  Recently, Altmannshofer, Dror and Gori (2022) claimed there is a four-point
interaction, $W$-$\ell$-$\nu$-$a$, in the electroweak-violating scenario of
axion-like particle (ALP) and lepton interactions which plays a critical role
in searching for ALPs from $\pi^{\pm}$, $K^{\pm}$ mesons and $W$ boson decays
because of the novel energy enhancements. Inspired by this interesting finding,
we first propose new t-channel processes, $e^{+}e^{-}\rightarrow\nu_e
a\bar{\nu_e}$ and $e^{-}p\rightarrow\nu_e a j$, for electrophilic ALPs
($e$ALPs) which also involve $W$-$\ell$-$\nu$-$a$ four-point interaction and
have obvious energy enhancement behaviors in their cross sections when the
collision energy is increasing. On the other hand, heavier $e$ALPs mainly decay
to a photon pair induced by the chiral anomaly instead of an electron-positron
pair. Therefore, studies of these t-channel processes with a photon pair plus
missing energy at $e^+ e^-$ and $ep$ colliders open a new door to search for
$e$ALPs at high energy colliders. The proposed search strategies are not only
aiming to generate a larger production rate of ALPs, but also trying to
distinguish electroweak-violating ALP-lepton interactions from
electroweak-preserving ones.
