Supersymmetric Higgs mediated lepton flavor violation at a Photon Collider

We study a new signature of lepton flavor violation (LFV) at the Photon Collider (PC) within Supersymmetric (SUSY) theories. We consider the minimal supersymmetric standard model within a large $\tan\beta$ scenario with all superpartner masses in the ${\cal O}$(TeV) while the heavy Higgs bosons masses lie below the TeV and develop sizable loop induced LFV couplings to the leptons. We consider a photon collider based on an $e^+e^-$ linear collider with $\sqrt{s}=800$ GeV with the parameters of the TESLA proposal and show that, with the expected integrated $\gamma\gamma$-luminosity $L_{\gamma\gamma}=200\div 500$ fb$^{-1}$, the "$\mu\tau$ fusion" mechanism is the dominant channel for the process $\gaga\to\mu\tau b\bar{b}$ providing detailed analytical and numerical studies of the signal and backgrounds. We impose on the parameter space present direct and indirect constraints from $B$ physics and rare LFV $\tau$-decays and find that the LFV signal can be probed for masses of the heavy neutral Higgs bosons $A,H$ from 300 GeV up to the kinematical limit $\simeq 600$ GeV for 30$\leq\tan\beta\leq$60.