New results on inclusive B\to X_{u} \ell ν decay from the Belle experiment
NNew results on inclusive 𝑩 → 𝑿 𝒖 ℓ𝝂 decay from the Belleexperiment Lu Cao , ∗ University of Bonn,Nussallee 12, Bonn, Germany
E-mail: [email protected]
We report on the measurement of inclusive charmless semileptonic B decays 𝐵 → 𝑋 𝑢 ℓ𝜈 . Theanalysis makes use of hadronic tagging and is performed on the full data set of the Belle experimentcomprising 772 million 𝐵 ¯ 𝐵 pairs. In the proceedings, the preliminary results of measurements ofpartial branching fractions and the CKM matrix element | 𝑉 𝑢𝑏 | are presented. On behalf of the Belle collaboration. ∗ Speaker © Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/ a r X i v : . [ h e p - e x ] J a n ew results on inclusive 𝐵 → 𝑋 𝑢 ℓ𝜈 decay from the Belle experiment Lu Cao
1. Introduction
In the Standard Model of particle physics (SM), the Cabibbo-Kobayashi-Maskawa (CKM)matrix [1, 2] describes the quark mixing and accounts for 𝐶𝑃 − violation in the quark sector. Oneof the crucial tests of the SM is precise determination of the magnitude of the matrix elements.In 𝑏 − flavor scope, the corresponding world averages of | 𝑉 𝑢𝑏 | from both exclusive and inclusivedeterminations [3] are (cid:12)(cid:12) 𝑉 excl. 𝑢𝑏 (cid:12)(cid:12) = ( . ± . ± . ) × − , (cid:12)(cid:12) 𝑉 incl. 𝑢𝑏 (cid:12)(cid:12) = (cid:16) . ± . + . − . (cid:17) × − , (1)where the uncertainties are from experiment and theory. The disagreement between them is aboutthree standard deviations.On the other hand, the experimental measurement of the inclusive semileptonic decay 𝐵 → 𝑋 𝑢 ℓ𝜈 is challenging due to the large background from the CKM-favoured 𝐵 → 𝑋 𝑐 ℓ𝜈 decay. Fig. 1illustrates the 𝐵 → 𝑋 𝑢 ℓ𝜈 and 𝐵 → 𝑋 𝑐 ℓ𝜈 decays with the generator-level distributions in twoimportant kinematic variables: the invariant mass of hadronic system 𝑀 𝑋 and the lepton energy inthe signal 𝐵 rest frame 𝐸 𝐵ℓ . It’s shown that the clear separation of the signal decay is only possiblein certain kinematic regions, e.g. the endpoint of lepton energy or the low 𝑀 𝑋 region. The detailsof the reconstruction and separation strategy is described in Sec. 2. The preliminary results on themeasured partial branching fractions and the | 𝑉 𝑢𝑏 | values are presented in Sec. 3. M X [GeV] E v e n t s / ( . G e V ) ×10 B X c (×0.02) BB BBB
Higher resonances& non-resonant E B [GeV] E v e n t s / ( . G e V ) ×10 Figure 1:
The generator-level 𝑀 𝑋 and 𝐸 𝐵ℓ distributions of the 𝐵 → 𝑋 𝑢 ℓ𝜈 decay comparing to that of 𝐵 → 𝑋 𝑐 ℓ𝜈 decay. The 𝐵 → 𝑋 𝑐 ℓ𝜈 component (gray) is scaled down by a factor of 50 for illustration.
2. Analysis strategy
The data used in this analysis were recorded with the Belle detector [4] at the KEKB acceleratorcomplex [5] with a center-of-mass energy of √ 𝑠 = .
58 GeV. The full data set contains an integratedluminosity of 711 fb − and corresponds to 772 million Υ ( 𝑆 ) → 𝐵 ¯ 𝐵 events. The Monte Carlo(MC) simulated events are generated by EVTGEN [6] and the detector response is modeled usingGEANT3 [7]. The signal 𝐵 → 𝑋 𝑢 ℓ𝜈 MC sample is a combination of resonances and non-resonantdecay using a hybrid modelling approach [8, 9]. The non-resonant component is based on the theorycalculation of Ref. [10] with the model parameters in the Kagan-Neubert scheme from Ref. [11].The hadronic decays of one of the 𝐵 mesons are reconstructed via the full reconstructionalgorithm [12] based on neural networks. In total, over 1104 decay cascades are considered and2 ew results on inclusive 𝐵 → 𝑋 𝑢 ℓ𝜈 decay from the Belle experiment Lu Caoreconstructed. The efficiencies for charged and neutral 𝐵 mesons are 0 .
