Higgs Physics at a \gamma \gamma Collider

High precision measurements of electroweak observables at $e^\pm$ colliders indicate the existence of a light Higgs boson below the $W^\pm$ threshold. If such a fundamental scalar should be found in the near future it is important to fully investigate the electroweak symmetry braking sector of the Standard Model. This is particularly important for an intermediate mass Higgs as its existence might indicate physics beyond the Standard Model, for instance in form of its minimal supersymmetric extension (MSSM). In this work we present first results on the expected precision of the partial $\Gamma (H \longrightarrow \gamma \gamma)$ width at the $\gamma \gamma$ option of a future linear collider. This quantity is sensitive to new physics as heavy particles do not decouple in general and differences between the SM and MSSM predictions can differ by up to 10% even in the decoupling limit of large pseudoscalar Higgs masses. This regime is difficult and for some values of $\tan \beta$ impossible to cover at the LHC. We find that the well understood background process $\gamma \gamma \longrightarrow q \bar{q}$ allows for a ${\cal O} (2$ determination of $\Gamma (H \longrightarrow \gamma \gamma)$ using conservative collider parameters.