Observation of tree-level B decays with ss production from gluon radiation.

We report on our search for decays proceeding via a tree-level b ! c quark transition in which a gluon radiates into an s (cid:1) s pair. We present observations of the decays B (cid:1) ! D (cid:2)(cid:3)(cid:4)(cid:5) s K (cid:1) (cid:1) (cid:1) and (cid:1) B 0 ! D (cid:5) s K 0 S (cid:1) (cid:1) and evidence for B (cid:1) ! D (cid:5) s K (cid:1) K (cid:1) and set upper limits on the branching fractions for (cid:1) B 0 ! D (cid:3)(cid:5) s K 0 S (cid:1) (cid:1) and B (cid:1) ! D (cid:3)(cid:5) s K (cid:1) K (cid:1) using 383 (cid:6) 10 6 (cid:2) (cid:2) 4 S (cid:4) ! B (cid:1) B events collected by the BABAR detector at SLAC. We present evidence that the invariant mass distributions of D (cid:2)(cid:3)(cid:4)(cid:5) s K (cid:1) pairs from B (cid:1) ! D (cid:2)(cid:3)(cid:4)(cid:5) s K (cid:1) (cid:1) (cid:1)

We report on our search for decays proceeding via a tree-level b ! c quark transition in which a gluon radiates into an s s pair. We present observations of the decays B ÿ ! D s K ÿ ÿ and B 0 ! D s K 0 S ÿ and evidence for B ÿ ! D s K ÿ K ÿ and set upper limits on the branching fractions for B 0 ! D s K 0 S ÿ and B ÿ ! D s K ÿ K ÿ using 383 10  Evidence for inclusive flavor correlated production of D s in B ÿ decays was reported recently [1] with a branching fraction of BB ÿ ! D s X 1:2 0:4% [2]. These decays, along with B ÿ ! D s X, are mediated by a b ! c quark transition and the production of an s s pair from the vacuum via radiative gluon pair production resulting in at least three final state particles. Examples for three-body B ÿ decays with a D s in the final state are B ÿ ! D s K ÿ ÿ . The dominant Feynman diagram for these decays is shown in Fig. 1. The corresponding B 0 decays are B 0 ! D s K 0 ÿ . By replacing the ÿ in Fig. 1 [3] despite their masses lying below the mD s K production threshold [4]. In this case, it may be possible to measure the parameters of the resonances such as their masses and widths, complementary to the analysis using B ! D decays [4]. No exclusive decays proceeding via radiative gluon s s pair production at the tree level have hitherto been observed. Upper limits on BB ÿ ! D s K ÿ ÿ and B B 0 ! D s K 0 S ÿ have been placed by ARGUS [5]. In this Letter we report first observations of the decay We also present D s K ÿ invariant mass distributions from B ÿ ! D s K ÿ ÿ decays and compare them to the spectra obtained from a phasespace model.
The analysis uses approximately 383 10 6 4S ! B B events created by the PEP-II e e ÿ collider and collected by the BABAR detector. The BABAR detector is described elsewhere [6].
Optimal selection criteria and probability density functions of selection variables are determined by an analysis based on Monte Carlo (MC) simulation of both signal and background events. We use GEANT4 [7] software to simulate interactions of particles traversing the BABAR detector, taking into account the varying detector conditions and beam backgrounds. We verify with MC simulation that resolutions and background levels correctly describe the data.
Candidate D s mesons are reconstructed in the modes D s ! , K 0 K , and K 0 S K , with ! K K ÿ , K 0 ! K ÿ , and K 0 S ! ÿ . The K 0 S candidates are reconstructed from two oppositely charged tracks coming from a common vertex displaced from the e e ÿ interaction point. We require the significance of this displacement (the measured K 0 S flight distance divided by its estimated error) to exceed 2. All other tracks are required to originate less than 1.5 cm away from the e e ÿ interaction point in the transverse plane and less than 10 cm along the beam axis. Charged kaon candidates must satisfy identification criteria that are typically around 92% efficient [8], depending on momentum and polar angle, and have a pion misidentification rate at the 5% level. The ! K K ÿ , K 0 ! K ÿ , and K 0 S ! ÿ candidates are required to have invariant masses within 15, 50, and 10 MeV=c 2 of their nominal masses, respectively [9].
The full polarization of the K 0 and mesons from the D s decays is exploited to reject backgrounds through the use of the helicity angle H , defined as the angle between the K ÿ momentum vector and the direction of flight of the D s in the K 0 or rest frame. The K 0 and candidates are required to have j cos H j > 0:5.
The All D s candidates are subjected to a mass-constrained fit after selection. The invariant mass of the D s is calculated after the mass constraint on the daughter D s has been applied. Subsequently, all D s candidates are subjected to mass-constrained fits. To eliminate S ÿ invariant mass must be outside a 40 MeV=c 2 window around the D ÿ mass.
Finally, the B meson candidates are formed using the reconstructed combinations of is suppressed based on the event topology. The event shape variables, R 2 (the ratio of the second to zeroth Fox-Wolfram moments [10]) and L 2 =L 0 (the ratio of the second and zeroth angular moments of the energy flow about the B thrust axis [11]), are combined in a Fisher discriminant (F ) to exploit the difference between the shapes of e e ÿ ! B B and e e ÿ ! q q events. A selection is applied to F such that 80% of continuum background is rejected while maintaining 80% signal efficiency.
