Vertexing displaced diphoton decays with recoil photons at Belle II

We propose a recoil-assisted strategy for vertexing displaced diphoton decays in $e^{+}{e}^{-}\to \gamma X$, $X\to \gamma \gamma$, using only one converted daughter photon. The initial state and recoil-photon momentum define the LLP flight line, whose closest approach to the converted-photon trajectory locates the decay vertex. This removes the need for a second conversion, making the conversion-related efficiency scale linearly rather than quadratically with the photon-conversion probability. For photophilic axionlike particles at Belle II, the existing $408$ fb${}^{-1}$ data set could probe previously unconstrained parameter space near $m_a\simeq 100$ MeV and $g_{a\gamma \gamma }\simeq 2\times {10}^{-4}$ GeV${}^{-1}$. With $50$ ab${}^{-1}$, the reach extends to $m_a\simeq 310$ MeV and $g_{a\gamma \gamma }\simeq 2\times {10}^{-5}$ GeV${}^{-1}$.