Nuclear Physics B Proceedings Supplement 00 (2014) 1–7
Supplement
Semileptonic B and B
sdecays at Belle
Robin Glattauer1
Institute of High Energy Physics Austrian Academy of Sciences
A-1050 Vienna, AUSTRIA
Abstract
Based on the large data sample accumulated by the Belle experiment at the KEKB asymmetric energye+e−collider at KEK, Japan, we present new results on semileptonicB(s)meson decays.
The semileptonic decays B → Xc`ν are the preferred modes for determining the Cabibbo-Kobayashi-Maskawa (CKM) matrix element|Vcb|, a fundamental parameter of the Standard Model. The decayB→D`¯ν`is measured for the first time with the full Belle data sample recorded at theΥ(4S) resonance. The preliminary result isηEWG(1)|Vcb|= (42.63±0.96stat±1.39syst)×10−3andρ2=1.001±0.051stat±0.018systfor the form factor parameterρ2.
Measurements of semileptonicBs decays provide a test of QCD calculations entering the |Vcb|extraction. The heaviness of the s quark compared to the u and d quarks facilitates the theoretical description of Bs decays.
We present preliminary results of branching fraction measurements of the semi-inclusive Bs → D(∗)s X`ν¯` decays:
B(Bs→DsX`ν)=(8.2±0.2stat±0.8syst±1.5NBs)% andB(Bs→D∗sX`ν)=(5.4±0.4stat±0.5syst±1.0NBs)%.
Keywords:
Belle, Vcb, semileptonic, hadronic tag, B, Bs
1. Introduction
There are two complementary approaches for mea- suring|Vcb|- inclusive and exclusive decays. In exclu- sive decays a specific charmed final state, e.g.DorD∗, is reconstructed. In inclusive decays all final states with a charm quarkXcare considered. Both the reconstruc- tion and the theoretical descriptions differ, thus the sys- tematic errors of the approaches can be seen as mostly independent.
Currently these two approaches yield different results for|Vcb|, with the inclusive value being up to 3σlarger than the one from exclusive decays. See Table 1 for a comparison. This has lead to the question whether there are systematic errors in the experimental or the- oretical procedure unaccounted for, or whether this is
Email address:[email protected](Robin Glattauer)
the result of physics beyond the standard model. This is especially interesting as in addition the sum of exclu- sive decays does not add up to the measured inclusive branching fraction - around 15% are missing.
Mode & model |Vcb|[10−3]
B→D∗`ν¯`, LQCD [1] 39.54±0.50exp±0.74th B→D∗`ν¯`, LQCD [2] 39.04±0.49exp±0.56th B→D∗`ν¯`, LCSR [3] 41.47±0.52exp±0.96th B→D`¯ν`, LQCD [4] 39.44±1.42exp±0.88th B→D`¯ν`, LCSR [5] 40.73±1.46exp±0.78th B→Xc`ν¯`[6] 42.42±0.86
Table 1: |Vcb| results based on different measurements and theo- retical models. The B → D∗`¯ν` calculations use F(1)|Vcb| = (35.90±0.11stat±0.44syst)×10−3 and for B → D`¯ν` a value of G(1)|Vcb|=(42.64±0.72stat±1.35syst)×10−3was used. Both values are taken from the Heavy Flavor Averaging Group [7]. One can see that the exclusive values are systematically higher than the inclusive ones.
We present two measurements performed at the Belle experiment at the asymmetric electron positron collider KEKB [8]. First, we show the analysis of the decay B → D`ν¯` which is used to measure|Vcb|and a form factor parameterρ2. Second, we determine the branch- ing fractions ofBs→ D(∗)s X`ν¯`, which have never been measured directly before and offer both a verification of theoretical models and a preparation for future measure- ments ofBs→D(∗)s `¯ν`.
2. Belle detector and data sets
The Belle detector is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an ar- ray of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter comprised of CsI(Tl) crystals (ECL) located inside a super-conducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return located outside of the coil is instrumented to detectKL0mesons and to iden- tify muons (KLM). The detector is described in detail elsewhere [9].
Over 1000 fb−1data were recorded at Belle, of those are 703 fb−1at theΥ(4S) resonance which decays dom- inantly into a BB¯ pair and 121 fb−1 at theΥ(5S) reso- nance which can also decay into aBsB¯spair.
3. B→ D`ν¯`
There are two exclusive decays with a branching frac- tion high enough to determine|Vcb|: B → D∗`¯ν` and B → D`¯ν`. While the former is preferred because of low backgrounds and high yields which results in a good precision, B → D`¯ν` allows independent verification and by using hadronic tagging can come close to the precision ofB→D∗`¯ν`.
