Study of B → p ¯ p ππ

Using a data sample of 772 × 10 6 B ¯ B pairs collected on the ϒ ð 4 S Þ resonance with the Belle detector at the KEKB asymmetric energy e þ e − collider, we report the observation of B 0 → p ¯ p π þ π − and the first observation of B þ → p ¯ p π þ π 0 . We measure a decay branching fraction of ð 0 . 83 (cid:2) 0 . 17 (cid:2) 0 . 17 Þ × 10 − 6 in B 0 → p ¯ p π þ π − for M π þ π − < 1 . 22 GeV =c 2 with a significance of 5.5 standard deviations. The contribution from B 0 → p ¯ pK 0 is excluded. We measure a decay branching fraction of ð 4 . 58 (cid:2) 1 . 17 (cid:2) 0 . 67 Þ × 10 − 6 for B þ → p ¯ p π þ π 0 with M π þ π 0 < 1 . 3 GeV =c 2 with a significance of 5.4 standard deviations. We study the difference of the M p ¯ p distributions in B 0 → p ¯ p π þ π − and B þ → p ¯ p π þ π 0 .

Using a data sample of 772 × 10 6 BB pairs collected on the ϒð4SÞ resonance with the Belle detector at the KEKB asymmetric energy e þ e − collider, we report the observation of B 0 → ppπ þ π − and the first observation of B þ → ppπ þ π 0 . We measure a decay branching fraction of ð0.83 AE 0.17 AE 0.17Þ × 10 −6 in B 0 → ppπ þ π − for M π þ π − < 1.22 GeV=c 2 with a significance of 5.5 standard deviations. The contribution from B 0 → ppK 0 is excluded. We measure a decay branching fraction of ð4.58 AE 1.17 AE 0.67Þ × 10 −6 for B þ → ppπ þ π 0 with M π þ π 0 < 1.3 GeV=c 2 with a significance of 5.4 standard deviations. We study the difference of the M pp distributions in B 0 → ppπ þ π − and B þ → ppπ þ π 0 . DOI: 10.1103/PhysRevD.101.052012 Charmless B decays offer a good opportunity to find sizable CP violation due to interference between the b → s penguin and b → u tree processes. Such decays can reveal new physics if measured results deviate from Standard Model expectations. In the B-factory era, both Belle and BABAR have discovered large direct CP violation in the B → Kπ system [1][2][3]. The LHCb Collaboration reported evidence of direct CP violation in B þ → ppK þ [4]. Here and throughout the text, the inclusion of the chargeconjugate mode is implied unless otherwise stated. This rare baryonic B decay presumably proceeds via the b → s penguin process with some non-negligible b → u contribution. It is intriguing that the invariant mass of the pp system peaks near threshold [5], and in the pp rest frame, K þ is produced preferably in thep direction [6]. Interestingly, this angular asymmetry is opposite to that observed in B þ → ppπ þ , which is presumably dominated by the b → u tree process [6]. Most of the baryonic B decays presumably proceed predominantly via the b → s process, except for B þ → ppπ þ and B 0 → ppπ 0 [7] decays. It is important to measure other b → u baryonic B decays to provide more information for theoretical investigation based on a generalized factorization approach [8]. B 0 → ppπ þ π − has been observed by LHCb [9], but there is still no observation for B þ → ppπ þ π 0 .
We report a study of both B 0 → ppπ þ π − and B þ → ppπ þ π 0 including the B → ppρ mass region using the full ϒð4SÞ dataset collected by the Belle detector [10,11] at the asymmetric energy e þ (3.5 GeV) e − (8 GeV) KEKB collider [12,13]. The data sample used in this study corresponds to an integrated luminosity of 711 fb −1 , which contains 772 × 10 6 BB pairs produced on the ϒð4SÞ resonance. The Belle detector surrounds the interaction point of KEKB. It is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector, 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 (ECL) comprised of CsI(Tl) crystals 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 identify muons.
For the study of B → ppππ, samples simulated with the Monte Carlo technique (MC) are used to optimize the signal selection criteria and estimate the signal reconstruction efficiency. These samples are generated with EvtGen [14] and a GEANT-based software package [15] to model the detector response. We generate the signal MC sample by a phase space model reweighted with the pp mass distribution obtained by LHCb [9] on B 0 → ppπ þ π − . The background samples include the continuum events (e þ e − → uū, dd, ss, and cc), generic B decays (b → c), and rare B decays (b → u; d; s). These simulated background samples are 6 times larger than the integrated luminosity of the accumulated Belle data.
