Speaker
Description
The smallest element of the CKM matrix, $|V_{ub}|$, can be extracted from measurements of semileptonic B meson decay $B\to X_ul\bar{\nu}$. However, the experimental signal of this process is obscured by large background $B\to X_cl\bar{\nu}$.
This background is kinematically forbidden at the edge of the phasespace, but this region is sensitive to nonperturbative effects. Factorization theorems derived in Soft-Collinear Effective Theory are used to isolate these nonperturbative effects into a so-called shape function and to systematically resum the perturbative corrections in this region. The shape function cannot be calculated perturbatively, but it can be measured in $B\to X_s\gamma$ decay.
I will present resummed predictions of differential decay rates for $B\to X_s\gamma$ at ${\rm N^3LL'{+}N^3LO}(c_k)$ and for $B\to X_ul\bar{\nu}$ at ${\rm N^3LL{+}NLO}$. The few unknown 3-loop perturbative ingredients are parameterized using nuisance parameters, and the corresponding error is estimated.
I will discuss the impact of different definitions of the b-quark mass on the convergence of perturbative series (the renormalon problem) and I will argue that the MSR mass scheme yield more stable results than the 1S mass scheme. I will highlight the importance of the missing fixed-order NNLO corrections to the differential $B\to X_ul\bar{\nu}$ decay. I will make some comparisons with experimental measurements of this decay by the Belle collaboration and point out some limitations of the inclusive approach related to violation of local quark-hadron duality.
