Measurements of the absolute branching fractions of $B^{+} \to X_{c\bar{c}} K^{+}$ and $B^{+} \to \bar{D}^{(\ast) 0} \pi^{+} $ at Belle

We present the measurement of the absolute branching fractions of $B^{+} \to X_{c\bar{c}} K^{+}$ and $B^{+} \to \bar{D}^{(\ast) 0} \pi^{+} $ decays, using a data sample of $772\times10^{6}$ $B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}e^{-}$ collider. Here, $X_{c\bar{c}}$ denotes $\eta_{c}$, $J/\psi$, $\chi_{c0}$, $\chi_{c1}$, $\eta_{c}(2S)$, $\psi(2S)$, $\psi(3770)$, $X(3872)$, and $X(3915)$. We do not observe significant signals for $X(3872)$ nor $X(3915)$, and set the 90$\%$ confidence level upper limits: ${\cal B}(B^{+} \to X(3872) K^{+} )<2.7 \times 10^{-4}$ and ${\cal B}(B^{+} \to X(3915) K^{+} )<2.9 \times 10^{-4}$. These represent the most stringent upper limit for ${\cal B}(B^{+} \to X(3872) K^{+} )$ to date and the first measurement for ${\cal B}(B^{+} \to X(3915) K^{+} )$. The measured branching fractions for $\eta_{c}$ and $\eta_{c}(2S)$ are the most precise to date: ${\cal B}(B^{+} \to \eta_{c} K^{+} )=(12.3\pm0.8\pm0.7) \times 10^{-4}$ and ${\cal B}(B^{+} \to \eta_{c}(2S)K^{+}) =(4.9\pm1.1\pm0.3) \times 10^{-4}$ , where the first and second uncertainties are statistical and systematic, respectively.


I. INTRODUCTION
The discovery of the X(3872) by the Belle collaboration [1] opened a new era in the field of hadron spectroscopy. The X(3872) does not correspond to any of the predicted charmonium states in the quark model [2], and is an exotic hadron candidate. The most natural interpretation of X(3872) is a D 0 andD * 0 molecular state, as its mass is quite close to the combined mass of these charmed mesons and it has J P C = 1 ++ [3], which is consistent with an S-wave D 0D * 0 molecule state. However, a pure molecular interpretation cannot explain the large cross section observed by the CDF experiment in pp collisions at √ s = 1.9 TeV [4]. Therefore, the most plausible explanation of X(3872) is an admixture of a molecular state and a pure charmonium χ c1 (2P ) [5]. The large value of the ratio B(X(3872) → ψ(2S)γ)/B(X(3872) → J/ψγ) [6,7] and the lack of observation of χ c1 (2P ) → χ c1 π + π − [8] also support this interpretation. In order to understand the nature of X(3872), a measurement of the absolute branching fraction B(B + → X(3872)K + ) is quite useful [9]. With this measurement in hand, we can determine B(X(3872) → f ), where f is a possible final state, since the product of B(B + → X(3872)K + ) and B(X(3872) → f ) is measured [10]. The measurement of B(B + → X(3872)K + ) is possible in B-factory experiments operating at a center-of-mass energy that corresponds to the mass of the Υ(4S) resonance, where the Υ(4S) almost exclusively decays into a BB pair. Therefore, by exclusively reconstructing one B meson and identifying the K + in the decay of the other B meson, the missing mass technique can be used to reconstruct the X(3872). In the past, BaBar used a similar approach to perform this measurement with an data set of 231.8 × 10 6 BB pairs, which resulted in an upper limit at 90% confidence level (C.L) of B(B + → X(3872)K + ) < 3.2 × 10 −4 [11]. The Belle collaboration measured the B(B + → X(3872)K + ) × B(X(3872) → D 0D0 π 0 ) to be (1.02 ± 0.31 0.21 0.29 ) × 10 −4 . This value provides the lower limit of the B(B + → X(3872)K + ) as B(X(3872) → D 0D0 π 0 ) is smaller than unity. In this paper, we present a measurement of B(B + → X(3872)K + ) using the full data sample of the Belle experiment, along with a simultaneous measurement of the various charmonium(-like) states (X cc ) that appear in the missing mass spectrum. We measure the branching fractions of nine states: η c , J/ψ, χ c0 , χ c1 , η c (2S), ψ(2S), ψ(3770), X(3872), and X(3915). In particular, the measurements of B(B + → η c K + ) and B(B + → η c (2S)K + ) are important. Past measurements of these values [11] limited the precision of the determination of the absolute branching fractions of η c and η c (2S) [10]. Also, this is the first limit for B(B + → X(3915)K + ). Finally, we present the measurement of B(B + →D ( * )0 π + ), using a similar technique, where theD ( * )0 is reconstructed from the missing mass. These are useful normalization modes for other B meson decays such as B + →D ( * )0 K + and B + →D ( * )0 π + π + π − .