28% and 0 . 𝐵 tag for each event. In addition, we require thebeam-constrained mass 𝑀 bc = √︃ (√ 𝑠 / ) − | p tag | > .
27 GeV to suppress continuum processes( 𝑒 + 𝑒 − → 𝑞 ¯ 𝑞 , 𝑞 = 𝑢, 𝑑, 𝑠, 𝑐 ) and beam background.All tracks and clusters not used in the construction of the 𝐵 tag candidate are used to reconstructthe signal side. With the fully reconstructed four-momentum of 𝐵 tag and the known beam-momentum, the signal 𝐵 rest frame can be defined as 𝑝 sig = 𝑝 𝑒 + 𝑒 − − (cid:18)√︃ 𝑚 𝐵 + (cid:12)(cid:12) p tag (cid:12)(cid:12) , p tag (cid:19) . (2)The signal lepton with 𝐸 𝐵ℓ = (cid:12)(cid:12) p B ℓ (cid:12)(cid:12) > 𝐽 / 𝜓 decay and photon conversions. In addition,the charge of lepton is required to be opposite to 𝐵 tag for the charged 𝐵 case. With the signal leptonselected, the four-momentum of hadronic system 𝑝 𝑋 is defined as a sum of the four-momenta oftracks and clusters which are not involved in reconstructing the 𝐵 tag and signal lepton. Furthermore,we reconstruct the missing mass squared and the four-momentum transfer squared 𝑞 as MM = (cid:0) 𝑝 sig − 𝑝 𝑋 − 𝑝 ℓ (cid:1) , 𝑞 = (cid:0) 𝑝 sig − 𝑝 𝑋 (cid:1) . (3)We utilise a machine learning based classification with boosted decision trees (BDTs) toseparate the signal 𝐵 → 𝑋 𝑢 ℓ𝜈 decay from the background events which are dominated by 𝐵 → 𝑋 𝑐 ℓ𝜈 . The feature variables used for training include MM , the number of charged kaons and 𝐾 𝑠 ,the total charge of event, the vertex fit 𝜒 / dof between the hadronic system and signal lepton, andthe MM and angular information of a partially reconstructed 𝐵 → 𝐷 ∗ ℓ𝜈, 𝐷 ∗ → 𝐷𝜋 slow decaywith the slow pions candidates, where 𝑝 cms 𝜋 slow < .
22 GeV. Due to the small difference betweenthe masses of 𝐷 and 𝐷 ∗ , the flight directions of the 𝜋 slow and 𝐷 ∗ are strongly correlated and weestimate the energy of 𝐷 ∗ as 𝐸 𝐷 ∗ ≈ 𝑚 𝐷 ∗ × 𝐸 𝜋 slow /( 𝑚 𝐷 ∗ − 𝑚 𝐷 ) . On the BDT classifier output, wechoose a selection criteria that reject 98 .
1% of 𝐵 → 𝑋 𝑐 ℓ𝜈 decays and retain 24 .
8% of 𝐵 → 𝑋 𝑢 ℓ𝜈 signal decays. The selection efficiency on data is 2 . 𝐵 tag reconstruction efficiency is calibrated using a data-driven approachdescribed in Ref. [14]. The uncertainty of calibration is considered in systematics. We also apply acontinuum efficiency correction to the simulated sample by comparing the difference to the numberof reconstructed off-resonance events in data.
