Impact of background effects on the inclusive Vcb determination

Abstract

Abstract The determination of the CKM element Vcb from inclusive semileptonic b → cℓ$$ \overline{\nu} $$ 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$$ \overline{\nu} $$ ν ¯ )$$ \overline{\nu} $$ 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 → Xℓ directly with the theoretical expressions, to which our paper facilitates.