A powerful tool for measuring Higgs boson associated Lepton Flavour Violation

In models with extended Higgs sectors, Higgs-boson-mediated Lepton Flavour Violation (LFV) can naturally appear. We study the physics potential of an electron-photon collider %as an option of the International Linear Collider on searching LFV processes $e^-\gamma\to\ell^-\varphi (\ell=\mu,\tau; \varphi=H, A)$ where $H$ and $A$ are extra CP even and odd Higgs bosons, respectively, in the minimal supersymmetric standard model and the effective two Higgs doublet model. The production cross section can be significantly large for the maximal allowed values of the LFV coupling constants under the current experimental data. Present experimental upper bounds on the effective LFV coupling constants would be considerably improved by searching these processes, which would be better than MEG and COMET experiments and also those at LHCb and SuperKEKB. Moreover, one can separately measure chirality of effective LFV coupling constants via these processes by selecting electron polarizations.