TESLA: Potentials of $\gamma\gamma$ and $e^+e^-$ Options in Stoponium   Searches
  In some supersymmetric extensions of the Standard Model fairly light superpartner of t-quark is predicted, which may form bound states - stoponiums. We estimate potentials of TESLA linear collider in search for stoponium, considering the basic e+e- option and the gamma-gamma option (Photon Linear Collider - PLC).   It is found that PLC could be the best machine for discovery of these new narrow strong resonances. It can produce thousands stoponiums per 100 fb$^-1$ integrated luminosity in the high energy peak. In the case of scenarios when stoponium decays mainly into gluons the signal/background ratio is about 1/4. The channel S->hh into two lightest Higgs bosons could be also seen with high significance. Thus, several weeks run is sufficient for the stoponium discovery, if its mass is approximately known (e.g. from observation of direct stops production at LHC). Then, in MSSM scenarios with dominant S->hh decay PLC shows excellent possibilities to discover bound state of stops, practically immediately after beginning of operating.   The e+e- option also has some prospects to observe stoponium but only in the case of scenarios with dominant decay into two lightest Higgs bosons, with tens of events per 100 $fb^{-1}$. Interesting possibility appears in the case when the resonance is seated on 0.1% width luminosity peak - one could resolve the stoponium exited states. 
D.S. Gorbunov (1), V.A. Ilyin (2) and V.I. Telnov (3) ((1) INR,   Moscow, (2) SINP MSU, Moscow, (3) INP, Novosibirsk)