Study of $B_c^+$ decays to the $K^+K^-\pi^+$ final state and evidence for the decay $B_c^+\to\chi_{c0}\pi^+$

A study of $B_c^+\to K^+K^-\pi^+$ decays is performed for the first time using data corresponding to an integrated luminosity of 3.0 $\mathrm{fb}^{-1}$ collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of $7$ and $8$ TeV. Evidence for the decay $B_c^+\to\chi_{c0}(\to K^+K^-)\pi^+$ is reported with a significance of 4.0 standard deviations, resulting in the measurement of $\frac{\sigma(B_c^+)}{\sigma(B^+)}\times\mathcal{B}(B_c^+\to\chi_{c0}\pi^+)$ to be $(9.8^{+3.4}_{-3.0}(\mathrm{stat})\pm 0.8(\mathrm{syst}))\times 10^{-6}$. Here $\mathcal{B}$ denotes a branching fraction while $\sigma(B_c^+)$ and $\sigma(B^+)$ are the production cross-sections for $B_c^+$ and $B^+$ mesons. An indication of $\bar b c$ weak annihilation is found for the region $m(K^-\pi^+)<1.834\mathrm{\,Ge\kern -0.1em V\!/}c^2$, with a significance of 2.4 standard deviations.

Heavy flavour physics involves studying the decays of hadrons containing at least one b or c valence quark, with the possibility of making precision measurements of Standard Model (SM) parameters and detecting effects of new physics. The B + c meson (bc), the only currently established hadron having two different heavy-flavour quarks, has the particularity of decaying weakly through either of its flavours. 1 In the SM, the B + c decays with no charm and beauty particles in the final or intermediate states can proceed only via bc → W + → uq (q = d, s) annihilation, with an amplitude proportional to the product of CKM matrix elements V * cb V uq . Calculations predict branching fractions in the range 10 −8 − 10 −6 [1][2][3]. Any significant enhancement could indicate the presence of bc annihilations involving particles beyond the SM, such as a mediating charged Higgs boson (see e.g. Ref. [4,5]).
Experimentally, the decays of B + c mesons to three light charged hadrons provide a good way to study such processes. These decay modes have a large available phase space and can include other processes such as B + c → D 0 (→ Kπ)h + (h = π, K) [6] [8] mediated by the b → c transition [9]. In this study, special consideration is given to decays leading to a K + K − π + final state in the region well below the D 0 mass, taken to be m(K − π + ) < 1.834 GeV/c 2 , where, after removing possible contributions from ([cc], B 0 s ) → K + K − , only the annihilation process remains. The other contributions listed above are also examined. The B + → D 0 (→ K + K − )π + decay is used as a normalization mode to derive the quantity where B is the branching fraction, and σ(B + c ) and σ(B + ) are the production crosssections of the B + c and B + mesons. The quantity R f is measured in the fiducial region p T (B) < 20 GeV/c and 2.0 < y(B) < 4.5, where p T is the component of the momentum transverse to the proton beam and y denotes the rapidity. The data sample used corresponds to integrated luminosities of 1.0 and 2.0 fb −1 collected by the LHCb experiment at 7 and 8 TeV centre-of-mass energies in pp collisions, respectively. Since the kinematics of B meson production is very similar at the two energies, the ratio σ(B + c ) σ(B + ) is assumed to be the same for all the measurements discussed in this Letter.
