Studies of the decays $B^+ \to p \bar p h^+$ and observation of $B^+ \to \kern 0.1em\bar{\kern -0.1em\Lambda}(1520)p$

Dynamics and direct $C\P$ violation in three-body charmless decays of charged $B$ mesons to a proton, an antiproton and a light meson (pion or kaon) are studied using data, corresponding to an integrated luminosity of 1.0$ {\,fb}^{-1}$, collected by the ${LHCb}$ experiment in $pp$ collisions at a center-of-mass energy of 7 TeV. Production spectra are determined as a function of Dalitz-plot and helicity variables. The forward-backward asymmetry of the light meson in the $p\bar p$ rest frame is measured. No significant $C\P$ asymmetry in $B^+ \to p \bar p K^+$ decay is found in any region of the Dalitz plane. We present the first observation of the decay $B^+ \to \kern 0.1em\bar{\kern -0.1em\Lambda}(1520)(\to K^+\bar p)p$ near the $K^+\bar p$ threshold and measure $\mathcal{B}(B^+ \to \kern 0.1em\bar{\kern -0.1em\Lambda}(1520)p)=(3.9^{+1.0}_{-0.9} (\mathrm{stat})\pm0.1 (\mathrm{syst})\pm0.3 (\mathrm{BF}))\times 10^{-7}$, where BF denotes the uncertainty on secondary branching fractions.


Introduction
Evidence of inclusive direct CP violation in three-body charmless decays of B + mesons 1 has recently been found in the modes B + → K + π + π − , B + → K + K + K − , B + → π + π + π − , and B + → K + K − π + [1,2]. In addition, very large CP asymmetries were observed in the low K + K − and π + π − mass regions, without clear connection to a resonance. The localization of the asymmetries and the correlation of the CP violation between the decays suggest that π + π − ↔ K + K − rescattering may play an important role in the generation of the strong phase difference needed for such a violation to occur [3,4]. Conservation of CP T symmetry imposes a constraint on the sum of the rates of final states with the same flavour quantum numbers, providing the possibility of entangled long-range effects contributing to the CP violating mechanism [5]. In contrast, h + h − ↔ pp (h = π or K throughout the paper) rescattering is expected to be suppressed compared to π + π − ↔ K + K − , and thus is not expected to play an important role.
The leading quark-level diagrams for the modes B + → pph + are shown in Fig. 1. The B + → ppK + mode is expected to be dominated by the b → s loop (penguin) transition while the mode B + → ppπ + is likely to be dominated by the b → u tree decay, which is CKM suppressed compared to the former. Since the short distance dynamics are similar to that of the B + → h + h + h − modes, a CP analysis of B + → pph + decays could help to clarify the role of long-range scatterings in the CP asymmetries of First studies were performed at the B factories on the production and dynamics of B + → pph + decays [6][7][8]. The results have shown a puzzling opposite behaviour of B + → ppK + and B + → ppπ + decays in the asymmetric occupation of the Dalitz plane. Charmonium contributions to the B + → ppK + decay have been studied by LHCb [9]. This paper reports a detailed study of the dynamics of the B + → pph + decays and a systematic search for CP violation, both inclusively and in regions of the Dalitz plane. The charmless region, defined for the invariant mass m pp < 2.85 GeV/c 2 , is of particular interest. The relevant observables are the differential production spectra of Dalitz-plot variables and the global charge asymmetry A CP , defined as where f ± = pph ± . The mode B + → J/ψ (→ pp)K + serves as a control channel. The first observation of the decay B + → Λ(1520)p is presented. Its branching fraction is derived through the ratio of its yield to the measured yield of the B + → J/ψ (→ pp)K + decay.