The remaining sections of the paper are organized as follows: in Sec. II, the Belle detector and the data samples used are described. In Sec. III, an overview of the analysis method is provided. In Sec. IV, the analysis approach for the B + →D ( * )0 π + decay is described. In Sec. V, the B + → X cc K + analysis is presented. In Sec. VI, the relevant systematic uncertainties are discussed. Finally in Sec. VII, the conclusion of this paper is presented.

II. DATA SAMPLES AND THE BELLE DETECTOR
We use a data sample of 772 × 10 6 BB pairs recorded with the Belle detector at the KEKB asymmetric-energy e + e − collider [12]. The Belle detector is a large-solidangle magnetic spectrometer that consists of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array 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 superconducting solenoid coil that provides a 1.5 T magnetic field. An iron flux-return located outside of the coil is instrumented to detect K 0 L mesons and to identify muons. The Belle detector is described in detail elsewhere [13].
We use Monte-Carlo (MC) simulated events generated using EvtGen [14] and JETSET [15] that include QED final-state radiation [16]. The events are then processed by a detector simulation based on GEANT3 [17]. We produce signal MC events to obtain the reconstruction efficiency and the mass resolution for signal events. We also use background MC samples to study the missing-mass distribution in the background process Υ(4S) → BB and e + e − → qq (q = u, d, s, c and b) with statistics six times that of data.

III. ANALYSIS OVERVIEW
In this analysis, we fully reconstruct one of the two charged B mesons (B tag ) via hadronic states and require at least one charged kaon or pion candidate among the charged particles not used for the B tag reconstruction. The kaon or pion, coming from the other charged B meson, B sig , is required to have a charge opposite that of B tag . The B tag is reconstructed in one of 1104 hadronic decays using a hierarchical hadronic full reconstruction algorithm based on the NeuroBayes neural-network package [18]. The quality of a B tag candidate is represented by a single NeuroBayes output-variable classifier (O NB ), which includes event-shape information to suppress continuum events. We require O NB to be greater than 0.01, which retains 90% of true B tag candidates and rejects 70% of fake B tag candidates. The beam constrained mass are the beam-energy and the reconstructed B tag threemomenta, respectively, in the center-of-mass frame, is required to be greater than 5.273 GeV/c 2 . About 18% of the events contain multiple B tag candidate that pass all the selection criteria. In such an event, the B tag with the greatest O NB is retained. The B tag reconstruction efficiency is roughly 0.3%. Figure 1 shows the M bc distribution for data with the O NB requirement applied. The selections of the charged kaon and pion daughters of B sig are performed based on vertex information from the tracking system (SVD and CDC) and likelihood values L K and L π provided by the hadron identification system, ionization loss in the CDC, the number of detected Cherenkov photons in the ACC, and the timeof-flight measured by the TOF [19]. A charged track is required to have a point of closest approach to the interaction point that is within 5.0 cm along the z axis and 0.40 cm in the transverse (r-φ) plane. The z axis is opposite the positron beam direction. A track is identified as a kaon (pion) if the likelihood ratio L(K : π) (L(π : K)) is greater than 0.6. The likelihood ratio is defined as L(i : j) = L i /(L i + L j ). The efficiencies of hadron identification are about 90% for both pions and kaons. The momentum-averaged probability to misidentify a pion (kaon) track as a kaon (pion) track is about 9% (10%). We identify the signal as a peak at the nominal X cc orD * 0 mass in the distribution of missing mass: where M miss(h) is the missing mass recoiling against the hadron h (π + or K + ), and p * e + e − , p * tag , and p * h are the four-momenta of the electron-positron initial state, B tag , and h, respectively, in the center-of-mass frame.
