Measuring Higgs boson associated Lepton Flavour Violation in electron-photon collisions at the ILC

We study the LFV Higgs production processes $e^-\gamma\to\ell^-\phi\;(\ell=\mu,\tau; \phi=H, A)$ as a probe of Higgs mediated LFV couplings at an electron-photon collider, where $H$ and $A$ are extra CP even and odd Higgs bosons, respectively, in the two Higgs doublet model. Under the constraints from the current data of muon and tau rare decay, the cross section can be significantly large. It would improve the experimental upper bounds on the effective LFV coupling constants. In addition, the chirality nature of the LFV Higgs coupling constants can be measured by selecting electron beam polarizations.