We require charged particles to originate within a 2.0 cm region along the beam and from a 0.3 cm region on the transverse plane around the interaction region. To identify charged particles, we utilize the likelihood information determined for each particle type by the CDC, TOF, and ACC and apply the same selection criteria listed in Ref. [6] to select pðpÞ and π þ ðπ − Þ. The π 0 is reconstructed from two photons with a minimum energy in the laboratory frame of 0.05 GeV measured by the ECL. To reduce combinatoric background, the π 0 energy is required to be greater than 0.5 GeV, and the reconstructed mass is in the range 0.111 < M γγ < 0.151 GeV=c 2 , which corresponds to a AE3.0 standard deviation (σ) window. We then perform a mass-constrained fit to the nominal π 0 mass [16] in order to improve the resolution of the reconstructed π 0 fourmomentum. To reject B → ppD ðÃÞ events, we restrict the invariant ππ mass M ππ to be less than 1.22 GeV=c 2 for B 0 → ppπ þ π − and 1.3 GeV=c 2 for B þ → ppπ þ π 0 based on studies of the simulated background. We use ΔE ¼ recon =P Ã recon and E Ã beam are the reconstructed B energy/momentum and the beam energy measured in the ϒð4SÞ rest frame, respectively. For further investigation, we keep candidates with 5.24 < M bc < 5.29 GeV=c 2 and jΔEj < 0.2 GeV.
We have further applied a D veto to reject candidate events with a charged pion, assumed to be a charged kaon, satisfying jM Kπ − M D j < 0.4 GeV=c 2 . We require only one B candidate in each event. We choose the candidate with the smallest value of χ 2 in the B vertex fit. The fractions of B 0 → ppπ þ π − and B þ → ppπ þ π 0 MC events with multiple B candidates are 16.4% and 20.3%, respectively. This selection removes 5.6% of the B 0 → ppπ þ π − and 8.7% of the B þ → ppπ þ π 0 signal. Based on the MC simulation, there are only a few events from generic or rare B decays in the candidate region (5.24 < M bc < 5.29 GeV=c 2 and jΔEj < 0.2 GeV); thus, they are ignored. The continuum background is the dominant component in the candidate region. Variables describing event topology are used to distinguish spherical BB events from jetlike continuum events. We use a neural network package, NeuroBayes [17], to separate the B signal from the continuum background. There are 28 input parameters for the neural network training, of which 23 parameters are modified Fox-Wolfram moments of particles of the signal B candidate, and separately those of particles in the rest of the event [18,19]. The remaining five parameters are the separation between the B candidate vertex and the accompanying B vertex along the longitudinal direction, the angle between the B flight direction and the beam axis in the ϒð4SÞ rest frame, the angle between the B momentum and the thrust axis of the event in the ϒð4SÞ rest frame, the sphericity [20] of the event calculated in the ϒð4SÞ rest frame, and the B flavor tagging quality parameter [21].
The output of NeuroBayes, C nb , ranges from −1 to þ1, where the value is close to þ1 for BB-like and close to −1 for continuum-like events. We require the C nb to be greater than 0.9 (0.87) for B 0 → ppπ þ π − (B þ → ppπ þ π 0 ) with optimizations based on a figure of merit (FOM) defined as where N s is the expected signal yield, assuming the branching fraction measured by LHCb for B 0 → ppπ þ π − and the same value for B þ → ppπ þ π 0 , and N b is the number of background events from the MC simulations. To extract the B → ppππ yield for events in the candidate region, we perform an extended unbinned likelihood fit to variables ΔE and M bc . These variables are assumed to be uncorrelated. The fit function used is where N is the number of total events, i denotes the event index, j stands for the component index (signal or background), and P represents the probability density function (PDF).
To model the signal distributions, we use double Gaussian functions for ΔE of B 0 → ppπ þ π − , a Crystal Ball function [22] and a Gaussian function for ΔE of B þ → ppπ þ π 0 , and a double Gaussian function for M bc . For the background, we use a second-order Chebyshev polynomial function and an ARGUS function [23] to describe ΔE and M bc , respectively. The signal distributions in ΔE and M bc are calibrated with B 0 → ppD 0 (D 0 → K þ π − ) and B 0 →D 0 π 0 (D 0 → K þ π − ) by comparing the shape difference between the predictions of the MC and data. These modes have the same multiplicity in the final state as our signal, much larger statistics, and small backgrounds. We fix the calibrated signal shapes from MC simulation and allow the component yields and all other PDF shape parameters to float. The fit results are shown in Figs. 1 and 2.