The B + (c) → K + K − π + decay candidates are reconstructed applying the same selection procedure as in Ref. [20]. A similar multivariate analysis is implemented, using a boosted decision tree (BDT) classifier [21]. Particle identification (PID) requirements are then applied to reduce the combinatorial background and suppress the cross-feed from pions misidentified as kaons. The BDT and PID requirements are optimized to maximize the sensitivity to small event yields. The B + c signal yield is determined from a simultaneous fit in three bins of the BDT output O BDT , 0.04 < O BDT < 0.12, 0.12 < O BDT < 0.18 and O BDT > 0.18, each having similar expected yield but different levels of background [20]. The normalization channel B + → D 0 (→ K + K − )π + uses the same BDT classifier, with tighter PID requirements to suppress the abundant background from B + → K + π − π + decays. Its yield is determined requiring O BDT > 0.04, and demanding 1.834 < m(K + K − ) < 1.894 GeV/c 2 to remove charmless B + → K + K − π + candidates. Signal and background yields are obtained from extended unbinned maximum likelihood fits to the distribution of the invariant mass of the K + K − π + combinations. The B + c → K + K − π + and B + → K + K − π + signals are each modelled by the sum of two Crystal Ball functions [22] with a common mean. For B + c → K + K − π + all the shape parameters and the relative yields in each bin of O BDT are fixed to the values obtained in the simulation, while for B + → K + K − π + the mean and the core width are allowed to vary freely in the fit. A Fermi-Dirac function is used to model a possible partially reconstructed component from decays with K + K − π + π 0 final states where the neutral pion is not reconstructed, resulting in a K + K − π + invariant mass below the nominal B + c or B + mass. All shape parameters of these background components are fixed to the values obtained from simulation. The combinatorial background is modelled by an exponential function. Figure 1 shows the result of the fit to determine the yield of In the B + c region 6.0 < m(K + K − π + ) < 6.5 GeV/c 2 , the signals are fitted separately for regions of the phase space corresponding to the different expected contributions: the annihilation region (m(K − π + ) < 1.834 GeV/c 2 ), the D 0 → K − π + region (1.834 < m(K − π + ) < 1.894 GeV/c 2 ), and the B 0

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GeV/c 2 ). For the first two regions, the ranges 3.38 < m(K + K − ) < 3.46 GeV/c 2 and 5.2 < m(K + K − ) < 5.5 GeV/c 2 are vetoed to remove contributions from χ c0 (as discussed below) and B 0 (s) → h + 1 h − 2 decays. A possible signal is seen in the annihilation region, as shown in Fig. 2. The corresponding yield is N c = 20.8 +11. 4 −9.9 , with a statistical significance of 2.5 standard deviations (σ), inferred from the difference in the logarithm of the likelihood for fits with and without the signal component.
The distribution of events in the m 2 (K − π + ) vs. m 2 (K + K − ) plane, for the B + c signal region 6.2 < m(K + K − π + ) < 6.35 GeV/c 2 , is shown in Fig. 3. A concentration of events is observed around m 2 (K + K − ) ∼ 11 GeV 2 /c 4 . A one-dimensional projection of m(K + K − ) shows clustering near 3.41 GeV/c 2 , close to the mass of the charmonium state χ c0 . Among all the charmonia, χ c0 has the highest branching fraction into the K + K − final state [23]. The accumulation of events near m 2 (K + K − ) ∼ 29 GeV 2 /c 4 for the loose O BDT cut appears to be mainly caused by B 0 s → K + K − decays combined with random pions since no peak is seen in m(K + K − π + ) at the B + c mass [9]. To determine the B + c → χ c0 (→ K + K − )π + signal yield, the two-dimensional m(K + K − π + ) vs. m(K + K − ) distributions are fitted simultaneously for each of the three BDT bins. The m(K + K − π + ) distribution is modelled in the same way as described above. The m(K + K − ) distribution is fitted in the range 3.20 < m(K + K − ) < 3.55 GeV/c 2 . The χ c0 → K + K − shape is modelled by a Breit-Wigner function, with mean and width fixed to their known values [23], convolved with a Gaussian resolution function, while a first-order polynomial is used to represent the K + K − background. Figure 4 shows the projections of the fit result. The yield obtained is N χ c0 = 20.8 +7.2 −6.4 , with a statistical significance of 4.1 σ. The fits for the D 0 and B 0 s regions, where no signal is observed, can be found at Ref.
