Penguin diagrams in the charm sector in K+→π+νν¯

We evaluate at next-to-next-to-leading order (NNLO) the QCD corrections to the charm contribution from penguin diagrams to the decay K+→π+νν¯. A NNLO calculation is already available in the literature (Buras et al., 2006 [1]). We provide an independent check of the results of non-anomalous and anomalous diagrams. We use Renormalization Group improvement and an effective theory framework to resum the large logarithms that appear. In the case of the non-anomalous diagrams, our results for the decoupling coefficients and anomalous dimensions, as well as the final numerical result, are in agreement with those of Buras et al. (2006) [1]. In the anomalous case, analytical and numerical disagreements are observed.