Electromagnetic logarithms in image Original Research Article

The image decay rate is known at the next-to-next-to-leading order in QCD. It is proportional to image and has a image scale uncertainty before including the image electromagnetic corrections. We evaluate these corrections and confirm the earlier findings of Bobeth et al. Furthermore, we complete the calculation of logarithmically enhanced electromagnetic effects by including also QED corrections to the matrix elements of four-fermion operators. Such corrections contain a collinear logarithm image that survives integration over the low dilepton invariant mass region image and enhances the integrated decay rate in this domain. For the low-image integrated branching ratio in the muonic case, we find image, where the error includes the parametric and perturbative uncertainties only. For image, in the current BaBar and Belle setups, the logarithm of the lepton mass gets replaced by angular cut parameters and the integrated branching ratio for the electrons is expected to be close to that for the muons.