Impact of background effects on the inclusive V-cb determination

Abstract: The determination of the CKM element Vcb from inclusive semileptonic b → c`¯ν
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 Vcb determination; the b → u background and the contribution of the tauonic
mode: b → c(τ → μν ¯ν)¯ν. 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 Vcb by comparing the data on B → X`
directly with the theoretical expressions, to which our paper facilitates.