ALPs) through various production channels in the leptonic final states, $e^+e^- \to f\bar{f} a$, where $f=e,\mu,\nu$. We show that the $e^+e^- \to e^+e^- a$ with $a \to \gamma\gamma$ provides the best bounds for the $g_{a\gamma\gamma}$ and $g_{aZZ}$ couplings, while $e^+e^- \to \nu\bar{\nu}a$, with $a \to \gamma\gamma$ offers the best bounds for the $g_{aZZ}$ and $g_{aZ\gamma}$ couplings. The $e^+e^- \to \mu^+\mu^- a$ with $a \to \gamma\gamma$ provides intermediate sensitivity to the $g_{aZZ}$ coupling. Our estimates of the bounds for the $g_{a\gamma\gamma}$, $g_{aZ\gamma}$, and $g_{aZZ}$ couplings as a function of ALP mass ($M_a$) ranging from 0.1 GeV to 100 GeV provide valuable insights for future experiments aiming to detect ALPs. We find that $g_{a\gamma\gamma}$ around $1.5\times10^{-4}~\rm GeV^{-1}$ for $M_a = 0.1-6$ GeV is currently not ruled out by any other experiments.