Evidence for CP violation in $B^+\to p \overline p K^+$ decays

Three-body $B^+\to p \overline p K^+$ and $B^+\to p \overline p \pi^+$ decays are studied using a data sample corresponding to an integrated luminosity of 3.0 $fb^{-1}$ collected by the LHCb experiment in proton-proton collisions at center-of-mass energies of $7$ and $8$ TeV. Evidence of CP violation in the $B^+\to p \overline p K^+$ decay is found in regions of the phase space, representing the first measurement of this kind for a final state containing baryons. Measurements of the forward-backward asymmetry of the light meson in the $p\overline p$ rest frame yield $A_{\mathrm{FB}}(p \overline p K^+,~m_{p\overline p}<2.85\mathrm{\,Ge\kern -0.1em V\!/}c^2)=0.495\pm0.012~(\mathrm{stat})\pm0.007~(\mathrm{syst})$ and $A_{\mathrm{FB}}(p\overline p \pi^+,~m_{p\overline p}<2.85\mathrm{\,Ge\kern -0.1em V\!/}c^2)=-0.409\pm0.033~(\mathrm{stat})\pm0.006~(\mathrm{syst})$. In addition, the branching fraction of the decay $B^+\to\kern 0.1em\overline{\kern -0.1em\Lambda}(1520)p$ is measured to be $\mathcal{B}(B^+ \to \kern 0.1em\overline{\kern -0.1em\Lambda}(1520)p)=(3.15\pm0.48~(\mathrm{stat})\pm0.07~(\mathrm{syst})\pm0.26~(\mathrm{BF}))\times 10^{-7}$, where BF denotes the uncertainty on secondary branching fractions.

topological variables related to the B + candidates and the individual tracks. The momentum, vertex and flight distance of the B + candidate are exploited, and track fit quality criteria, impact parameter and momentum information of final-state particles are also used. The BDT is trained using simulated signal events, and events in the high sideband of the pph + invariant mass (5.4 < m(pph + ) < 5.5 GeV/c 2 ), which represent the background. Tight particle identification (PID) requirements are applied to reduce the combinatorial background and suppress the cross-feed between ppK + and ppπ + . The PID efficiencies are derived from calibration data samples of kinematically identified pions, kaons and protons originating from the decays D * + → D 0 (→ K − π + )π + and Λ → pπ − . Signal and background yields are extracted using unbinned extended maximum likelihood fits to the invariant mass distribution of the pph + combinations. The B + → ppK + signal is modeled by the sum of two Crystal Ball functions [18], for which the common mean and core width are allowed to float in the fit. Beside the signal component, the fit includes the parameterizations of the combinatorial background and partially reconstructed B → ppK * decays, where a pion from the K * decay is not reconstructed, resulting in a ppK invariant mass below the nominal B mass. An asymmetric Gaussian function with power-law tails is used to model a possible ppπ + cross-feed component, where the pion is misidentified as a kaon. This contribution is found to be small.
The fit to the B + → ppπ + decay uses similar parameterizations for the signal, combinatorial background, ppK + cross-feed and partially reconstructed background from B → ppρ decays (with a missing pion from the ρ decay). The cross-feed is found to be negligible.
The distribution of events in the Dalitz plane, defined by (m 2 pp , m 2 hp ) where hp denotes the neutral combinations h − p and h + p, is examined. From the fits to the B + candidate invariant mass, shown in Fig. 1, signal weights are calculated with the sPlot technique [19]. These weights are corrected for trigger, reconstruction and selection efficiencies, which are estimated with simulated samples and calibration data. The Dalitz-plot variables are calculated constraining the pph + invariant mass to the known B + meson mass [20,21]. Figure 2 shows the Dalitz distributions of the B + → pph + events. Similarly to the results reported in Ref. [6,22], clear signals of J/ψ , η c and ψ(2S) resonances are observed, while B + → ppK + and B + → ppπ + non-charmonium events both accumulate near the pp threshold. However, B + → ppK + events preferentially occupy the region with low Kp invariant mass while B + → ppπ + events populate the region with large πp invariant mass. This difference in the Dalitz distribution can also be observed as a difference in the distribution of the helicity angle θ p of the pp system, defined as the angle between the charged meson h and the oppositely charged baryon in the rest frame of the pp system. The distributions of cos(θ p ) are depicted in Fig. 3. Data and simulation are used to assign systematic uncertainties, accounting for the PID correction and fit model, to the angular and charge asymmetries, and to the relative branching fractions. The systematic uncertainty associated to the PID correction cancels in the asymmetry measurements. The forward-backward asymmetry is measured as where N pos (N neg ) is the efficiency-corrected yield for cos θ p > 0 (cos θ p < 0). The obtained asymmetries are A FB (ppK + , m pp < 2.85 GeV/c 2 ) = 0.495 ± 0.012 (stat) ± 0.007 (syst) and A FB (ppπ + , m pp < 2.85 GeV/c 2 ) = −0.409 ± 0.033 (stat) ± 0.006 (syst), where the systematic uncertainty is due to the ratio of average efficiencies in the regions cos θ p > 0 and cos θ p < 0. As reported in previous studies [6,23], the value for B + → ppK + contradicts the short-range analysis expectation [24]. The values of A FB in bins of m pp are shown in Fig. 4; in both cases, they depend strongly on m pp . The yields of the decays B + → pph + in the region m pp < 2.85 GeV/c 2 are obtained in the same way as for the integrated signals. Those of the resonant modes are extracted through two-dimensional extended unbinned maximum likelihood fits to invariant mass distributions of pph + and pp or K + p, using the same signal and background models for m pp or m K + p as in Ref. [6]. The results are shown in Table 1. The branching fractions of the decays B + → Λ(1520)(→ K + p)p and B + → ppπ + , m pp < 2.85 GeV/c 2 are measured relative to the J/ψ modes as The systematic uncertainties also include contributions from the background model. Using