The probability to observe multiple kaon or pion candidates in the M miss(h) range of interest (2.6 GeV/c 2 < M miss(K + ) < 4.1 GeV/c 2 and M miss(π + ) < 2.5 GeV/c 2 ) in an event is 2.8% and 0.3%, respectively. We do not apply a best-candidate selection if multiple candidates are found.
The beam-energy resolution is a dominant contribution to the M bc resolution, and event-by-event fluctuations of M bc from the nominal B meson mass are directly correlated to the event-by-event fluctuation of the beam-energy. We apply a correction to account for the event-by-event fluctuation of the beam-energy using a linear relation to M bc . The corrected beam-energy improves the missing mass resolution by 8%, 4%, and 2% for X(3872), J/ψ, and D 0 , respectively. The validity of the beam-energy correction is checked using high-statistics samples B + → D ( * )0 π + , B + → D ( * )0 π + π + π − , and B + → J/ψK + samples. We divide the samples into two sets with M bc smaller or larger than the nominal B + mass [10]. The peak positions in the M miss(h) distribution for both data sets without the beam-energy correction are significantly different from their expected masses and are consistent within uncertainty after the correction. We blinded the missing mass distribution in the range 3.3 GeV/c 2 < M miss(K + ) < 4.0 GeV/c 2 until the analysis procedure was fixed. Branching fractions are obtained using the following equations: where N sig is the signal yield obtained from the fit to the missing mass distribution, ǫ is the reconstruction efficiency for B tag and pion or kaon in B sig , and N Υ(4S) is the number of accumulated Υ(4S) events. We use a value of 0.514 for B(Υ(4S) → B + B − ) [10]. The factor of two in Eq. (2) originates from the inclusion of the charge-conjugate mode.
IV. ANALYSIS OF B + →D ( * )0 π + DECAY Figure 2 shows the observed M miss(π + ) distribution, where clear peaks corresponding toD 0 andD * 0 are visible. In order to extract the signalD ( * )0 yields, a binned likelihood fit is performed. The probability density function (PDF) for the signal peak is the sum of three Gaussian functions based on a study of large simulated samples of signal decays. The mean value for one Gaussian function is allowed to differ from that of the other two to accommodate for the tail in high-mass regions resulting from B tag decays with photons. The relative weights of the three Gaussian functions are fixed to the values obtained from the signal MC. We introduce two parameters: the global offset of the mean (µ data −µ MC ) and the global resolution scale factor (σ data /σ MC ) to accommodate for a possible difference in the shape in the signal MC and data. The PDF for background events is represented by a second-order exponential: exp(ax + bx 2 ), where a and b are free parameters in the fit. The validity of using this function as a background PDF is confirmed by fitting to the background MC and sideband data, which is defined within the region 5.22 GeV/c 2 < M bc < 5.26 GeV/c 2 . The fit returns a reasonable χ 2 /ndf , where ndf is number of degree of freedom. χ 2 is not improved by increasing the exponential order. The mass range above 2.3 GeV/c 2 is not included in the fit to avoid contributions from excited D mesons. Table I summarizes the branching fraction measurements for B + → π +D( * )0 . The values of (µ data − µ MC ) and (σ data /σ MC ) are found to be quite consistent at 0 MeV/c 2 and 1, respectively, indicating that the signal MC describes the signal shape well. The measured branching fractions are consistent with the world averages [10] within 1.1σ taking into account the fact that almost all past measurements assumed B(Υ(4S) → B + B − ) = 0.5. Figure 3 shows the observed and fitted M miss(K + ) distributions. We again perform a binned likelihood fit to extract the signal X cc yields. In the analysis of the highstatistics sample of B + →D ( * )0 π + , we confirm that the signal shape is consistent between data and MC. Therefore, we fix the signal PDF to be the histogram PDF from signal MC generated with the mass and natural width of the X cc states fixed to the world averages [10]. We consider nine X cc in the fit: η c , J/ψ, χ c0 , χ c1 , η c (2S), ψ(2S), ψ(3770), X(3872), and X(3915). We do not include h c and χ c2 because their branching fractions are measured to be very small [10]: B(B + → K + h c ) < 3.8 × 10 −5 at 90% C.L. and B(B + → K + χ c2 ) = (1.1±0.4)×10 −5 . The background PDF is a second-order exponential, as for B + → π +D( * )0 , and is again validated with background MC and the data sideband. The statistical significance of each X cc state is determined from the log-likelihood ratio −2 ln (L 0 /L), where L 0 (L) is the likelihood for the fit without (with) the signal component. When we evaluate the significance for a X cc state, the other X cc states are included in the fit. The branching fractions are determined using Eq. (2). For χ c0 , ψ(3770), and X(3872), the significances are smaller than three standard deviations (σ). We also set 90% C.L. upper limit for branching fractions to these states using the CLs technique [21].
