Polishing a shiny Higgs with matrix elements

After the recent discovery of a Standard Model Higgs boson-like particle at the LHC, the question of its couplings to known and unknown matter is eminent. In this letter, we present a method that allows for an enhancement in S/B(irreducible) of the order of 100% in $pp\to (h\to \gamma\gamma) jj$ for a center of mass energy of 8 and 14 TeV. This is achieved by applying the matrix element method. We discuss the implications of detector resolution effects and various approximations of the involved event simulation and reconstruction. The matrix element method provides a reliable, stable, and efficient handle to separate signal from background, and the gluon and weak boson fusion components involved in this process. Employing this method, a more precise Higgs boson coupling extraction can be obtained, and our results are of immediate relevance for current searches.