3. Partial branching fractions and | 𝑉 𝑢𝑏 | results A binned likelihood fit is performed to extract the signal yield, where the systematic un-certainties are incorporated via nuisance-parameter constraints. The fit uses MC templates forbackground, and for signal in and out-side of the selected phase-space regions. In total, we carryout five separate fits to measure the three partial branching fractions as summarised in Table 1.Fig. 2 shows the main fit results. The result based on the two-dimensional fit of 𝑀 𝑋 and 𝑞 , i.e.3 ew results on inclusive 𝐵 → 𝑋 𝑢 ℓ𝜈 decay from the Belle experiment Lu Cao (a) Preliminary (b) Preliminary (c1) Preliminary (c2) Preliminary (d) Preliminary (d) Preliminary
Figure 2:
The post-fit distributions for various phase-space regions and kinematic variables. The distribu-tions of the two-dimensional fit (d) are shown on the projections of 𝑀 𝑋 and 𝑞 Δ BF = ( . ± . ± . ) × − , is in a good agreement with the one obtained by fitting the leptonspectrum, covering the same phase-space region. It also agrees well with the most precise measure-ment to date of this region [15], where Δ BF = ( . ± . ) × − . For other phase-space regions,the measured partial branching fractions are also compatible with the previous measurements [16].Based on the measured partial branching fractions, we calculate the | 𝑉 𝑢𝑏 | value with thetheoretical input of decay rate as | 𝑉 𝑢𝑏 | = √︄ Δ B ( 𝐵 → 𝑋 𝑢 ℓ𝜈 ) 𝜏 𝐵 ΔΓ ( 𝐵 → 𝑋 𝑢 ℓ𝜈 ) , (4)where the average 𝐵 meson lifetime is taken as ( . ± . ) ps [17] and the state-of-the-arttheory predictions on ΔΓ are listed in Table 2. Table 3 summarises the measured | 𝑉 𝑢𝑏 | values. Toquote a single value for | 𝑉 𝑢𝑏 | we adapt the procedure of Ref. [17] and calculate a simple arithmeticFit Fit variable Phase-space region 10 Δ BF (a) 𝑀 𝑋 𝐸 𝐵ℓ > 𝑀 𝑋 < . . ± . ± . 𝑞 𝐸 𝐵ℓ > 𝑀 𝑋 < . 𝑞 > . ± . ± . 𝐸 𝐵ℓ 𝐸 𝐵ℓ > 𝑀 𝑋 < . . ± . ± . 𝐸 𝐵ℓ 𝐸 𝐵ℓ > . ± . ± . 𝑀 𝑋 − 𝑞 𝐸 𝐵ℓ > . ± . ± . Table 1:
The measured partial branching fractions for various phase-space regions. The first uncertainty isstatistical and the second one is systematics. ew results on inclusive 𝐵 → 𝑋 𝑢 ℓ𝜈 decay from the Belle experiment Lu CaoPhase-space region BLNP [20] DGE [21, 22] GGOU [23] ADFR [24, 25] 𝑀 𝑋 < . . + . − . . + . − . . + . − . . + . − . 𝑀 𝑋 < . , 𝑞 > . + . − . . + . − . . + . − . . + . − . 𝐸 𝐵ℓ > . + . − . . + . − . . + . − . . + . − . Table 2:
The theory predicted decay rates in the three phase-space regions ( ps − ). Fit 10 | 𝑉 𝑢𝑏 | BLNP | 𝑉 𝑢𝑏 | DGE | 𝑉 𝑢𝑏 | GGOU | 𝑉 𝑢𝑏 | ADFR (a) 3 . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . (b) 4 . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . (c1) 3 . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . (c2) 4 . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . (d) 4 . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . . + . , + . , + . − . , − . , − . Table 3:
The extracted | 𝑉 𝑢𝑏 | values based on four theoretical inputs on the decay rates. The first uncertaintyis statistical, the second one is systematic and the last term comes from the corresponding theory calculation. average of the most precise determinations for the phase-space region 𝐸 𝐵ℓ > | 𝑉 𝑢𝑏 | = ( . ± . ± . ± . ) × − . (5)This value is smaller than the previous inclusive measurements of | 𝑉 𝑢𝑏 | in Ref. [16, 18]. Thecompatibility with the exclusive measurement of | 𝑉 𝑢𝑏 | in Eq.1 is 1.4 standard deviations; it isalso compatible with the value expected from CKM unitarity from a global fit of Ref. [19] of | 𝑉 𝑢𝑏 | = ( . + . − . ) × − within 1.6 standard deviations.
4. Summary and outlook
The preliminary results are obtained with the hadronic tagged analysis based on the full Belledata set. The measured partial branching fractions for the three phase-space regions are compatiblewith the previous measurements. The preliminary | 𝑉 𝑢𝑏 | value extracted in this analysis is largerbut compatible with the exclusive determination within 1.4 standard deviations. Based on thispreliminary result, the final analysis will incorporate a few modifications, including the aspectsof increasing the simulated sample size and considering additional systematics accounting for thesignal modeling. The separate-mode branching fractions for 𝐵 + / 𝐵 and 𝑒 / 𝜇 will be also provided. References [1] N. Cabibbo, Phys. Rev. Lett. , 531 (1963).[2] M. Kobayashi and T. Maskawa, Prog. Theor. Phys. , 652 (1973).5 ew results on inclusive 𝐵 → 𝑋 𝑢 ℓ𝜈 decay from the Belle experiment Lu Cao[3] Y. S. Amhis et al. (HFLAV), (2019), arXiv:1909.12524 [hep-ex] .[4] A. Abashian et al. , Nucl. Instrum. Meth.
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