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The Higgs factory is designed for precise measurement of Higgs characters andsearch for new physics. In this paper we propose that $e^+e^- \to \gamma h$process could be a useful channel for new physics, which is normally expressedmodel independently by effective field theory. We calculate the cross sectionin both the Standard Model and effective field theory approach, and find thatthe new physics effects of $\gamma h$ have only two degrees of freedom, muchfewer than the Higgsstrahlung process. This point could be used to reduce thedegeneracies of Wilson coefficients. We also calculated for the first time the2$\sigma$ bounds of $\gamma h$ at the Higgs factory, and prove that $\gamma h$is more sensitive to some dimension-6 operators than the current experimentaldata. In the optimistic scenario new physics effects may be observed at theCEPC or FCC-ee after the first couple of years of their run.

New Physics Searches with Higgs-photon associated production at the Higgs Factory