Precision Higgs physics at a $\gamma \gamma$ collider

The loop induced coupling of an intermediate mass Higgs boson to two photons is a sensitive and unique measure for precision tests of physics beyond the Standard Model. In this work we summarize recent results on the expected precision of the partial $\Gamma (H \to \gamma \gamma)$ width at the $\gamma \gamma$ option of a future linear collider. Heavy particles do not decouple in general and differences between the SM and MSSM predictions or 2HD-models can differ in the percentile regime. Large non-Sudakov DL corrections need to be resummed and consistency requirements demand the use of the Sterman-Weinberg jet definition in order to avoid additional DL terms from three jet final states. We find that the well understood background process $\gamma \gamma \to q \bar{q}$ allows for a ${\mathcal O}$(2%) determination of $\Gamma (H \to \gamma \gamma)$ using conservative collider parameters. Recent improvements in the expected $\gamma \gamma$ luminosity suggest that the precision for the diphoton partial Higgs width can be further improved and is dominated by the error in BR($H \to b \bar{b}$) from the $e^\pm$ mode, which is presently estimated to be in the one percent regime.