We present the preliminary measurement of B → D`ν¯` with the full Belle data sample of 703 fb−1at the Υ(4S) resonance. This is the first time B → D`¯ν` is measured at Belle using hadronic tagging. This method has been used before at the BaBar experiment [10].
3.1. Theory
The determination of the CKM matrix element|Vcb| is based on semileptonic Bdecays [11]. The theoreti- cal description of semileptonic decays takes advantage of the large mass of theW-boson relative to the ener- gies relevant inB → Xc`ν¯` (mW mb) and allows to
integrate over the dynamic degrees of freedom of theW boson at tree-level, leading to a Fermi-like Hamiltonian:
H = GF
√ 2
Vcb(¯cγµ(1−γ5)b)(`γµ(1−γ5)ν`), (1) Residual electroweak interactions between the hadronic and leptonic current are usually taken into account by introducing an electroweak correction factorηEW (e.g.
ηEW=1.0066 from [12]).
The leptonic current can be calculated perturbatively with QED while the main theoretical challenge is the description of the hadronic current, which can be treated e.g. in the frameworks of Lattice QCD (LQCD) or Light Cone Sum Rules (LCSR).
Parameterizing the hadronic current of the Hamilto- nian with a form factorG(w) [13], one obtains the dif- ferential decay width ofB→D`¯ν`:
dΓ
dw =G2Fm3D
48π3 (mB+mD)2(w2−1)3/2
|ηEW|2|Vcb|2|G(w)|2,
(2)
where w is the product of the 4-velocities of theBand Dmeson:
w=vB·vD= M2B+MD2 −q2
2MBMD . (3)
and ranges from 1.0 to∼1.6.
Using the parameterization by Capriniet al.[14], the form factor can be approximated as
G(w)=G(1)(1−8ρ2z+(51ρ2−10)z2−(252ρ2−84)z3), (4) with
z=
√ w+1−
√
√ 2
w+1+√ 2
. (5)
The decay width is expressed in terms of two param- eters, ηEWG(1)|Vcb|andρ2. G(1) is the form factor at zero recoil andηEW is the aforementioned electroweak correction factor. The current status of the art is to mea- sureηEWG(1)|Vcb|and to calculateηEWandG(1) in the theoretical frameworks in order to extract|Vcb|.
3.2. Hadronic tagging
Hadronic tagging at theΥ(4S) resonance aims at the full reconstruction of one Bmeson (Btag) in a hadronic mode. This reduces combinatorial background when reconstructing the second B meson and constrains its kinematics.
The newest version of hadronic tagging at Belle ap- plies a neural network based algorithm [15]. Compared
to previous cut based approaches this results in twice the efficiencies - 0.28 % forB±and 0.18 % forB0, with over 1000 different exclusive hadronic decay channels being reconstructed.
These channels includeBmesons decaying toD(∗)(s)or J/ψ, either as pairs (e.g. B− → D0D−s ) or in combina- tion with kaons and pions (e.g.J/ψ→J/ψK−π+π−).
3.3. Reconstruction and extraction of|Vcb|
The CKM matrix element|Vcb|is determined inde- pendently in 4 disjunct samples, separating electrons and muons, as well as charged and neutral Bmesons.
The results of the 4 samples are then averaged for a fi- nal result taking into account correlations between the samples.
B→ D`ν¯`is reconstructed in events with a hadronic tag from the charged tracks and neutral energy mea- surements not already assigned to Btag. This reduces the combinatorial background to a very high degree.
Lepton candidates are charged tracks with a sufficiently high likelihood of being an electron or muon based on the particle identification possibilities of the Belle de- tector.
TheDmeson is reconstructed in one of 15 hadronic decay channels, for D+: K−π+π+, K−π+π+π0, Ks0π+, K0sπ+π0, K+K−π+, Ks0K+, K0sπ+π+π−, and for D0: K−π+,K−π+π0,K−π+π+π−,K0sπ+π−,K0sπ+π−π0,K0sπ0, K+K−,π+π−.
One then compares the 4-momenta of the recon- structed particles to the known 4-momentum of the electron-positron beam and calculates the square of the invariant missing mass:
Mmiss2 =(pbeam−pBtag−pD−p`)2, (6) For a genuinely reconstructed decay the only missing momentum belongs to the undetectable neutrino and one expects M2miss to be equal to the neutrino mass of approximately 0, see for example Fig. 1.
