Impact of background effects on the inclusive V-cb determination

The determination of the CKM element V-cb from inclusive semileptonic b -> cl (nu) over bar decays has reached a high precision thanks to a combination of theoretical and experimental efforts. Aiming towards even higher precision, we discuss two processes that contaminate the inclusive V-cb determination; the b -> u background and the contribution of the tauonic mode: b -> c(tau -> mu nu(nu) over bar)(nu) over bar. Both of these contributions are dealt with at the experimental side, using Monte-Carlo methods and momentum cuts. However, these contributions can be calculated with high precision within the Heavy-Quark Expansion. In this note, we calculate the theoretical predictions for these two processes. We compare our b -> u results qualitatively with generator-level Monte-Carlo data used at Belle and Belle II. Finally, we suggest to change the strategy for the extraction of V-cb by comparing the data on B -> Xl directly with the theoretical expressions, to which our paper facilitates.