On the Resummation of Large QCD Logarithms in Higgs $\to$ 2 Photons Decay

We study the strong corrections to the Higgs coupling to two photons. This coupling is the dominant mechanism for Higgs production in photon-photon collisions. In addition, the two photon decay mode of the Higgs is an important and relatively background free channel of relevance at the LHC and the Tevatron. We develop a method for the resummation of large QCD corrections in the form of Sudakov-like logarithms of the type \alpha_s^n\ln^{2n}(m/m_H) and \alpha_s^n\ln^{2n-1}(m/m_H) (where m is the light quark mass) which can contribute to this process in certain models (for example, the MSSM for large tan \beta) up to next-to-leading-logarithmic (NLL) accuracy. The NLL correction is large, of order -30 %, the dominant part of which comes from terms not related to running coupling effects