Mode
Yield where BF denotes the uncertainty on the aforementioned secondary branching fractions. The former measurement supersedes what is reported in Ref. [6].
The raw charge asymmetry is measured from the yields N as and is investigated in the Dalitz plane using signal weights inferred from the fits shown in Fig. 1, for B − and B + samples. This asymmetry includes production and detection asymmetries. The statistics of the B ± → ppπ ± decays is not sufficient to perform such an analysis, so only the B ± → ppK ± case is studied. An adaptative binning algorithm is used so that the sum of B − and B + events in each bin is approximately constant. Figure 5 shows the distribution of A raw in the Dalitz plane. A clear pattern is observed near the pp threshold where A raw is negative for m 2 Kp < 10 GeV 2 /c 4 and positive for m 2 Kp > 10 GeV 2 /c 4 . Figure 6 shows the m 2 pp projections of N (B − ) − N (B + ) in the regions of interest. To quantify the effect, unbinned extended maximum likelihood simultaneous fits to B − and B + samples are performed in regions of the Dalitz plane, using the same models as the global fits. The raw asymmetry is corrected for acceptance, by taking into account the small difference in average efficiency due to the B − and B + samples populating differently the Dalitz plane. Physical asymmetries are obtained after acceptance correction (A acc raw ) and accounting for the production A P (B ± ) and kaon detection A det (K ± ) asymmetries: The decay B ± → J/ψ (pp)K ± , part of the selected sample, is used to determine A ∆ = A P (B ± ) + A det (K ± ):  The value A CP (B ± → J/ψ K ± ) = (0.6 ± 0.4)% is taken from Ref.
[26]. When using A raw (B ± → J/ψ (pp)K ± ), differences in the momentum asymmetry of the pp pair between B ± → J/ψ (pp)K ± and nonresonant B ± → ppK ± decays are accounted for. A similar procedure is applied to obtain A CP (B ± → η c (pp)K ± ) and A CP (B ± → ψ(2S)(pp)K ± ). The B ± → ppπ ± decays are also considered in the region m pp < 2.85 GeV/c 2 . In this case, the correction also involves the pion detection asymmetry, Table 2 shows the results, including asymmetries of resonant modes. Closer to the pp threshold enhancement, m 2 pp < 6 GeV 2 /c 4 , the asymmetry is found to reach the value −0.066 ± 0.026 (stat) ± 0.004 (syst), for m 2 Kp < 10 GeV 2 /c 4 . Table 2: CP asymmetries for B ± → ppK ± and B ± → ppπ ± decays. The systematic uncertainties are dominated by the precision on the measurement A CP (B ± → J/ψ K ± ). The systematic uncertainties are estimated by using alternative fit functions and splitting the data sample according to trigger requirements and magnet polarity. The overall systematic uncertainties are dominated by the uncertainty on the A CP (B ± → J/ψ K ± ) measurement.

Mode/region
In summary, an interesting sign-inversion pattern of the CP asymmetry appears at low pp invariant masses in B ± → ppK ± decays. Although this resembles what is observed at low h + h − masses in the B ± → h ± h + h − decays, the strong phase difference could involve a specific mechanism such as interfering long-range pp waves with different angular momenta [24]. In the region m pp < 2.85 GeV/c 2 , m 2 Kp > 10 GeV 2 /c 4 , the measured asymmetry is positive with a significance of nearly 4σ, which represents the first evidence of CP violation in b-hadron decays with baryons in the final state. In the region (m 2 pp < 6 GeV 2 /c 4 , m 2 Kp < 10 GeV 2 /c 4 ), the asymmetry is negative with a significance of 2.5σ. The h hadron forward-backward asymmetry in non-charmonium B + → pph + decays is measured as A FB (ppK + , m pp < 2.85 GeV/c 2 ) = 0.495±0.012 (stat)±0.007 (syst) and A FB (ppπ + , m pp < 2.85 GeV/c 2 ) = −0.409±0.033 (stat)±0.006 (syst). These asymmetries could be interpreted as being due to the dominance of nonresonant pp scattering [24]. Finally, an improved measurement of B(B + → Λ(1520)p) = (3.15 ± 0.48 (stat) ± 0.07 (syst) ± 0.26 (BF)) × 10 −7 is obtained.
KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), PIC (Spain), GridPP (United Kingdom). We are indebted to the communities behind the multiple open source software packages on which we depend. We are also thankful for the computing resources and the access to software R&D tools provided by Yandex LLC (Russia). Individual groups or members have received support from EPLANET, Marie Sk lodowska-Curie Actions and ERC (European Union), Conseil général de Haute-Savoie, Labex ENIGMASS and OCEVU, Région Auvergne (France), RFBR (Russia), XuntaGal and GENCAT (Spain), Royal Society and Royal Commission for the Exhibition of 1851 (United Kingdom). [27] LHCb collaboration, R. Aaij et al., Measurement of CP asymmetry in D 0 → K − K + and D 0 → π − π + decays, JHEP 07 (2014) 041, arXiv:1405.2797.