I make no pretense at understanding the standard model myself, but would like to mention Connes and Marcolli's "Noncommutative Geometry, Quantum Fields and Motives" (see http://www.alainconnes.org/en/downloads.php) chapters 9-19. This quote is from the introduction to chapter 9:
"Our main purpose is to show that the full Lagrangian of the Standard Model minimally coupled to gravity, in a version that accounts for neutrino mixing, can be derived entirely from a very simple mathematical input, using the tools of noncommutative geometry. This will hopefully contribute to providing a clearer conceptual understanding of the wealth of information contained in the Standard Model, in a form which is both palatable to mathematicians and that at the same time can be used to derive specific physical predictions and computations."
