First extraction of inclusive Vcb from q2 moments

Abstract

We present the first determination of Vcb from inclusive $$ B\to {X}_c \ell {\overline{v}}_{\ell} $$ B → X c ℓ v ¯ ℓ using moments of the dilepton invariant mass, q2. These moments are reparametrization invariant quantities and depend on a reduced set of non-perturbative parameters. This reduced set of parameters opens a new path to extract these parameters up to $$ 1/{m}_b^4 $$ 1 / m b 4 purely from data and can potentially reduce the uncertainty on Vcb. In this paper, we present our first determination of Vcb using this method. Combining the recent measurements of q2 moments by Belle and Belle II, our default fit gives |Vcb| = (41.69±0.63)·10−3. This result presents an important independent cross check of, and is consistent with, the previous state-of-the-art inclusive determinations using lepton energy and hadronic invariant mass moments.

Standard Model predictions for lepton flavour universality ratios of inclusive semileptonic B decays

“…However, table 6 provides the HQE parameters up to 1/m 3 b in the full covariant derivative basis, which can be directly compared. We note that the values for m b and m c are similar, as these are used as constraints on the fit in [2]. However, as was discussed in [2], especially the value of ρ 3 D = 0.03 ± 0.02 GeV 3 differs from the value of [1] quoted in table 1.…”

“…We note that the values for m b and m c are similar, as these are used as constraints on the fit in [2]. However, as was discussed in [2], especially the value of ρ 3 D = 0.03 ± 0.02 GeV 3 differs from the value of [1] quoted in table 1. The difference between the two should be clarified, possibly by performing a combined analysis of lepton energy, hadronic invariant mass and q 2 moments.…”

“…The above definitions differ from e.g. [2,18,19] where the full covariant derivative was used and not only the spatial component as above, linked via iD µ = v µ ivD + D ⊥ . To differentiate, we therefore add a ⊥ superscript to HQE parameters.…”

“…These values can be compared with those obtained from a recent analysis using q 2 moments [2]. In the default analysis of [2], also 1/m 4 b terms were included, such that the HQE elements cannot directly be compared. However, table 6 provides the HQE parameters up to 1/m 3 b in the full covariant derivative basis, which can be directly compared.…”

“…Employing the heavy quark expansion (HQE), allows the parametrization of these decays in perturbative Wilson coefficients and nonperturbative HQE elements. Thanks to a combined theoretical and experimental effort, these HQE parameters can be extracted from moments of the decay spectrum giving an impressive 2% uncertainty on the inclusive V cb determinations [1,2]. The experimental measurements of semileptonic B → X c usually combine the muon and electron modes (and B 0 and B + ).…”