Detector and software
The LHCb detector [10] is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, designed for the study of particles containing ōrquarks. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift tubes placed downstream. The combined tracking system has momentum resolution ∆p/p that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and impact parameter (IP) resolution of 20 µm for tracks with high transverse momentum. Charged hadrons are identified using two ring-imaging Cherenkov detectors (RICH) [11]. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and preshower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers.
The trigger [12] consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a software stage which applies a full event reconstruction. Events triggered both on objects independent of the signal, and associated with the signal, are used. In the latter case, the transverse energy of the hadronic cluster is required to be at least 3.5 GeV. The software trigger requires a two-, three-or four-track secondary vertex with a large sum of the transverse momentum, p T , of the tracks and a significant displacement from all primary pp interaction vertices. At least one track must have p T > 1.7 GeV/c, track fit χ 2 per degree of freedom less than 2, and an impact parameter χ 2 (χ 2 IP ) with respect to any primary interaction greater than 16. The χ 2 IP is defined as the difference between the χ 2 of the primary vertex reconstructed with and without the considered track. A multivariate algorithm is used to identify secondary vertices [13].
The simulated pp collisions are generated using Pythia 6.4 [14] with a specific LHCb configuration [15]. Decays of hadronic particles are described by EvtGen [16] in which final state radiation is generated using Photos [17]. The interaction of the generated particles with the detector and its response are implemented using the Geant4 toolkit [18] as described in Ref. [19]. Non-resonant B + → pph + events are simulated, uniformly distributed in phase space, to study the variation of efficiencies across the Dalitz plane, as well as resonant samples such as

Signal reconstruction and determination
Candidate B + → pph + decays are formed by combining three charged tracks, with appropriate mass assignments. The tracks are required to satisfy track fit quality criteria and a set of loose selection requirements on their momenta, transverse momenta, χ 2 IP , and distance of closest approach between any pair of tracks. The requirement on the momentum of the proton candidates, p > 3 GeV/c, is larger than for the kaon and pion candidates, p > 1.5 GeV/c. The between the decay vertex and the primary vertex is required to be greater than 3 mm, and the vector formed by the primary and decay vertices must align with the B + candidate momentum. Particle identification (PID) is applied to the proton, kaon and pion candidates, using combined subdetector information, the main separation power being provided by the RICH system. The PID efficiencies are derived from data calibration samples of kinematically identified pions, kaons and protons originating from the decays D * + → D 0 (→ K − π + )π + and Λ → pπ − . Signal and background are extracted using unbinned extended maximum likelihood fits to the mass of the pph + combinations. The B + → ppK + signal is modelled by a double Gaussian function. The combinatorial background is represented by a second-order polynomial function. A Gaussian function accounting for a partially reconstructed component from B → ppK * decays is used. A possible ppπ + cross-feed contribution is included in the fit and is found to be small. An asymmetric Gaussian function with power law tails is used to estimate the uncertainties related to the variation of the signal yield.
In the case of the B + → ppπ + decay, the signal yield is smaller and the background is larger. The ranges of the signal and cross-feed parameters are constrained to the values obtained in the simulation within their uncertainties. The signal and the ppK + cross-feed contribution are modelled with Gaussian functions. The combinatorial background is represented by a third-order polynomial function.
The B + → pph + invariant mass spectra are shown in Fig. 2. The signal yields obtained from the fits are N (ppK ± ) = 7029 ± 139 and N (ppπ ± ) = 656 ± 70, where the uncertainties are statistical only.

Dynamics of B + → pph + decays
To probe the dynamics of the B + → pph + decays, differential production spectra are derived as a function of m pp and cos θ p , where θ p is the angle between the charged meson h and the opposite-sign baryon in the rest frame of the pp system. The pph + invariant mass is fitted in bins of the aforementioned variables and the signal yields are corrected for trigger, reconstruction and  selection efficiencies. They are estimated with simulated samples and corrected to account for discrepancies between data and simulation. The signal yields are determined with the fit models described in the previous section, but allowing the combinatorial background parameters to vary. The systematic uncertainties are determined for each bin and include uncertainties related to the PID correction, fit model, trigger efficiency, and the size of the simulated samples. The latter is evaluated from the differences between data and simulation as a function of the Dalitz-plot variables. No trigger-induced distortions are found.   Table 3 shows the yields of contributing charmonium modes. The results are consistent with those reported in Ref. [9]. After unfolding, the efficiency-corrected differential distributions are shown in Fig. 3. An enhancement is observed at low pp mass both for B + → ppK + and B + → ppπ + , with a more sharply peaked distribution for B + → ppπ + . This accumulation of events at low m pp is a well known feature that has also been observed in different contexts such as Υ(1S) → γpp [20], J/ψ → γpp [21] and B 0 → D ( * )0 pp [22] decays. It appears to be caused by proton-antiproton rescattering and is modulated by the particular kinematics of the decay from which the pp pair originates [23].

