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# Comment on form factor shape and extraction of |V_ub| from B --> pi l nu

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### Abstract

We point out that current experimental data for partial B --> pi l nu branching fractions reduce the theoretical input required for a precise extraction of |V_ub| to the form factor normalization at a single value of the pion energy. We show that the heavy-quark expansion provides a bound on the form factor shape that is orders of magnitude more stringent than conventional unitarity bounds. We find |V_ub| = (3.7 +/- 0.2 +/- 0.1) x [0.8/F_+(16 GeV^2)]. The first error is from the experimental branching fractions, and the second is a conservative bound on the residual form factor shape uncertainty, both of which will improve with additional data. Together with current and future lattice determinations of the form factor normalization this result gives an accurate, model independent determination of |V_ub|. We further extract semileptonic shape observables such as |V_ub F_+(0)| = 0.92 +/- 0.11 +/- 0.03 and show how these observables can be used to test factorization and to determine low-energy parameters in hadronic B decays.

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### A model independent determination of $$|V_{ub}|$$ using the global $$q^2$$ dependence of the dispersive bounds on the $$B\to\pi l\nu$$ form factors

(2004)
We propose a method to determine the CKM matrix element $$|V_{ub}|$$ using the global $$q^2$$ dependence of the dispersive bound on the form factors for $$B\to \pi l\nu$$ decay. Since the lattice calculation of the $$B\to \pi l\nu$$ form factor is limited to the large $$q^2$$ regime, only the experimental data in a limited kinematic range can be used in a conventional method. In our new method which exploits the statistical distributions of the dispersive bound proposed by Lellouch, we can utilize the information of the global $$q^2$$ dependence for all kinematic range. As a feasibility study we determine $$|V_{ub}|$$ by combining the form factors from quenched lattice QCD, the dispersive bounds, and the experimental data by CLEO. We show that the accuracy of $$|V_{ub}|$$ can be improved by our method.
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### Author and article information

###### Journal
09 September 2005
2006-01-05
###### Article
10.1016/j.physletb.2005.11.063
hep-ph/0509090
FERMILAB-PUB-05-385-T, SLAC-PUB-11468
Phys.Lett.B633:61-69,2006
14 pages, 3 figures; journal version, results and conclusions unchanged
hep-ph hep-ex