Measuring the \Gamma (h\rightarrow \gamma \gamma )\ BR (h\rightarrow b\overline b) decay at the photon collider at TESLA is studied for a Standard Model Higgs boson of mass m_h=120 GeV. The main background due to the process \gamma \gamma \rightarrow Q\overline Q(g), where Q = b,c , is estimated using the NLO QCD program (G. Jikia); the results obtained are compared with the corresponding LO estimate. Using a realistic luminosity spectrum and performing a detector simulation with the SIMDET program, we find that the \Gamma (h\rightarrow \gamma \gamma )BR(h\rightarrow b\overline b) decay can be measured with an accuracy better than 2% after one year of photon collider running.

PACS numbers: 14.80.Bn, 13.88.+e