Invariant mass squared of the Kp system
The B + → ppK + signal yield as a function of the Dalitz-plot variable m 2 Kp is considered, where Kp denotes the neutral combinations K − p or K + p. Table 4 shows the yields and efficiencies, after the charmonium bands have been vetoed in the ranges m pp ∈ [2.85, 3.15] GeV/c 2 and [3.60, 3.75] GeV/c 2 . The differential spectrum derived after efficiency correction is shown in Fig. 4. Contrary to the situation for m pp , the data distribution is in reasonable agreement with the uniform phase space distribution, with some discrepancies in the region m 2 Kp ∈ [4, 12] (GeV/c 2 ) 2 .

Helicity angle of the pp system
The B + → pph + signal yields are considered as a function of cos θ p . Tables 5 and 6 show the corresponding yields and efficiencies. The differential distributions are shown in Fig. 5. The forward-backward asymmetries are derived by comparing the yields for cos θ p > 0 and where pos = (cos θ p > 0) and neg = (cos θ p < 0) are the averaged efficiencies, f = pos / neg and N pos = N (cos θ p > 0), N neg = N (cos θ p < 0). The values obtained are: A FB (ppK + ) = 0.370 ± 0.018 (stat) ± 0.016 (syst) and A FB (ppπ + ) = −0.392 ± 0.117 (stat) ± 0.015 (syst). A clear opposite angular correlation between B + → ppK + and B + → ppπ + decays is observed; the light meson h tends to align with the opposite-sign baryon for B ± → ppK ± while it aligns with the same-sign baryon for the B ± → ppπ ± mode. A quark level analysis suggests that the meson should align with the same-sign baryon, since the opposite-sign baryon has larger momentum, being formed by products from the decaying quark [24]. This is in agreement with the angular spectrum of B + → ppπ + but not for B + → ppK + decays. Kp for B + → ppK + . The data points are shown with their statistical and total uncertainties. The solid line represents the expectation for a uniform phase space production, normalized to the efficiency-corrected area, for comparison.

Dalitz plot
From the fits to the B-candidate invariant mass, shown in Fig. 2, signal weights are calculated with the sPlot technique [25] and are used to produce the signal Dalitz-plot distributions shown in Fig. 6. To ease the comparison, the cos θ p curves corresponding to the boundaries of the eight bins used to make the angular distributions in Fig. 5 are superimposed. With the exception of the charmonium bands (η c , J/ψ , ψ(2S) for B + → ppK + , and J/ψ for B + → ppπ + ), the structure of the low pp mass enhancement is very different between B + → ppK + and B + → ppπ + . The B + → ppK + events are distributed in the middle and lower m 2 Kp half, exhibiting a possible pp band structure near 4 GeV 2 /c 4 . An enhancement at low m Kp is also observed and is caused to a large extent by a Λ(1520) signal, as will be shown in the next section. The B + → ppπ + events are mainly clustered in the upper m 2 πp half, with also a p θ cos

