Observation of B 0 s → ¯ D (cid:1) 0 ϕ and search for B 0 → ¯ D 0 ϕ decays

The first observation of the B 0 s → ¯ D (cid:1) 0 ϕ decay is reported, with a significance of more than seven standard deviations, from an analysis of pp collision data corresponding to an integrated luminosity of 3 fb − 1 , collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The branching fraction is measured relative to that of the topologically similar decay B 0 → ¯ D 0 π þ π − and is found to be B ð B 0 s → ¯ D (cid:1) 0 ϕ Þ ¼ ð 3 . 7 (cid:3) 0 . 5 (cid:3) 0 . 3 (cid:3) 0 . 2 Þ × 10 − 5 , where the first uncertainty is statistical, the second systematic, and the third from the branching fraction of the B 0 → ¯ D 0 π þ π − decay. The fraction of longitudinal polarization in this decay is measured to be f L ¼ ð 73 (cid:3) 15 (cid:3) 4 Þ % . The most precise determination of the branching fraction for the B 0 s → ¯ D 0 ϕ decay is also obtained, B ð B 0 s → ¯ D 0 ϕ Þ ¼ ð 3 . 0 (cid:3) 0 . 3 (cid:3) 0 . 2 (cid:3) 0 . 2 Þ × 10 − 5 . An upper limit, B ð B 0 → ¯ D 0 ϕ Þ < 2 . 0 ð 2 . 3 Þ × 10 − 6 at 90% (95%) confidence level is set. A constraint on the ω − ϕ mixing angle δ is set at j δ j < 5 . 2 ° (5.5°) at 90% (95%) confidence level.

The precise measurement of the angle γ of the Cabibbo-Kobayashi-Maskawa (CKM) Unitarity Triangle [1,2] is a central topic in flavor physics experiments. Its determination at the subdegree level in tree-level open-charm b-hadron decays is theoretically clean [3,4] and provides a standard candle for measurements sensitive to new physics effects [5]. In addition to the results from the B factories [6], various measurements from LHCb [7][8][9] allow the angle γ to be determined with an uncertainty of around 5°. However, no single measurement dominates the world average, as the most accurate measurements have an accuracy of Oð10°− 20°Þ [10,11]. Alternative methods are therefore important to improve the precision. Among them, an analysis of the decays B 0 s →D ðÃÞ0 ϕ open possibilities to offer competitive experimental precision on the angle γ [12][13][14][15], where theD Ã0 meson can be partially reconstructed [16].
The tree-level Feynman diagrams for the B 0 s →D ðÃÞ0 ϕ decays are shown in Fig. 1(a). The inclusion of chargeconjugated processes is implied throughout the paper. The decay B 0 s →D 0 ϕ was first observed by the LHCb collaboration [17] using a data sample corresponding to an integrated luminosity of 1 fb −1 , while no prior results exist for B 0 s →D Ã0 ϕ decays. The branching fraction BðB 0 s → D 0 ϕÞ is ð3.0 AE 0.8Þ × 10 −5 [17,18]. The B 0 s →D Ã0 ϕ decay is a vector-vector mode and can proceed through different polarization amplitudes. A measurement of its fraction of longitudinal polarization (f L ) is of particular interest because a significant deviation from unity would confirm previous results from similar color-suppressed B 0 decays [19,20], as expected from theory [21,22]. This also helps to constrain QCD models and to search for effects of physics beyond the Standard Model (see review of polarization in B decays in Ref. [18]). The B 0 →D 0 ϕ decay can proceed by leading-order Feynman diagrams shown either in Fig. 1(b) or in Fig. 1(c), followed by ω − ϕ mixing. The W-exchange decay is suppressed by the Okubo-Zweig-Iizuka (OZI) rule [23][24][25]. Assuming that the color-suppressed B 0 →D 0 ω decay dominates, the branching fraction of B 0 →D 0 ϕ is predicted and can be used to determine the mixing angle δ [26]. The relation between the branching fractions and mixing angle can be written as tan 2 δ ¼ BðB 0 →D 0 ϕÞ= BðB 0 →D 0 ωÞ × ΦðωÞ=ΦðϕÞ, where ΦðωÞ and ΦðϕÞ are the integrals of the phase-space factors computed over the resonant line shapes. A calculation, using a recent result on BðB 0 →D 0 ωÞ [19] and taking into account phasespace factors, gives BðB 0 →D 0 ϕÞ ¼ ð1.6 AE 0.1Þ × 10 −6 . The ratio ΦðωÞ=ΦðϕÞ ¼ 1.05 AE 0.01 is used, where the uncertainty comes from the limited knowledge regarding the shape parameters of the two resonances. The previous experimental upper limit on this branching fraction was BðB 0 →D 0 ϕÞ < 11.7 × 10 −6 at 90% confidence level (C.L.) [27]. The new measurement presented in this paper also allows the ω − ϕ mixing angle to be determined [26,28].
