Study of $B \to p {\bar p} \pi \pi$

K. Chu, M.-Z. Wang, I. Adachi, 12 H. Aihara, S. Al Said, 35 D. M. Asner, V. Aulchenko, 62 T. Aushev, R. Ayad, V. Babu, I. Badhrees, 34 S. Bahinipati, A. M. Bakich, P. Behera, C. Beleño, J. Bennett, V. Bhardwaj, B. Bhuyan, J. Biswal, A. Bobrov, 62 G. Bonvicini, A. Bozek, M. Bračko, 31 M. Campajola, 54 L. Cao, D. Červenkov, P. Chang, V. Chekelian, A. Chen, B. G. Cheon, K. Chilikin, H. E. Cho, K. Cho, S.-K. Choi, Y. Choi, S. Choudhury, D. Cinabro, S. Cunliffe, N. Dash, F. Di Capua, 54 S. Di Carlo, Z. Doležal, T. V. Dong, S. Eidelman, 62, 42 D. Epifanov, 62 J. E. Fast, T. Ferber, A. Frey, B. G. Fulsom, R. Garg, V. Gaur, N. Gabyshev, 62 A. Garmash, 62 A. Giri, P. Goldenzweig, B. Golob, 31 O. Hartbrich, K. Hayasaka, H. Hayashii, W.-S. Hou, C.-L. Hsu, T. Iijima, 52 K. Inami, A. Ishikawa, 12 R. Itoh, 12 M. Iwasaki, Y. Iwasaki, W. W. Jacobs, H. B. Jeon, Y. Jin, D. Joffe, K. K. Joo, G. Karyan, T. Kawasaki, D. Y. Kim, S. H. Kim, K. Kinoshita, P. Kodyš, S. Korpar, 31 P. Križan, 31 R. Kroeger, P. Krokovny, 62 R. Kulasiri, Y.-J. Kwon, Y.-T. Lai, I. S. Lee, S. C. Lee, L. K. Li, L. Li Gioi, J. Libby, K. Lieret, D. Liventsev, 16 T. Luo, M. Masuda, D. Matvienko, 62, 42 M. Merola, 54 K. Miyabayashi, R. Mizuk, 51 T. Mori, R. Mussa, E. Nakano, T. Nakano, M. Nakao, 12 K. J. Nath, M. Nayak, 16 N. K. Nisar, S. Nishida, 12 K. Nishimura, H. Ono, 61 Y. Onuki, P. Oskin, P. Pakhlov, 50 G. Pakhlova, 51 B. Pal, T. Pang, S. Pardi, C. W. Park, H. Park, S.-H. Park, S. Paul, T. K. Pedlar, R. Pestotnik, L. E. Piilonen, V. Popov, 51 E. Prencipe, M. T. Prim, P. K. Resmi, M. Ritter, A. Rostomyan, N. Rout, G. Russo, D. Sahoo, Y. Sakai, 12 S. Sandilya, L. Santelj, V. Savinov, O. Schneider, G. Schnell, 19 J. Schueler, C. Schwanda, Y. Seino, K. Senyo, M. E. Sevior, C. P. Shen, J.-G. Shiu, E. Solovieva, M. Starič, Z. S. Stottler, T. Sumiyoshi, W. Sutcliffe, M. Takizawa, 17, 68 U. Tamponi, K. Tanida, F. Tenchini, T. Uglov, 51 Y. Unno, S. Uno, 12 P. Urquijo, Y. Usov, 62 G. Varner, A. Vinokurova, 62 A. Vossen, B. Wang, C. H. Wang, P. Wang, X. L. Wang, J. Wiechczynski, E. Won, S. B. Yang, H. Ye, J. Yelton, J. H. Yin, Y. Yusa, Z. P. Zhang, V. Zhilich, 62 V. Zhukova, and V. Zhulanov 62

PACS numbers: 13.25.Hw, 13.25.Ft, 13.25.Gv,14.20.Gk, 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 + → ppK + [4]. Here and throughout the text, the inclusion of the charge-conjugate mode is implied unless otherwise stated. This rare baryonic B decay presumably proceeds via the b → s penguin process with some nonnegligible 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 + is produced preferably in the p direction. [6]. Interestingly, this angular asymmetry is opposite to that observed in B + → ppπ + 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 + → ppπ + 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].
We report a study of both B 0 → ppπ + π − and B + → ppπ + π 0 including the B → ppρ mass region using the full Υ(4S) data set collected by the Belle detector [9,10] at the asymmetric-energy e + (3.5 GeV) e − (8 GeV) KEKB collider [11,12]. 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 Υ(4S) 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 barrellike 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 [13], and a Geant [14]-based software package 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 [15]. The background samples include the continuum events (e + e − → uu, dd, ss, and cc), generic B decays (b → c) and rare B decays (b → u, d, s). These simulated background samples are six 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 [6] to select p(p) and π + (π − ). 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 about a ±3.0 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 four-momentum. To reject B → ppD ( * ) events, we restrict the invariant ππ mass M ππ to be less than 1.22 GeV/c 2 for B 0 → ppπ + π − and 1.3 GeV/c 2 for B + → ppπ + π 0 based on studies of the simulated background. We use recon /P * recon and E * beam are the reconstructed B energy/momentum and the beam energy measured in the Υ(4S) rest frame, respectively. For further investigation, we keep candidates with 5.24 < M bc < 5.29 GeV/c 2 and |∆E| < 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 |M Kπ âĂŞM D | < 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 + π − and B + → ppπ + π 0 MC events with multiple B candidates are 16.4% and 20.3%, respectively. This selection removes 5.6% of B 0 → ppπ + π − and 8.7% of B + → ppπ + π 0 signal. Based on the MC simulation, there are only a few events from generic or rare B decays in the candidate region (5.27 < M bc < 5.29 GeV/c 2 and |∆E| < 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 jet-like 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 Υ(4S) rest frame; the angle between B momentum and the thrust axis of the event in the Υ(4S) rest frame; the sphericity [20] of the event calculated in the Υ(4S) rest frame; and the B flavor tagging quality parameter [21].