We use this distinct shape to separate signal from background. The main background sources are B → D∗`¯ν`decays and erroneous tag side reconstructions. A binned extended maximum likelihood fit [16] is used to extract the number of signal events. We model the different components with Monte Carlo templates and leave signal, background fromB → D∗`ν¯` and wrong tags floating while other smaller backgrounds (e.g. fake or non-prompt leptons) are fixed to their Monte Carlo expectations. All in all we reconstruct 14057 signal events. A fit in a subrange ofwin the sample ¯B0 → D+e−ν¯`can be seen in Fig. 2.
4)
2/c (GeV
2
Mmiss
-0.50 0 0.5 1 1.5 2
100 200 300 400 500 600 700
800 B → Dlν (3325.4)
(2109.2) ν
→ D*l B
wrong B tag (2058.2)
other BG (832.8) ν
D e
→ B0
Figure 1: The M2
missdistribution of the sample ¯B0 → D+e−ν¯`for Monte Carlo simulated events.
4)
2/c (GeV
2
Mmiss
-0.50 0 0.5 1 1.5 2
10 20 30 40 50 60 70
Fit results:
±1 other bg (fixed) 86
±41 wrong tag 26
±47 D* 381
±21 signal 193
) = 0.352 χ2 p(
w<1.30
≤ 1.24
data other bg (fixed) wrong tag D*
signal
Data and Fit
Figure 2: The yield fit for the range 1.24≤w<1.30 in the sample B¯0→D+e−ν¯`.
Given equations 2-5 one can predict the signal yields for a given value of ηEWG(1)|Vcb|,ρ2 andw. We per- form signal yield measurements in 10 bins of w and extract ηEWG(1)|Vcb| andρ2 via a χ2 fit to the result- ing distribution. This is shown in Fig. 3 for the sample B¯0→D+e−ν¯`.
3.4. Results
Table 2 and Fig. 4 show the results of the fits for the 4 subsamples and their average. Comparing the results to those of theB→D`ν¯`measurement with hadronic tag- ging at BaBar [10] we see a perfect agreement of|Vcb|,
w
1 1.1 1.2 1.3 1.4 1.5 1.6
0 100 200 300 400 500
Sum of measured yields 2469 Sum of fitted yields 2460
0.0019
± = 0.0400 η Vcb G1
0.1057
± = 1.0097 ρ2
Correlation = 0.9577 = 6.58 χ2 measured yield fitted yield
Signal yield
Figure 3: Theχ2 fit ofηEWG(1)|Vcb| andρ2 in the sample ¯B0 → D+e−ν¯`.
but theρ2measured by Belle is about 2σsmaller than that of BaBar. The reducedρ2 leads to higher branch- ing fractions of B( ¯B0 → D+`−ν¯`) = (2.49±0.17)%
andB(B− → D¯0`−ν¯`) = (2.70±0.19)% which would close∼20% of the gap between inclusive and exclusive branching fractions.
The main sources of systematic errors for ηEWG(1)|Vcb| are the calibration of the hadronic tagging with a relative error of 2.9 %, the efficiencies of charged track reconstruction (1.75 %) and the branching fractions of background events (1.51 %).
ρ2
0.6 0.8 1 1.2 1.4
]-3 | [10 cb |V× G(1) × EWη
35 40 45 50
B0 e µ B0 B+ e
µ B+
AVERAGE
2 = 1 χ
∆
/dof = 10.9/ 6 χ2
Figure 4: Results ofηEWG(1)|Vcb|andρ2extraction withB→D`¯ν`. The ellipses show the two dimensional 1σcontour.
4. Bs → D(∗)s X`ν¯`
Besides the 703 fb−1 of data taken at theΥ(4S) res- onance, Belle also gathered 121 fb−1at theΥ(5S) reso- nance which by its higher energy allows production of BsB¯s pairs. ThisΥ(5S) sample allows detailed studies ofBsmeson decays.
Bs mesons offer different advantages compared toB mesons, such as easier theoretical description due to the higher mass of the spectator quark. Bs measure- ments are very useful to verify the results fromBmea- surements and to test the predictions of QCD calcula- tions. On the other hand, in contrast to Υ(4S) only (17.2±3.0)% [17] of theΥ(5S) resonances decay into BsB¯spairs, the rest intoBB¯pairs.