In this paper, results on the B 0 ðsÞ →D ðÃÞ0 ϕ decays are presented, where the ϕ meson is reconstructed through its decay to a K þ K − pair and theD 0 meson decays to K þ π − . The B 0 s →D Ã0 ϕ decay is partially reconstructed without inclusion of the neutral pion or photon from theD Ã0 meson decay. The analysis is based on a data sample corresponding to 3.0 fb −1 of integrated luminosity, of which approximately one third (two thirds) were collected by the LHCb detector from pp collisions at a center-of-mass energy of 7 (8) TeV.
The LHCb detector is a single-arm forward spectrometer covering the pseudorapidity range 2 < η < 5, described in detail in Refs. [29,30]. The online event selection is performed by a trigger [31], which 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 and requires a two-, three-or fourtrack secondary vertex with a large sum of the component of the momentum transverse to the beam, p T , of the tracks and a significant displacement from all primary pp-interaction vertices (PV).
The selection requirements for the B 0 ðsÞ →D ðÃÞ0 ϕ signals are the same as those used for the branching fraction measurements of B 0 ðsÞ →D 0 K þ K − , as described in detail in Ref. [32]. The selection criteria are optimized using the B 0 →D 0 π þ π − decay as a normalization channel. Signal B 0 ðsÞ →D 0 K þ K − candidates are formed by combiningD 0 candidates, reconstructed in the final states K þ π − , with two additional particles of opposite charge, identified as kaons, whose tracks are required to be inconsistent with originating from a PV. They must have sufficiently high p and p T and be within the fiducial acceptance of the two ringimaging Cherenkov detectors [33] used for particle identification (PID) of charged hadrons. TheD 0 decay products are required to form a good quality vertex with an invariant mass within 25 MeV=c 2 of the knownD 0 mass [18]. TheD 0 and two kaon candidates must form a good vertex. The reconstructedD 0 and B vertices are required to be significantly displaced from any PV. To improve the B-candidate invariant-mass resolution, a kinematic fit [34] is used, constraining theD 0 candidate invariant mass to its known value [18] and the B momentum to point back to the PV with smallest χ 2 IP , where χ 2 IP is defined as the difference in the vertex-fit χ 2 of a given PV reconstructed with and without the particle under consideration. By requiring the recon-structedD 0 vertex to be displaced downstream from the reconstructed B 0 vertex, backgrounds from both charmless B decays and charmed mesons produced at the PV are reduced to a negligible level. Background from B 0 → D Ã ð2010Þ − K þ decays is removed by requiring the reconstructed mass difference mD0 π − − mD0 not to be within AE4.8 MeV=c 2 of its known value [18] after assigning the pion mass to the kaon. To further distinguish signal from combinatorial background, a multivariate analysis based on a Fisher discriminant [35] is applied. The discriminant is optimized by maximizing the statistical significance of B 0 →D 0 π þ π − candidates selected in a similar way. The discriminant uses the following information: the smallest values of χ 2 IP and p T of the prompt tracks from the B-decay vertex; the B flight-distance significance; the Dχ 2 IP , and the signed minimum cosine of the angle between the direction of one of the prompt tracks from the B decay and theD 0 meson, as projected in the plane perpendicular to the beam axis.
Candidate B 0 ðsÞ →D 0 K þ K − decays with invariant masses in the range ½5000; 6000 MeV=c 2 are retained. After all selection requirements are applied, less than 1% of the events contain multiple candidates, and a single candidate is chosen based on the fit quality of the Band D-meson vertices and on the PID information of theD 0 decay products. The effect due to the multiple candidate selection is negligible [36].