Measurement of A CP for B + → ppK + decays
The raw charge asymmetry is obtained by performing a simultaneous extended unbinned maximum likelihood fit to the B − and B + samples. The B ± yields are defined as a function of the total yield N and the raw asymmetry, A raw , by N ∓ = N (1 ± A raw )/2. The CP asymmetry is then derived after correcting for the B ± production asymmetry A P (B ± ) and the kaon detection asymmetry A D (K ± ) (3)  The correction A ∆ = A P (B ± ) + A D (K ± ) is measured from data with the decay B ± → J/ψ (→ pp)K ± which is part of the data sample where A CP (J/ψ K ± ) = (1 ± 7) × 10 −3 [26]. Another correction has been applied to account for the proton antiproton asymmetry, which exactly cancels for J/ψ (→ pp)K ± but not necessarily in the full phase space of ppK ± events. This effect has been estimated in simulation studying the difference in the interactions of protons and antiprotons with the detector material between J/ψ (→ pp)K ± and ppK ± events generated uniformly over phase space. We obtained a m 2 Kp -dependent bias, up to 3% for the highest bin, for A raw .
To measure A raw for charmonium modes, and in particular J/ψ (→ pp)K ± , a two dimensional (m B , m pp ) simultaneous fit to the B + and B − samples is performed. The systematic uncertainties are estimated by varying the fit functions and splitting the data sample according to trigger requirements or magnet polarities, and recombining the results from the sub-samples. The procedure is applied to obtain a global value of A CP as well as the variation of the asymmetry as a function of the Dalitz-plot variables. The results are: A CP = −0.022 ± 0.031 (stat) ± 0.007 (syst) for the full ppK ± spectrum, and A CP = −0.047 ± 0.036 (stat) ± 0.007 (syst) for the region m pp < 2.85 GeV/c 2 . Figure 7 shows the variation of A CP as a function of the Dalitz-plot variables.
6 Observation of the B + → Λ(1520)p decay In the ppK + spectrum, near the threshold of the neutral Kp combination, a peak in invariant mass at 1.52 GeV/c 2 is observed, as shown in Fig. 8, corresponding to the uds resonance Λ(1520).   Figure 9 shows the B signal weighted Kp invariant mass, and the expected Λ(1520) shape obtained from a model based on an asymmetric Breit-Wigner function derived from an EvtGen [16] simulation of the decay B + → Λ(1520)p, convolved with a Gaussian resolution function, and a second-order polynomial function representing the tail of the non-Λ(1520) B + → ppK + decays.
These shapes are then used in a two dimensional (m ppK + , m Kp ) extended unbinned maximum likelihood fit to obtain the B + → Λ(1520)p yield. The fit results in N (B + → Λ(1520)p) = 47 +12 −11 with a statistical significance of 5.3 standard deviations, obtained by comparing the likelihood at its maximum for the nominal fit and for the background-only hypothesis. Figure 10 shows the  projections of the fit for the Kp and ppK + invariant masses.
To test the robustness of the observation, different representations of the Kp background have been used, combining first or second order polynomials and a contribution modelled by a Breit-Wigner function, for which the mean (µ) and width (Γ) are allowed to vary within the known values of the Λ(1600) baryon (µ ∈ [1.56, 1.7] GeV/c 2 , Γ ∈ [0.05, 0.25] GeV/c 2 ). Fits in a wider m Kp range were also considered. In all cases the yield was stable with a statistical significance similar to the nominal fit case.
The branching fraction for the decay B + → Λ(1520)p is derived from the ratio where N i is the yield of the decay chain i, gen denotes the efficiency after geometrical acceptance and simulation requirements. The global selection efficiency sel includes the reconstruction, the trigger, the offline selection, and the particle identification requirements. The ratio of branching The systematic uncertainties include effects of the Kp background model, the particle identification, the limited simulation sample size, the uncertainties on the relative trigger efficiencies, and are summarized in Table 7. Convolving the systematic uncertainty with the statistical likelihood profile, the global significance is 5.1 standard deviations. Using B(B + → J/ψ K + ) = (1.016 ± 0.033) × 10 −3 , B(J/ψ → pp) = (2.17 ± 0.07) × 10 −3 [26], and B(Λ(1520) → K − p) = 0.234 ± 0.016 [27], the branching fraction is The last error corresponds to the uncertainty on the secondary branching fractions. This result is in agreement with the upper limit set in Ref. [6], B(B + → Λ(1520)p) < 1.5 × 10 −6 . Considering the separate B ± signals in the range m Kp ∈ [1.44, 1.585] GeV/c 2 , the yields are N (B − ) = 50 ± 12 and N (B + ) = 27 ± 11.

Summary
Based on a data sample, corresponding to an integrated luminosity of 1.0 fb −1 , collected in 2011 by the LHCb experiment, an analysis of the three body B + → pph + decays (h = K or π) has been performed. The dynamics of the decays has been probed using differential spectra of Dalitz-plot variables and signal-weighted Dalitz plots. The charmless B + → ppK + decay populates mainly the low m 2 pp and lower m 2 K + p -half regions whereas the B + → ppπ + decay has a similar enhancement at low m 2 pp but with an upper m 2 π + p -half occupancy. From the occupation pattern of the Dalitz plots, it is likely that the B + → ppK + decay is primarily driven by pp rescattering with a secondary contribution from neutral Kp rescattering while the B + → ppπ + decay is also dominated by pp rescattering but with a secondary contribution from doubly-charged (pπ) ++ rescattering, along the lines of the rescattering amplitude analysis performed in Ref. [28]. This difference of behaviour is reflected in the values of the forward-backward asymmetry of the light meson in the pp rest frame A FB (ppK + ) = 0.370 ± 0.018 (stat) ± 0.016 (syst), A FB (ppπ + ) = −0.392 ± 0.117 (stat) ± 0.015 (syst).