The results are summarized in Table II. The upper limit for B(B + → X(3872)K + ) is the most stringent to date. The upper limit for the B(B + → X(3915)K + ) is determined for the first time. The measurements for B(B + → η c K + ) and B(B + → η c (2S)K + ) are the most precise to date. In particular, this is the first significant measurement of B(B + → η c (2S)K + ). For B(B + → ψ(3770)K + ), we do not see a significant signal and the measured value is smaller than world average by 2.7σ. For the other measurements, the values are consistent with world averages within 1.7σ.
In Figure 3 (c), we see an enhancement near 3545 MeV/c 2 , where no known charmonium state exists. We attempt to fit this by including an additional contribution using signal MC PDF with a mass of 3545 MeV/c 2 and a natural width of 0 MeV. An offset for the peak position is introduced as a free parameter. The signal yield is 738 ± 189 events at the peak position of 3544.2 ± 2.8 MeV/c 2 , which is 4.3σ lower than the mass of the χ c2 . The −2 ln (L 0 /L) value is 16.5. Since the signal region is very wide compared to the experimental resolution, we estimate the probability to observe such an enhancement in a single experiment. We perform one million pseudoexperiments in which background events are generated with the same shape and yield as data. Multiple fits,  I: Summary of the branching fraction measurements for B + →D ( * )0 π + decays. The first uncertainties for the branching fractions are statistical and the second are systematic.

Mode
Nsig each including signal with a natural width of zero and a mass value incremented by 1 MeV/c 2 across the fit range for successive fits, are performed and the highest −2 ln (L 0 /L) in one pseudo-experiment is retained. The probability to observe an enhancement with −2 ln (L 0 /L) greater than 16.5 is 0.43%, which corresponds to a global significance of 2.8σ. We therefore conclude that the enhancement is not significant.

VI. SYSTEMATIC UNCERTAINTY
A summary of the systematic uncertainties for each X cc andD ( * )0 state is provided in Table III. We consider the following systematic uncertainties for the branching fraction measurements. The systematic uncertainty for the efficiency of the charged hadron identification is estimated from the yield of D * + → D 0 π + , D 0 → K − π + with and without the hadron identification requirements. We apply a correction factor to the particle identification efficiencies based on the ratio of the efficiencies found in the MC and data samples. The uncertainty of the correction factor is treated as the systematic uncertainty.
