A Precision Model Independent Determination of |Vub| from B -> pi e nu

TL;DR

A precision method for determining |V(ub)| using the full range in q(2) of B --> pilnu data is presented, and it is found that this is competitive with inclusive methods.

Abstract

A precision method for determining |Vub| using the full range in q^2 of B-> pi \ell nu data is presented. At large q^2 the form factor is taken from unquenched lattice QCD, at q^2=0 we impose a model independent constraint obtained from B-> pi pi using the soft-collinear effective theory, and the shape is constrained using QCD dispersion relations. We find |Vub| =(3.54\pm 0.17\pm 0.44) x 10^{-3}. With 5% experimental error and 12% theory error, this is competitive with inclusive methods. Theory error is dominated by the input points, with negligible uncertainty from the dispersion relations.

Figures (3)

• Figure 1: Upper and lower bounds on the form factors from dispersion relations, where $\hat{q}^2=q^2/m_{B^*}^2$ and the $(1\!-\!\hat{q}^2)$ factor removes the $B^*$ pole. The overlapping solid black lines are bounds $F_{\pm}$ derived with the SCET point, 3 lattice points, and the ChPT point (diamonds with error bars). The dashed lines are the bounds derived using instead four lattice points (shown by the dots). Input point errors are not included in these lines, and are analyzed in the text.
• Figure 2: Results from the $\chi^2$ fit of $|V_{ub}|$ and $f^{0-4}$ to the $q^2$ spectra ($\hat{q}^2=q^2/m_{B^*}^2$). The two solid lines are obtained using either the $F_+$ or $F_-$ solutions from Eq. (\ref{['fp']}). The two dashed lines repeat this analysis without using the SCET point.
• Figure 3: The curves are as in Fig.2, but for the decay rate.