First-principles calculation of the nonperturbative B-meson shape function

Develop a first-principles calculation of the non-perturbative $B$-meson shape function $\hat S$ that supplies the shape-function input needed for predictions of partial decay rates in inclusive $\bar B \to X_u l \bar\nu_l$ decays.

Background

In the BLNP factorization theorem, the non-perturbative shape function encodes the internal dynamics of the $B$ meson and enters the convolution with the hard and jet functions. The perturbative ingredients can be computed at high orders, but the shape function is modeled phenomenologically rather than derived from QCD from first principles.

The paper uses an exponential model and discusses ongoing work to incorporate its perturbative radiative tail. A first-principles determination would reduce the model dependence of the partial-rate predictions and their resulting determination of $|V_{ub}|$.