Magnitudes of V(xb) CKM matrix elements

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Abstract

We review the current status of the absolute values of the CKM matrix elements V(xb), with particular attention to latest determinations.

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Treating the b quark distribution function with reliable uncertainties

Frank Tackmann, Iain W. Stewart, Zoltan Ligeti (2008)

The parton distribution function for a b quark in the B meson (called the shape function) plays an important role in the analysis of the B -> X_s gamma and B -> X_u l nu data, and gives one of the dominant uncertainties in the determination of |Vub|. We introduce a new framework to treat the shape function, which consistently incorporates its renormalization group evolution and all constraints on its shape and moments in any short distance mass scheme. At the same time it allows a reliable treatment of the uncertainties. We develop an expansion in a suitable complete set of orthonormal basis functions, which provides a procedure for systematically controlling the uncertainties due to the unknown functional form of the shape function. This is a significant improvement over fits to model functions. Given any model for the shape function, our construction gives an orthonormal basis in which the model occurs as the first term, and corrections to it can be studied. We introduce a new short distance scheme, the "invisible scheme", for the kinetic energy matrix element, lambda_1. We obtain closed form results for the differential rates that incorporate perturbative corrections and a summations of logarithms at any order in perturbation theory, and present results using known next-to-next-to-leading order expressions. The experimental implementation of our framework is straightforward.

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Precision determination of |V_{ub}| from inclusive decays

Zoltan Ligeti, Michael Luke, Christian W Bauer (2001)

We propose determining |V_{ub}| from inclusive semileptonic B decay using combined cuts on the leptonic and hadronic invariant masses to eliminate the b->c background. Compared to a pure dilepton invariant mass cut, the uncertainty from unknown order (\Lambda_{QCD}/m_b)^3 terms in the OPE is significantly reduced and the fraction of b->u events is roughly doubled. Compared to a pure hadronic invariant mass cut, the uncertainty from the unknown light-cone distribution function of the b quark is significantly reduced. We find that |V_{ub}| can be determined with theoretical uncertainty at the 5-10% level.

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$B \to \pi \ell \nu_l$ Width and $|V_{ub}|$ from QCD Light-Cone Sum Rules

Y. M. Wang, N. Offen, A. Khodjamirian … (2011)

We employ the

$B\to\pi$ form factors obtained from QCD light-cone sum rules and calculate the

$B\to \pi \ell \nu_l$ width (

$\ell=e,\mu$ ) in units of

$1/|V_{ub}|^2$ , integrated over the region of accessible momentum transfers,

$0\leq q^2\leq 12.0 ~GeV^2$ . Using the most recent BABAR-collaboration measurements we extract

$|V_{ub}|=(3.50^{+0.38}_{-0.33}\big|_{th.}\pm 0.11 \big|_{exp.})\times 10^{-3}$ . The sum rule results for the form factors, taken as an input for a

$z$ -series parameterization, yield the

$q^2$ -shape in the whole semileptonic region of

$B\to \pi\ell\nu_\ell$ . We also present the charged lepton energy spectrum in this decay. Furthermore, the current situation with

$B\to \tau\nu_\tau$ is discussed from the QCD point of view. We suggest to use the ratio of the

$B\to \pi \tau\nu_\tau$ and

$B\to \pi\ell \nu_l ~(\ell =\mu,e)$ widths as an additional test of Standard Model. The sensitivity of this observable to new physics is illustrated by including a charged Higgs-boson contribution in the semileptonic decay amplitude.