Different semileptonic decays of the Bs have been studied, e.g. Bs → X`ν at Babar [18] and Belle [19], B(¯b → Bs)· B(Bs → D(∗)s X`¯ν`) at LEP [20, 21, 22] or B¯0s →D∗s2+Xµ−ν¯at LHCb [23].
The modes Bs → D(∗)s `ν¯` have not been measured so far. We present the first measurement of the semi- inclusive decays Bs → D(∗)s X`¯ν`, where X stands for zero or more additional particles.
Assuming little down-feed from higher excited states D∗∗s to D∗s, the Bs → D∗sX`ν¯` branching fraction can be interpreted as Bs → D∗s`ν¯` branching fraction.
The Bs → DsX`¯νmeasurement on the other hand al- lows in particular to draw conclusions about the Bs → D∗∗s (D(∗)K)`ν¯branching fractions without explicitly re- constructing the D∗∗s states. Assuming that these are the dominant sources ofD(∗)mesons from semileptonic Bs decays their size can be estimated by calculating B(Bs→X`¯ν)− B(Bs→DsX`ν).¯
4.1. Reconstruction
The analysis is based on reconstructed D−s`+ and D∗−s `+pairs. Ds mesons are reconstructed in the clean decay mode to φ(K+K−)π− andD∗s mesons are recon- structed in their dominant modeD∗s → Dsγby adding a reconstructed photon to a Ds. Combinatorial back- ground is reduced by applying a mass range for the φ meson: 1004 MeV/c2 ≤ mφ ≤1034 MeV/c2. For the Ds meson a wide range of 1903.5 MeV/c2 ≤ mDs ≤ 2033.5 MeV/c2is applied containing enough side bands to allow fitting. The D(∗)s mesons are then combined with a lepton of opposite charge.
The number of genuinely reconstructed Ds and D∗s mesons can be measured by fits to the distribution of the reconstructed Ds mass; or for the D∗s by fitting
∆m=mD∗s−mDs, see Fig. 6 and 7. The shape of genuine Ds is modeled with a sum of two Gaussian functions with a common mean and the background is modeled
Sample ηEWG(1)|Vcb|[10−3] ρ2 correlation B¯0→D+e−ν¯` 40.01±1.89stat±1.66syst 1.010±0.106stat±0.029syst 0.692 B¯0→D+µ−ν¯` 40.66±2.07stat±1.70syst 1.075±0.115stat±0.031syst 0.713 B−→D¯0e−ν¯` 43.70±1.86stat±1.67syst 0.909±0.099stat±0.014syst 0.711 B−→D¯0µ−ν¯` 46.73±1.87stat±1.79syst 1.075±0.091stat±0.014syst 0.680 Average 42.63±0.96stat±1.39syst 1.001±0.051stat±0.018syst 0.494
Table 2: Results ofηEWG(1)|Vcb|andρ2extraction withB→D`¯ν`.
with a first order Chebychev polynomial. The PDF of D∗s is modeled with a sum of a Gaussian function and a Crystal Ball function with a common mean and for mis- reconstructedD∗sa third order Chebychev polynomial is used.
4.2. Branching fraction extraction
Events containing a trueD(∗)s meson can be organized in five categories: 1. background fromc¯c continuum events, 2. Bs → D(∗)s K`νevents, 3. wrong-side com- binations where the D(∗)s meson and the lepton candi- date stem from differentBsdecays, 4. other background where the lepton candidate stems either from a sec- ondary decay or is a misreconstructed hadron, 5. signal decays comprisingDs`¯ν,D∗s`ν¯andD∗∗s `ν.¯
Background (1) is determined from an off-resonance data sample and background (2) is estimated from MC simulation. The normalization of the remaining back- grounds and the signal component is determined by di- viding the data sample in three regions according to the decay kinematics and comparing the MC expectations to the data event yields in each region. The regions are defined using the lepton momentump∗`and the variable
Xmis=(E∗B−E∗vis)−p∗vis
p∗B , (7)
with
p∗vis=|~p`∗+~pD∗|, (8) E∗vis=E∗`+E∗D (9) Fig. 5 shows the Xmis distribution of correctly recon- structedDsmesons in theBs→ DsXeνsample. Signal events peak in the regionXmis>−1.
The reconstructed events are separated into 3 distinct regions, each of which enhances a certain component:
A Xmis<−1 enhances wrong side background B Xmis > −1, p∗ < 1.4 GeV/cenhances other back-
ground
C Xmis>−1,p∗>1.4 GeV/cenhances signal
The separation can be seen in Fig. 5. The signal and the two remaining background components (3 and 4) form 3 degrees of freedom. Counting the events in each region constitutes 3 equations, which can be solved in order to determine the signal yields.
