Semileptonic B decays at Belle

Recent results from the Belle experiment on semileptonic decays of B-mesons are reviewed, including their effect on the determination of the CKM matrix elements |Vcb| and |Vub|.


Introduction
Precise experimental determinations of the values of the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements is the way to test unitarity of the matrix and thus to probe phenomena beyond the Standard Model (SM) of Particle Physics, which can potentially violate this unitarity.
In the most commonly studied Unitarity Triangle (UT) based on the CKM matrix, the well measured angle φ 1 (also known as β in the literature) is opposite to the side whose length is proportional to the ratio |V ub |/|V cb |, which is currently known much less precisely, as shown in Fig. 1 made by the CKMfitter group [1]. In this ratio, the main contribution to the uncertainty comes from the value of |V ub |. The usual way to obtain the values of |V cb | and |V ub | is to extract them from semileptonic decays of B-mesons, in which the decay rate is directly proportional to, to first order, the matrix element squared, and where QCD uncertainties due to hadronic recoil are under control. Vast numbers of B − u , B 0 d and B 0 s mesons were collected by the Belle experiment at the e + e − asymmetric-energy KEKB collider, operating at the Υ(4S) and Υ(5S) resonances. This provides the opportunity to study their properties in great detail using various analysis techniques and theoretical approaches.
where the main uncertainty comes from the estimate N B 0 s of the number of B 0 s mesons.

Semileptonic decays with a fully reconstructed tag at Belle
In e + e − collisions at the Υ(4S) resonance it is possible to fully reconstruct one B-meson decay in a known hadronic "tagging" mode where all decay products are registered by a detector, and by using energy-momentum conservation the kinematic variables of the other B meson can be calculated. This is extremely useful for the exclusive semileptonic decays B → X ν , where a particular hadronic final state X is reconstructed in the detector and the kinematic properties of the missing neutrino are reconstructed using tag-side information, providing a clean signal sample with very little background. Recently a new reconstruction procedure for B hadronic decays based on the NeuroBayes neural net package has been introduced in Belle [6]. This procedure tries to reconstruct B mesons in more than 1100 exclusive hadronic decay channels. Compared to the previous cutbased algorithm it offers roughly a factor of two efficiency gain and about 2.1 × 10 6 (1.4 × 10 6 ) fully reconstructed B ± (B 0 ) decays with 711 fb −1 collected at the Υ(4S) resonance.
Using this new tagging method Belle has studied the exclusive semileptonic decays B → D ν , [9]. The study is based on the full data set of 711 fb −1 at the Υ(4S) resonance.

Preliminary study of B → D ν decays
With the new hadronic tag the Belle study the B → D ν decays compliments previous |V cb | evaluation from the B → D * ν decays [7].

Results for B → ρ ν decays
The maximum likelihood fit result for B + → ρ 0 ν decays is also shown in Fig. 2, where again the signal peak is clearly visible and the signal-to-background ratio is excellent. The extracted branching fractions are B(B 0 → ρ + ν ) = (3.22 ± 0.27 stat ± 0.24 syst ) × 10 −4 and B(B + → ρ 0 ν ) = (1.83 ± 0.10 stat ± 0.10 syst ) × 10 −4 . The isospin average of measured branching fractions is 43% (2.7σ) higher than the previous PDG [17] value and its precision is almost a factor of two better.  Figure 3. Projection of the fitted distribution to data for the B + → ρ 0 ν decay onto the M ππ axis.
The projection onto the M ππ axis in the region |M 2 miss | < 0.25 GeV/c 2 of the two-dimensional binned likelihood fit in the M 2 miss -M ππ plane is shown in Fig. 3. The extracted number of B − → f 2 −ν decays from the fit is N (B − → f 2 −ν ) = 154 ± 22 which is more than 5σ away from zero and almost 3 times larger than the ISGW2 model prediction, whereas the main anticipated background from the HQE model and the PYTHIA package, the non-resonant process B → X u (ππ) −ν , is compatible with zero. This study can help to better estimate the uncertainty in inclusive determinations of |V ub | which comes from modeling of charmless semileptonic decays, and might decrease the tension with the exclusive measurements.

Conclusions
The Belle detector was decommissioned in 2010 but analysis of the collected data is not finished and is still producing outstanding scientific results. The clean environment of e + e − colliders is especially useful for studying semileptonic decays of B mesons in order to derive fundamental parameters of the SM such as the elements |V cb | and |V ub | of the CKM matrix.
Belle has significant progress in the (semi-)inclusive semileptonic branching fractions measurements of the B 0 s meson. Belle has also recently developed a new procedure for B-meson full reconstruction in hadronic decay modes. This allows a number of semileptonic modes: B → D ν , B − → pp −ν , B → π ν , B → ρ ν and B + → ω ν to be studied.
There is much progress in the determination of |V cb | and |V ub | from B-meson semileptonic decays, where recent high-statistic measurements allow the form factor shapes to be constrained from the experimental data. Together with theory calculations this allows |V cb | and |V ub | values to be determined with high precision.
Despite all of this progress, there are still tensions at the 3σ level between exclusive and inclusive measurements of |V cb | and |V ub |. This might yet be solved by improved theoretical calculations of hadronic form factors, better description of charmless semileptonic decays, and more sophisticated analysis of the existing data.