We find the signal yields of B 0 → ppπ þ π − and B þ → ppπ þ π 0 to be 73.8 þ15. 8 −14.9 and 151 AE 39 with fit significances of 5.5σ and 5.4σ, respectively. The significance is defined as ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi −2 × lnðL 0 =L s Þ p ðσÞ, where L 0 is the likelihood with zero signal yield and L s is the likelihood for the measured yield. In this calculation, we have used the likelihood function which is smeared by including the additive systematic uncertainties that affect the yield. With the large significance of both modes, we then measure the signal yields in different M ππ bins with the same fit method. Table I and Fig. 3 show the yield and statistical significance in different M ππ bins for B 0 → ppπ þ π − ; Table II and Fig. 4 show them for B þ → ppπ þ π 0 . For B 0 → ppπ þ π − , signal events in the bin 0.46 < M ππ < 0.53 GeV=c 2 are mostly from B 0 → ppK 0 S , and hence we exclude this range in the contribution shown in Table I and Fig. 3, and from the measurement of BðB 0 → ppπ þ π − Þ. Assuming the ϒð4SÞ decays to charged and neutral BB pairs equally, we use the efficiency obtained from the MC simulation and fitted signal yield to calculate the branching fraction. After calculating overall efficiencies for B 0 →ppπ þ π − and B þ → ppπ þ π 0 , the branching fractions of B 0 → ppπ þ π − and B þ → ppπ þ π 0 for M π þ π − < 1.22 GeV=c 2 and M π þ π 0 < 1.3 GeV=c 2 are found to be ð0.83 AE 0.17 AE 0.17Þ × 10 −6 and ð4.58 AE 1.17 AE 0.67Þ × 10 −6 ; the signal efficiencies are 11.5% and 4.3%, respectively. We attempted to find the contribution of B þ → ppρ þ by minimizing the χ 2 between the observed data and the assumed nonresonant B þ → ppπ þ π 0 and B þ → ppρ þ decays. To describe the M ππ distribution, we use the phase space model for nonresonant B þ → ppπ þ π 0 and a Breit-Wigner function convolved with a Gaussian function for B þ → ppρ þ . We set the Breit-Wigner function with its mean and width to the nominal values for the ρ þ convolved with a Gaussian resolution function of 5 MeV=c 2 width. The result is shown in Fig. 4.
There are modes sharing the same final-state particles as our signal, such as B →pΔ þþ π or B →pΛ 0 π. Examining the M Δðpπ þ Þ and M Λðpπ − Þ spectra, we find no obvious contribution from these modes.  We investigate the M pp distribution of B signals in three regions: M pp < 2.85 GeV=c 2 for the threshold enhancement region, 2.85 < M pp < 3.128 GeV=c 2 for the charmonium-enhanced region, and 3.128 GeV=c 2 < M pp for the phase-space-dominant region. We perform a 2D (ΔE; M bc ) likelihood fit to extract the signal yields of the B → ppππ decays in each region.
Tables III and IV show the fitted yields with statistical fit significances for B 0 →ppπ þ π − and B þ → ppπ þ π 0 , respectively. The charmonium-enhanced region, 2.85 < M pp < 3.128 GeV=c 2 , includes other expected resonant modes such as B → J=ψρ [16]. We find that B 0 → ppπ þ π − events are equally distributed in the bins below and above the charmonium-enhanced region, while B þ → ppπ þ π 0 events are dominant in the bin below the charmoniumenhanced region. We also calculated the branching fraction of B 0 → ppπ þ π − in the threshold enhancement region to be ð0.35 AE 0.13 AE 0.07Þ × 10 −6 , which is consistent with the observed result from LHCb [9]. Sources of systematic uncertainties are summarized in Table V. The number of BB pairs is known to within 1.4%. By using the partially reconstructed D Ãþ → D 0 π þ with D 0 → π þ π − K 0 S events, the uncertainty due to the charged-track reconstruction  efficiency is estimated to be 0.35% per track. We use a Λ → pπ − (D Ãþ → D 0 π þ , D 0 → K − π þ ) sample to calibrate the MC p (π þ ) identification efficiency and assign uncertainties of 3.3% and 2.4% for B 0 → ppπ þ π − and B þ → ppπ þ π 0 decays, respectively. For π 0 reconstruction, we determine its uncertainty by using a τ − → π − π 0 ν data sample [24]. To estimate the systematic error due to continuum suppression, we use the B 0 → ppD 0 and B 0 → D 0 π 0 data/MC samples, whereD 0 → K þ π − . We choose the efficiency of the phase space model for B 0 → ppπ þ π − and the efficiency of the reweighted phase space model for B þ → ppπ þ π 0 , and we estimate the efficiency uncertainty as a difference of signal efficiencies for B 0 → ppπ þ π − in the reweighted phase space model and B þ → ppπ þ π 0 in the phase space model. The uncertainty associated with the parameters of the ΔE and M bc PDFs is examined by repeating the fit with each parameter varied by 1 standard deviation from its nominal value. The assumption of no correlation between ΔE and M bc is examined by replacing the PDF of B signal events with the corresponding 2D histogram function. In summary, we report the observation of B 0 → ppπ þ π − and the first observation of B þ → ppπ þ π 0 with branching fractions of ð0.83 AE 0.17 AE 0.17Þ × 10 −6 and ð4.58 AE 1.17 AE 0.67Þ × 10 −6 for M π þ π − < 1.22 GeV=c 2 and M π þ π 0 < 1.3 GeV=c 2 , respectively. In contrast to the theoretical prediction [8], the measured B for B þ → ppπ þ π 0 in the ρ-enhanced region is an order of magnitude smaller than the theoretical expectation. Similar deviation from the theoretical expectation has also been found in B þ → ppμ þ ν μ by LHCb [25] and Belle [26]. We find that the B þ → ppπ þ π 0 decay should be dominated by the lower M pp bin, which is not the case in the B 0 → ppπ þ π − decay. These findings are useful for future theoretical investigation.