If we assume that the 3 components have the same distribution as in the Monte Carlo, but a different overall scale factor, the number of events in each region can be calculated to be:
NiData=X
j
ajNi,jMC, (10) whereidenotes the region and jthe component. ajare the scale factors for each component. These scale fac- tors can be calculated using aχ2fit with:
χ2=X
i
(NiData−P
jajNi,jMC)2 (∆NDatai )2+(P
jaj∆Ni,MCj )2 (11) The resulting signal yields are then:
Nsignal=X
i
asignalNi,signalMC (12) From the number of signal events the branching fraction can be calculated by:
B= Nsignal
· B(D−s →φ(K+K−)π−)·NBs, (13) whereis the efficiency of the reconstruction andNBs
is the number ofBsmesons.
4.3. Results
The preliminary results of the branching fractions ob- tained can be seen in Table 3. The dominant source of systematic error is the number of Bs mesons produced at theΥ(5S) resonance at Belle and is thus listed sepa- rately. Other sources includeB(Ds →φπ;φ→K+K−) with a relative error of 5.3 %, the impact of signal and background modeling on the yield measurements (3-5 %) and detection efficiencies and fake rates (2.5- 3.4 %).
Xmis
-4 -2 0 2
Events / 0.60
0 0.5 1 1.5 2 2.5 3 3.5
103
× Belle preliminary
A B+C
Figure 5: Xmisand lepton momentum in the center of mass frame for the sampleBs →DsXeν. White is continuum background, greenBs → D(∗)s K`νdecays, blue describes different kinds of wrong side background while yellow contains “other background” and red denotes the various signal components: solid red isBs →Ds`¯ν, hatched red isBs→D∗s`¯νand crosshatched red isBs→D∗∗s`¯ν. The letters “A”,“B” and “C” denote the 3 signal regions used in the counting experiment.
Figure 6: Fit to theDsmass in the three different regions of the sampleBs→DsXeν
Comparing these results to recent theoretical estima- tions ofBs→D(∗)s `¯ν`from [24] withB(Bs→DsX`ν)= 2.1±0.2 and B(Bs → D∗sX`ν) = 5.3±0.5, or from [25] withB(Bs → DsX`ν)=1.55±0.15 andB(Bs → D∗sX`ν) =5.45±0.35 we see that the results are com- patible with theory predictions within the experimen- tal uncertainty and hint at a small branching fraction of Bs→D∗∗s `ν`.
The result onBs→DsX`νalso agrees with the small Bs→D∗∗s (D(∗)K)`ν¯branching fractions as measured by D0 [26] and LHCb [23].
5. Conclusion
We presented two new preliminary measurements at the Belle experiment which explore the semileptonic de-
cays ofB(s)mesons.
B → D`ν¯` was used to determine ηEWG(1)|Vcb| and the form factor parameter ρ2. The result for ηEWG(1)|Vcb| = (42.63±0.96stat±1.39syst)×10−3 is perfectly compatible with previous measurements by BaBar, while the result for ρ2 = 1.001±0.051stat ± 0.018syst differs at a level of 2σ, which raisesB(B → D`¯ν`) and reduces the branching fraction gap of inclu- sive and exclusive measurements.
The branching fractions of the semi-inclusive decays Bs→D(∗)s X`¯ν`were measured to beB(Bs→DsX`ν)= (8.2±0.2stat±0.8syst±1.5NBs)% andB(Bs→D∗sX`ν)= (5.4±0.4stat±0.5syst±1.0NBs)%. These results were di- rectly measured for the first time and are in good agree- ment with theoretical predictions and measurements of other semileptonicBsdecays.
Figure 7: Fit to∆min the three different regions of the sampleBs→D∗sXeν
sample B[%]
Bs→DsXeν 8.2±0.3stat±0.7syst±1.5NBs
Bs→DsXµν 8.3±0.3stat±0.8syst±1.5NBs
Bs→D∗sXeν 5.2±0.6stat±0.5syst±0.9NBs
Bs→D∗sXµν 5.8±0.6stat±0.6syst±1.0NBs
Bs→DsX`ν 8.2±0.2stat±0.8syst±1.5NBs Bs→D∗sX`ν 5.4±0.4stat±0.5syst±1.0NBs
Table 3: Preliminary branching fractions ofBs →D(∗)s X`¯ν`decays measured separately for electrons and muons. The combinations of the measurements take into account the correlations between the two modes.
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