The systematic uncertainty due to the charged track reconstruction efficiency is estimated using the decay chain D * + → π + D 0 , D 0 → π + π − K 0 S , and K 0 S → π + π − where K 0 S → π + π − is either partially or fully reconstructed. The ratio between the yields of partially and fully reconstructed signals are compared between data and MC; the difference of 0.35% per track is taken as the systematic uncertainty. The systematic uncertainty from the reconstruction efficiency of B tag is estimated using a hadronictag analysis in which B sig decays to D ( * ) ℓν, where l is electron or muon [22]. The yield for this signal is compared between data and MC, and the difference is implemented as a correction factor for each B tag decay mode. The averaged correction factor used in this analysis is 0.76 independent of X cc . The signal and background efficiencies are multiplied by this factor. The main origin of the correction factor is understood to result from the fact that branching fractions for some of the B tag decays in the MC generation are outdated and inconsistent withe the most recent measurements. Furthermore, this correction factor is also determined in the B − → τ − ν analysis independently using sideband region of extra ECL energy [23]. The correction factor is found to be consistent with that obtained from D ( * ) ℓν, which indicates that it is generally independent of the B sig decay  mode. The uncertainty of this correction factor, 4.6%, is regarded as the systematic uncertainty. Note that the correction for lepton identification efficiency and associated systematic uncertainty were not taken into account in Ref. [22]. These are implemented in this analysis. The world average of B(Υ(4S) → B + B − ) is (51.4±0.6)% [10], which corresponds to a systematic uncertainty of 1.2%. The systematic uncertainty for the N Υ(4S) is assigned as 1.4%. The systematic uncertainty due to the mass and width of each state is estimated by performing fits while varying the mass and width by the world-average uncertainties [10]. The systematic uncertainty on the fitter bias is estimated by performing pseudo-experiments. We generate pseudo-data from the background and signal shapes determined from the background MC and the signal MC, respectively. The background yields are taken from the sideband of data defined as M miss(K + ) < 3.3 GeV/c 2 or M miss(K + ) > 4.0 GeV/c 2 , and signal yields are determined from the world averages of the branching fractions and the reconstruction efficiencies. We perform a binned likelihood fit to extract the signal yields in each pseudo-experiment. The difference between the mean of the extracted signal yields and the input mass value is taken as the systematic uncertainty. The systematic uncertainty due to the B + → X cc K + signal PDF arises from uncertainties of µ data − µ MC and σ data /σ MC in the B + → D 0( * ) π + fit. This is evaluated by performing a fit with the PDF shape parameters changed within their uncertainties after averaging the result forD 0 andD * 0 . All the charmonium states are changed simultaneously in this case. The systematic uncertainty arising from the finite statistics of the signal MC is estimated by repeatedly modifying the histogram-PDF bin contents within the Poisson uncertainty and then refitting. The root mean square of the extracted signal yield distribution is regarded as the systematic uncertainty. The reconstruction efficiency of the B tag may depend on the decay of X cc states. As our knowledge of the decay modes of each X cc is limited, a systematic uncertainty is assigned in the following way. For each X cc except ψ(3770), the sum of the known branching fractions is not equal to 100%. In the default estimation of the branching fraction, unknown decay modes are filled with decays into uū, dd, and ss, that hadronize via PYTHIA. The systematic uncertainty is estimated by eliminating the PYTHIA-generated decay and taking the difference with the nominal efficiency. For X(3872) and X(3915), the PYTHIA decay is not implemented by default. Therefore, the systematic uncertainty is estimated by implementing the PYTHIA decay with a branching fraction of 50%. The systematic uncertainty on the background assumption is estimated by performing a fit after changing the order of the exponential background's polynomial exponent from quadratic to cubic. We perform a fit including h c and χ c2 with yields fixed to their world averages and upper limit for the branching fractions, respectively. The difference of the yields from the default fit is regarded as a systematic uncertainty. The statistical uncertainty of the signal reconstruction efficiency due to signal MC statistics is regarded as systematic uncertainty. BaBar [11]. Our measurement significantly improves the precision of B(η c (2S) → KKπ). In addition, this measurement can contribute to many other decays involving the η c (2S) such as ψ(2S) → γη c (2S) by BESIII [24] and η c (2S) → pp by LHCb [25]. Finally, we measure B(B + →D 0 π + ) = (4.34 ± 0.10 ± 0.25) × 10 −3 and B(B + →D * 0 π + ) = (4.82 ± 0.12 ± 0.35) × 10 −3 , which are consistent with the world averages [10]. The latter is the most precise measurement from a single experiment.