[9]. For each region of phase-space considered, the efficiencies for the signals, c , and normalization channel, u , are inferred from simulated samples and are corrected using datadriven methods as described in Ref. [20]. They include the effects of reconstruction, selection and detector acceptance. An efficiency map defined in the m 2 (K − π + ) vs. m 2 (K + K − ) plane is computed. Because of limited statistics, the distribution of the signal events in the annihilation region is not well known. Therefore, the efficiency for the annihilation region is estimated in two ways: first, by taking the simple average efficiency from the map for m(K − π + ) < 1.834 GeV/c 2 and alternatively, by taking the efficiency weighted according to the sparse distribution of candidates in data in the m 2 (K − π + ) vs. m 2 (K + K − ) plane. The average of the two values is taken as the efficiency and the difference is treated as a systematic uncertainty (labelled as "event distribution" in Table 1). A correction accounting for the vetoed m(K + K − ) regions described above is included. In the calculation of the observable R f the efficiency ratio u / c is required. The values obtained are 1.698 ± 0.015 for the annihilation region and 1.241 ± 0.012 for the B + c → χ c0 (K + K − )π + mode. The uncertainties are due to the limited sizes of the simulated samples. The differences between the B + and B + c efficiencies are caused by the different lifetimes and c → χ c0 (→ K + K − )π + signal. The contributions from the B + c → χ c0 (→ K + K − )π + signal, combinatorial background (Comb.), possible pollution from the annihilation region B + c → (K − π + )K + , and combinations of χ c0 → K + K − with a random track X are shown. masses of the two mesons. The measured quantities are determined as for the annihilation region, and for the B + c → χ c0 π + decay, where x are the efficiencies and N x are the yields obtained from the fits.
Systematic uncertainties are associated with the yield ratios, the efficiency ratios and the branching fractions B(B + → D 0 π + ) = (4.81 ± 0.15) × 10 −3 , B(D 0 → K − K + ) = (4.01 ± 0.07) × 10 −3 and B(χ c0 → K − K + ) = (5.91 ± 0.32) × 10 −3 [23]. Table 1 summarizes the uncertainties. The yields are affected by the uncertainties on the fit functions and parameters, and by the variation of the yield fractions in the BDT output bins, due to the uncertainty on the BDT output distribution. The uncertainties on the efficiency ratios reflect the PID calibration, the limited sizes of the simulated samples, the effect of the detector acceptance, the B + c lifetime 0.507 ± 0.009 ps [24], and the trigger and fiducial cut corrections.
In summary, a study of B + c meson decays to the K + K − π + final state has been performed in the fiducial region p T (B) < 20 GeV/c and 2.0 < y(B) < 4.5. Evidence for the decay B + c → χ c0 π + is found at 4.0 σ significance. This result can be compared to the measurement involving another charmonium mode, σ(B + c ) obtained from Refs. [23,29]. A indication of bc weak annihilation with a significance of 2.4 σ is reported in the region m(K − π + ) < 1.834 GeV/c 2 . The branching fraction of B + c → K * 0 (892)K + has been recently predicted to be (10.0 +1.8 −3.4 ) × 10 −7 [3]. The contribution of the mode B + c → K * 0 (892)(→ K − π + )K + to R an,KKπ could be prominent, for which an estimate is made as follows. Using the predictions listed in Ref.
[30] for B(B + c → J/ψ π + ), which span the range [0.34, 2.9] × 10 −3 , and the value of σ(B σ(B + ) × B(B + c → K * 0 (892)(→ K − π + )K + ) ∼ [0.1, 1.7] × 10 −8 is obtained, including the theoretical uncertainties and the K * 0 (892) → K − π + branching fraction. This estimate is lower than the R an,KKπ measurement. The statistical uncertainty, however, is at present too large to make a definite statement. The data being accumulated in the current run of the LHC will allow LHCb to clarify whether the weak annihilation process of B + c meson decays involves significant contributions from heavier K − π + states, or is enhanced by other sources.