Next we will discussflavor-changing neutral current (FCNC) processes. In the SM such processes can only occur first at the one-loop level due to Glashow–liopoulos–Maiani (GIM) mechanism, a very important mechanism in the field of weak decays. We will first present the general structure of these processes, which will involve a set of basic master one-loop functions. We will calculate most ofthese functions explicitly without including first QCD corrections. Subsequently we will show how these functions enter the operator product expansion. Nextwe will include QCD and electroweak corrections to a number of FCNC processes. This will result in a number of effective Hamiltonians for most important processes thatinvolve new operators not encountered in previous chapter: the so-called penguin operators. In this step we will study several properties of these Hamiltonians but we will postpone detailed phenomenology of these processesto later chapters.