The distribution of the invariant mass of the K þ K − pair, m K þ K − , shown in Fig. 2, is obtained from a narrow window, ½2m K ; 2m K þ 90 MeV=c 2 , covering the ϕ meson mass [18] and where m K is the known kaon mass. An extended unbinned maximum-likelihood fit to the invariant-mass distribution of the ϕ candidates, m K þ K − , is performed to statistically separate ϕ signal from background by means of the sPlot technique [37,38]. The ϕ meson invariant-mass distribution is modeled with a Breit-Wigner probability density function (PDF) convolved with a Gaussian resolution function. The width of the Breit-Wigner function is fixed to the known ϕ width [18]. The PDF for the background is a phase space factor p × q multiplied by a quadratic function ½1 þ ax þ bð2x 2 − 1Þ, where p and q are the momentum of the kaon in the K þ K − rest frame and the momentum of thē The parameters a and b are free to vary in the fit. The fit describes the data well (χ 2 =ndf ¼ 61=82). The yields determined by the fit are 427 AE 30 for the ϕ → K þ K − decay and 1152 AE 41 for the background. Figure 3 displays the sPlot-projected invariant-mass mass is used as the discriminating variable and it is only weakly correlated with the mD0 K þ K − invariant mass (less than 6%). A B 0 s →D 0 ϕ signal peak is visible at the B 0 s mass, while there is a statistically insignificant excess of B 0 →D 0 ϕ candidates at the B 0 mass. In the region below m B 0 s − m π 0 (up to resolution effects), a wider structure is visible and can be attributed to the vector-vector decay B 0 s →D Ã0 ½→D 0 π 0 =D 0 γϕ. An extended unbinned maximum-likelihood fit is performed to determine the number of B 0 and B 0 s decaying into theD 0 ϕ final state and that of the mode B 0 s →D Ã0 ϕ together with the value of the longitudinal polarization fraction f L . The B 0 s →D 0 ϕ mode is modeled by a Gaussian function, for which the mean value and resolution are free parameters. The B 0 signal is modeled by a Gaussian function with the same resolution as the B 0 s mode and a mean constrained with respect to that of the B 0 s signal using the known m B 0 s − m B 0 mass difference [18]. The B 0 s →D Ã0 ϕ signal is modeled by nonparametric PDFs, built from large simulated samples, using a kernel estimation technique [39]. Its shape, as a function of theD 0 K þ K − invariant-mass distribution, strongly depends on the polarization of the decay amplitude. Two extreme polarization configurations are considered: fully longitudinal (f L ¼ 1) or transverse (f L ¼ 0). A global PDF for each polarization (P long=trans ) is obtained as the average of the PDF of the two decays D Ã0 →D 0 π 0 =D 0 γ, weighted according to their relative branching fraction [18]. The total PDF for theD Ã0 ϕ signal is then modeled as the sum f L × P long þ ð1 − f L Þ × P trans . The residual background is accounted for with a first-order polynomial function. The yields obtained from this fit are The branching fractions of B 0 ðsÞ →D ðÃÞ0 ϕ are measured as where F is 1 for B 0 decays and f d =f s for B 0 s decays. In this ratio, the ratio between the signal and normalization modes is required. The efficiency and the number of selected signals for the normalization mode are: ϵðB 0 →D 0 π þ π − Þ¼ ð10.6AE0.3Þ×10 −4 and N B 0 →D 0 π þ π − ¼ 29 940 AE 240 (see Ref. [32] for details). The efficiency includes various  effects related to reconstruction, triggering and selection of the signal events. Efficiencies are determined from simulation with data-driven corrections applied. The efficiencies of the modes B 0 s →D 0 ϕ and B 0 →D 0 ϕ are statistically consistent and are equal to ϵðB 0 ðsÞ →D 0 ϕÞ ¼ ð11.1 AE 0.3Þ × 10 −4 . For the B 0 s →D Ã0 ϕ decay, the efficiency is obtained as the average of the four following sets of simulated events: fully transverse/longitudinal decays with the decaysD Ã0 →D 0 π 0 =D 0 γ, where the obtained f L ¼ ð73 AE 15Þ% and the branching fractions of theD Ã0 subdecays are used. The efficiency, after data corrections, is found to be ϵðB s →D Ã0 ϕÞ ¼ ð10.8 AE 0.1Þ × 10 −4 .