The output of NeuroBayes, C nb , ranges from −1 to +1, where the value is close to +1 for BB-like and −1 for continuum-like events. We require the C nb to be greater than 0.9 (0.87) for B 0 → ppπ + π − (B + → ppπ + 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 + π − , the same value for B + → ppπ + 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 ∆E 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 a double Gaussian functions for ∆E of B 0 → ppπ + π − , a Crystal Ball function [22] and a Gaussian function for ∆E of B + → ppπ + 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 ∆E and M bc , respectively. The signal distributions in ∆E and M bc are calibrated with the B 0 → ppD 0 (D 0 → K + π − ) and B 0 → D 0 π 0 (D 0 → K + π − ) by comparing the shape difference between the prediction 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 signal yields of B 0 → ppπ + π − and B + → ppπ + π 0 to be 73.8 +15.8 −14.9 and 151 ± 39 with a fit significance of 5.5σ and 5.4σ, respectively. The significance is defined as −2 × ln(L 0 /L s )(σ), 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 5 method. Table I and Fig. 3 show the yield and statistical significance in different M ππ bins for B 0 → ppπ + π − and Table II/ Fig. 4 for B + → ppπ + π 0 . For B 0 → ppπ + 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 B(B 0 → ppπ + π − ). Assuming the Υ(4S) 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 + π − and B + → ppπ + π 0 , the branching fractions of B 0 → ppπ + π − and B + → ppπ + π 0 for M π + π − < 1.22 GeV/c 2 and M π + π 0 < 1.3 GeV/c 2 are found to be (0.83 ± 0.17 ± 0.17)× 10 −6 and (4.58 ± 1.17 ± 0.67)× 10 −6 ; the signal efficiencies are 11.5% and 4.3%, respectively.
We attempted to find the contribution of B + → ppρ + by minimizing the χ 2 between the observed data  and the assumed non-resonant B + → ppπ + π 0 and B + → ppρ + decays. To describe the M ππ distribution, we use the phase space model for non-resonant B + → ppπ + π 0 and a Breit-Wigner function convolved with a Gaussian function for B + → ppρ + . We set the Breit-Wigner function with its mean and width to the nominal values for the ρ + convolved with a Gaussian resolution function of 5 MeV/c 2 width. The result is shown in Fig. 4.
The fit gives a yield of 86 ± 41 events with a χ 2 n dof of 17.0/11 for B + → ppρ + . Our current data sample is not large enough to separate the contributions of B + → ppρ + and non-resonant B + → ppπ + π 0 . The measured B(B + → ppπ + π 0 ) with B + → ppρ + included is almost a factor of ten smaller than the predicted 6 B(B + → ppρ + ) [8].
There are modes sharing the same final state-particles as our signal, such as B → p∆ ++ π or B → pΛ 0 π. Examining the M ∆(pπ + ) and M Λ(pπ − ) 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 (∆E, 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 + π − and B + → ppπ + 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 B 0 → ppπ + π − events are equally distributed in the bins below and above the charmonium-enhanced region, while B + → ppπ + π 0 events are dominant in the bin below the charmonium enhanced region.
Sources of systematic uncertainties are summarized in Table V. The number of BB pairs is known to 1.4%. By using the partially reconstructed D * + → D 0 π + with D 0 → π + 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 * + → D 0 π + , D 0 → K − π + ) sample to calibrate the MC p (π + ) identification efficiency and assign an uncertainty of 3.3% and 2.4% for B 0 → ppπ + π − and B + → ppπ + 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, where D 0 → K + π − . We choose the efficiency of the phase space model for B 0 → ppπ + π − and the efficiency of the reweighted phase space model for B + → ppπ + π 0 , and estimate the efficiency uncertainty as a difference of signal efficiencies for B 0 → ppπ + π − in the reweighted phase space model and B + → ppπ + π 0 in the phase space model. The uncertainty associated with fit parameters is examined by repeating the fit with each parameter varied by one standard deviation from its nominal value. The resulting difference is taken as the systematic uncertainty.
The assumption of no correlation between ∆E and M bc is examined by replacing PDF of B signal events with the corresponding 2-D histogram function. In summary, we report the observations of B 0 → ppπ + π − and B + → ppπ + π 0 with branching fractions of (0.83 ± 0.17 ± 0.17) × 10 −6 and (4.58 ± 1.17 ± 0.67) × 10 −6 for M π + π − < 1.22 GeV/c 2 and M π + π 0 < 1.3 GeV/c 2 , respectively. In contrast to the theoretical prediction [8], the measured B for B + → ppπ + π 0 in the ρ-enhanced region is an order of magnitude smaller than the theoretical expectation. We find the B + → ppπ + π 0 decay dominated by the lower M pp bin, which is not the case in the B 0 → ppπ + π − decay. These findings are useful for the future theoretical investigation.