The signals are extracted using the energy-substituted is the beam energy in the laboratory frame, p i is the momentum of the daughter particle i of the B meson candidate also in the laboratory frame, and m i is the mass hypothesis for particle i. For signal events, m ES peaks at the B meson mass with a resolution of about 2:6 MeV=c 2 and E peaks near zero with a resolution of 13 MeV. The B candidates are required to have jEj < 25 MeV and m ES > 5:2 GeV=c 2 . After all selection criteria are applied, we find the fraction of events containing more than one B candidate to be between 3% and 11% depending on the decay mode. In these instances, the B candidate with E closest to zero is chosen. Estimated B reconstruction efficiencies are shown in Table I.
Background events that pass these selection criteria are represented by approximately equal amounts of q q continuum and B B events. We parametrize their m ES distributions by a threshold function [12]: where x 2m ES = s p , s p is the total energy of the beams in their center of mass frame, and is a fit parameter.
A study using simulated B decays reveals significant numbers of background events peaking in the regions of 5:272 < m ES < 5:288 GeV=c 2 and jEj < 25 MeV similar to the reconstructed signal candidates. This peaking background is due to charmless and charmonium B decays with the same sets of final state particles as signal. The peaking contribution is evaluated using data by reconstructing  Table I shows the fit yields of peaking background contributions under the m ES peaks for each mode.
A matrix is constructed to study the cross feed between the signal modes. Its elements describe the contributions of each mode according to the levels seen in MC samples. No off-diagonal element of the cross-feed matrix exceeds 2%; this near-diagonal structure indicates effective suppression of the cross-feed contributions by application of the selection criteria. Figure 2 shows the m ES spectra of the reconstructed B candidates. For each mode, we perform an extended unbinned maximum likelihood fit to the m ES distributions using candidates from all D s decay modes combined. The distributions are then fit with the sum of two functions: where P sig i and P bkg i are the probability density functions for signal and background, n sig and n bkg are the number of signal and background events, and N is the total number of events in the fit.
Final signal yields (column n sig of Table I) are obtained by subtracting the estimated peaking background and cross-feed contributions from the yields of the m ES fits described in the preceding paragraph. No peaking background is subtracted from modes that have n peaking less than zero in Table I because these values are consistent with zero. However, their errors are still propagated. The total signal yield in each B decay mode is related to the B branching fraction by B n sig =N B B is the number of produced B B pairs, B i is the product of the intermediate branching ratios, " i is the reconstruction efficiency (from Table I), and the sum is over D s modes (i , K 0 K , K 0 S K ). As an input to the calculations, we used branching fraction numbers from [9]. Results are summarized in Table I. The total relative systematic uncertainty in the B branching fractions is estimated to be approximately 19%-25% depending on the decay mode. The largest contribution, an uncertainty of 15%, comes from the D s branching fractions. The differences between selection efficiencies in MC simulation and in the data (estimated using the control mode B ÿ ! D ÿ s D 0 , D 0 ! K ÿ ) contribute to the sys-tematic uncertainty (5%-10%) as does the efficiency dependence on the D s K ÿ invariant mass spectrum (7%-9%). In the m ES fits of the lower statistics modes (D s K 0 S ÿ , D s K ÿ K ÿ ) the signal Gaussian parameters and s p in fm ES are fixed to ensure fit convergence. The associated systematic uncertainties are 14% and 9%, respectively. The cross-feed matrix elements affecting the D s K ÿ K ÿ modes vary by 8% (5%) when estimated with MC events weighted according to the observed spectra of the D s K ÿ invariant mass. The invariant mass spectra of the D s K ÿ system in B ÿ ! D s K ÿ ÿ reveal distributions incompatible with those of three-body phase space. As shown in Fig. 3, there are enhancements in the number of events at the lower ends of the mD s K ÿ spectra, suggesting the presence of charm resonances lying below the D s K ÿ threshold [3]. In summary, B ÿ ! D s K ÿ ÿ , B ÿ ! D s K ÿ ÿ , and B 0 ! D s K 0 S ÿ decays are observed for the first time each with a significance greater than 5. Evidence for B ÿ ! D s K ÿ K ÿ is found with a significance slightly greater than 3. For channels with significances lower than 2, upper limits are set on B B 0 ! D s K 0 S ÿ and B B 0 ! D s K 0 S ÿ using a frequentist approach [9] and taking into account the systematic uncertainties. The ratios BB ÿ ! D s K ÿ K ÿ =BB ÿ ! D s K ÿ ÿ are consistent with the expected Cabibbo suppression. That B B 0 ! D s K 0 S ÿ is less than half of BB ÿ ! D s K ÿ ÿ may be due to the W-exchange diagram correction to the neutral mode and the color-suppressed contribution to the charged mode.
We are grateful for the excellent luminosity and machine conditions provided by our PEP-II colleagues, and for the substantial dedicated effort from the computing organizations that support BABAR. The collaborating institutions wish to thank SLAC for its support and kind hospitality.