Heavy quark production at a $\gamma\gamma$ collider: the effect of large logarithmic perturbative corrections

We present quantitative results on the cross section for $\gamma + \gamma \left( J_z=0 \right) \longrightarrow b \bar{b}\longrightarrow$ two b–jets based on the recently achieved all orders resummation of large soft (Sudakov) and hard (non-Sudakov) double logarithms. The next–to–leading order QCD perturbative corrections are included exactly. We find that one needs to include at least four loops for the novel hard leading logarithms, on the cross section level, in order to be safe from large opposite sign cancellations that plagued earlier phenomenological studies. We find that the background to intermediate mass Higgs boson production at a future photon linear collider (PLC) is thus reasonably well under control and should allow the direct determination of the partial Higgs width $\Gamma \left( H \longrightarrow \gamma + \gamma \right)$ . Assuming high efficiency b-tagging, the total Higgs width measurement at a PLC is thus a realistic goal.