A model independent determination of |Vub|

Abstract

It is shown that measuring the lepton invariant mass spectrum in inclusive semileptonicB → X u ν decay yields a model independent determination of |V ub |. Unlike the lepton energy and hadronic invariant mass spectra, nonperturbative effects are only important in the resonance region, and play a parametrically suppressed role when dΓ/dq 2 is integrated over q 2 > (m B − m D ) 2 , which is required to eliminate the charm background. Perturbative and nonperturbative corrections are presented to order α 2 s β 0 and Λ 2 QCD /m 2 b , and the Λ 3 QCD /m 3 b corrections are used to estimate the uncertainty in our results. The utility of theB → X s + − decay rate above the ψ(2S) resonance is discussed.

Theory of charmless inclusiveBdecays and the extraction ofVub

“…It has also been argued [54,55] that a cut on q 2 can reduce the shape-function sensitivity, since the large P − region is avoided and the P + integration domain is rather large. In order to optimize signal efficiency and theoretical uncertainties, a q 2 cut is often combined with a cut on hadronic invariant mass.…”

“…Perhaps somewhat surprisingly, for this cut a substantial sensitivity to shape-function effects remains even for fixed m b and µ 2 π . It is well known that the partial rate with a cut q 2 ≥ (M B − M D ) 2 can be calculated using a local OPE in powers of Λ QCD /m c [38,54], thereby avoiding the notion of shape-function sensitivity. Differences between the functional forms of the shape functions in our approach correspond to effects that are formally of order 1/m 3 c and higher.…”

The Status of ∣Vub∣

“…All current analyses have, instead, relied on modeling an intermediate shape function. The role of the shape function can be mitigated by restricting measurement to regions of large q 2 , where validity of the OPE expansion is restored [30,31]. Restriction to the region kinematically forbidden to b → cℓν, 2 , however, introduces a low mass scale [32,33] into the OPE, introducing uncertainties of order (Λ QCD /m c ) 3 .…”

CP Violation and the CKM Matrix

“…Distributions in various kinematic variables (lepton energy, hadronic invariant mass) have been considered at the price of a more complicated and uncertain theory. A cut on the leptonic and hadronic invariant mass avoids the kinematic region, where the heavy quark expansion (in local operators) is invalid, but the scale of the expansion is now around 2 GeV rather than m b [25][26][27]. While the ultimate accuracy of this method is not known, it should be possible to halve the error on |V ub |.…”