In the fit to the m K þ K − distribution, the background is modeled by a single set of parameters a and b. However, the background receives contributions from broad K þ K − Swave amplitudes, which could be different for the various B 0 ðsÞ →D ðÃÞ0 K þ K − modes. Since a full amplitude analysis is beyond the scope of this measurement, the following study is performed: the candidates shown in Fig. 2 are divided into three subsamples: B 0 s →D ðÃÞ0 ϕ-like candidates with mD0 K þ K − ∈½5000;5240∪½5310;5400MeV=c 2 , B 0 →D 0 ϕ-like candidates with mD0 K þ K − ∈ ½5240; 5310 MeV=c 2 , and combinatorial background candidates with mD0 K þ K − above 5400 MeV=c 2 . The parameters a and b of the quadratic background function are determined independently for the three subsamples and are found to be consistent with each other. Using the results from the fits to the three subsamples to describe the K þ K − background, pseudoexperiments are generated to produceD 0 K þ K − samples that mimic the data. The signal PDF for the B 0 ðsÞ → D ðÃÞ0 ϕ decays and the PDFs for various b -hadron decays are taken from the nominal fit to mD0 K þ K − as described in Ref. [32] are considered. The fits to the m K þ K − and mD0 ϕ distributions are then repeated to determine the pull distributions of N B 0 s →D 0 ϕ , N B 0 →D 0 ϕ , N B 0 s →D Ã0 ϕ and f L . The coverage tests perform as expected, except for N B 0 s →D 0 ϕ , for which the data uncertainty is overestimated by about 10%. No correction is applied for this overcoverage. While the fit is unbiased when using a single set of parameters to generate the K þ K − background, when allowing for different true values of a and b in the different mass regions a bias on the parameter N B 0 →D 0 ϕ is found and corresponds to an overestimation by 7 candidates. This is corrected for the computation of the branching fraction.
Potential sources of systematic uncertainty on the efficiencies are correlated and largely cancel in the quoted ratios of branching fractions. The main differences are related to the PID selection for the π þ π − and K þ K − pairs and to the hardware trigger. For each effect, a systematic uncertainty of 2% is computed, mainly from the PID calibration method and differences between the trigger response in data and simulation [32]. The uncertainty on the known value of Bðϕ → K þ K − Þ is 1% [18]. For the B 0 s modes, an uncertainty of 5.8% related to the fragmentation factor ratio f s =f d [40] is accounted for. The yield of the normalization mode is assigned a systematic uncertainty of 2%, where the main contributions are from the modeling of the signal and partially reconstructed background shapes [32].
Sources of systematic uncertainty on the determination of N B 0 ðsÞ →D ðÃÞ0 ϕ and f L are related to the fit model of the m K þ K − distribution and that of the fit to the weightedD 0 K þ K − invariant-mass spectrum. The weights from the fits are calculated and the B 0 ðsÞ →D ðÃÞ0 ϕ yields and f L are fitted with three different configurations: by varying the natural width of the ϕ meson by its uncertainty [18]; by replacing the quadratic part of the m K þ K − background PDF with a third-order Chebyshev polynomial; and by replacing the m K þ K − background PDF with an empirical function [41], where m 0 is fixed to 2m K and the parameters c, d and f are free to vary in the fit. The largest variations from the nominal model are taken as systematic uncertainties. For the fit to the invariant-mass distribution of theD 0 ϕ candidates, alternative models for B 0 ðsÞ →D 0 K þ K − and B 0 s →D Ã0 ϕ are considered: one changing the fit model of the B 0 ðsÞ →D 0 ϕ decays to that used to model B 0 ðsÞ →D 0 K þ K − , as described in Ref. [32], and others in which the PDFs of the fully transversally/longitudinally polarized B 0 s →D Ã0 ϕ decays are varied within the uncertainties on the ratio of branching fractions BðD Ã0 →D 0 π 0 Þ=BðD Ã0 →D 0 γÞ [18] and of the efficiencies obtained from simulation. Possible partially reconstructed background from the B 0 →D 0 ϕπ þ and B 0 s → D 0 ϕπ þ decays are also considered in the fit model. The resulting uncertainties are summed linearly assuming maximal correlation for this kind of systematic uncertainty and correspond to relative values of 4.7%, 31.1%, 5.4% and 4.9% on N B 0 s →D 0 ϕ , N B 0 →D 0 ϕ , N B 0 s →D Ã0 ϕ and f L , respectively. As the efficiencies depend on the signal decay-time distribution, the effect due to the different lifetimes of the B 0 s eigenstates [42] is considered and found to be 0.8%. When considering the ratio between BðB 0 s →D Ã0 ϕÞ and BðB 0 s →D 0 ϕÞ and the longitudinal polarization fraction f L , this systematic uncertainty is doubled to account for unknown strong phases between decay amplitudes and unknown fractions between different angular momenta. See supplemental material [43] for a summary of the various sources of systematic uncertainties.

ACKNOWLEDGMENTS
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (