Observation of tree-level B decays with $s\bar{s}$ Production from Gluon Radiation

We report on our search for $B^- \to D^{(*)+}_s K^- \pi^-$, $\bar{B^0} \to D_s^{(*)+} K_S^0 \pi^-$, and $B^- \to D^{(*)+}_s K^- K^-$ decays in 383 million $\FourS \to B \Bbar$ events collected by the Babar detector at the PEP2 asymmetric-energy $B$-factory. The decays proceed via a tree-level $b\to c$ quark transition in which a gluon radiates into an $s\bar{s}$ pair. Their branching fractions are measured to be ${\cal B}(B^- \to D^+_s K^- \pi^-) = (2.02 \pm 0.13_{stat} \pm 0.38_{syst}) \times 10^{-4},$ ${\cal B}(B^- \to D^{*+}_s K^- \pi^-)= (1.67 \pm 0.16_{stat} \pm 0.35_{syst}) \times 10^{-4},$ ${\cal B}(\bar{B^0} \to D_s^{+} K_S^0 \pi^-)= (0.55 \pm 0.13_{stat} \pm 0.10_{syst}) \times 10^{-4},$ and ${\cal B}(B^- \to D_s^{+} K^- K^-) = (0.11 \pm 0.04_{stat} \pm 0.02_{syst}) \times 10^{-4}$. Upper limits at the 90% C.L. are set on ${\cal B}(\bar{B^0} \to D_s^{*+} K_S^0 \pi^-)<0.55 \times 10^{-4}$ and ${\cal B}(B^- \to D_s^{*+} K^- K^-)<0.15 \times 10^{-4}$. We present evidence that the invariant mass distributions of $D^{(*)+}_s K^-$ pairs from $B^- \to D^{(*)+}_s K^- \pi^-$ decays are inconsistent with the phase-space model, suggesting the presence of charm resonances lying below the $D^{(*)+}_s K^-$ threshold.

We report on our search for B − → D PACS numbers: 13.25.Hw,12.15.Hh,11.30.Er Evidence for inclusive flavor correlated production of D + s in B − decays was reported recently [1] with a branching fraction of B(B − → D + s X) = (1.2 ± 0.4)% [2].Along with B − → D * + s X decays, these decays are mediated by a b → c quark transition and require at least three final state particles, including the production of an ss pair from the vacuum via radiative gluon pair production.Examples for three-body B − decays with a D  [3] despite their masses lying below the m(D s K) production threshold [4].In this case, it may be possible to measure the parameters of the res-onances such as their masses and widths, complementary to the analysis using B → Dππ decays [4].
Along with exclusive B − → D ( * )+ s X and B0 → D ( * )+ s X three-body decays, no decays proceeding via radiative gluon ss pair production at the tree level have hitherto been observed.Upper limits on the branching fractions of the S π − modes have been placed by ARGUS [5].In this paper we report first observations of the decay modes , and limits on the branching fractions of decays and compare it to the spectrum obtained from a phase-space model.
The analysis uses approximately 383 million Υ (4S) → BB events created by the PEP-II e + e − 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.
Candidates for D + s mesons are reconstructed in the modes D + s → φπ + , K * 0 K + , and S candidates are reconstructed from two oppositely-charged tracks that come from a common vertex displaced from the e + e − 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 − 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 , expected peaking background events n peaking with statistical uncertainties from fits of the mES distributions obtained using the D + s invariant mass sidebands, final signal (nsig) and background (n bkg ) yields with statistical uncertainties from mES fits adjusted to account for estimated peaking backgrounds, and cross-feed contributions, branching fractions B with statistical and systematic uncertainties, significances s(σ) calculated by comparing the likelihood maximum of the nominal fit to that of the fit with the signal yield fixed to the difference between the raw and corrected signal yields, and upper limits UL on the branching fractions for rate at the 5% level.The φ → K + K − , K * 0 → K − π + and K 0 S → π + π − candidates are required to have invariant masses within ±15 MeV/c 2 , ±50 MeV/c 2 and ±10 MeV/c 2 of their nominal masses, respectively [9].The full polarization of the K * 0 and φ mesons from the D + s decays are exploited to reject backgrounds through the use of the helicity angle θ H , defined as the angle between the K − momentum vector and the direction of flight of the D + s in the K * 0 or φ rest frame.The K * 0 and φ candidates are required to have | cos θ H | greater than 0.5.Finally, the B meson candidates are formed using the reconstructed combinations of , and D * + s K − K − .The background from continuum q q production (where q = u, d, s, c) 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 effectively exploit the difference between the shapes of e + e − → B B and e + e − → 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 mass m ES ≡ E * 2 b − ( i p * i ) 2 and the energy difference , where E * b 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 |∆E| < 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.The estimated B reconstruction efficiencies, excluding the subsequent branching fractions, 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, √ s is the total energy of the beams in their center of mass frame, and ξ 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 |∆E| < 25 MeV similar to the reconstructed signal candidates.This peaking background is due to charmless and charmonium B decays with the same set of particles as signal in the final state.The peaking contribution is evaluated using the data by reconstructing s " candidates are selected from 25 -40 MeV/c 2 sidebands around the D + s nominal mass.In this procedure, we use the same selection requirements as for the signal except that "D + s " candidates are not mass constrained.Studies revealed that constraining the D + s mass did not significantly affect the resolutions of m ES and ∆E distributions and that events in the D + s mass sidebands are a good representation of the background under the D + s peak.Table I shows the fit yields of the peaking background contribution under the m ES peak 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 (ML) fit to the m ES distributions using the candidates from all D + s decay modes combined.The m ES distributions are fit with the sum of two functions: f (m ES ) characterizing the combinatorial background and a Gaussian function to describe the signal.The likelihood function is given by: where P sig i and P bkg i are the probability density functions for the 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 The final signal yields 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 since these values are consistent with zero although their errors are still propagated.The final values are given in the n sig column of Table I.The total signal yield in each B decay mode is related to the B branching fraction B using the following expression:  where N B B is the number of produced B B pairs, B i is the product of the intermediate branching ratios, ε i is the reconstruction efficiency (from Table I) and the sum is over D + s modes (i = φπ + , K * 0 K + , K 0 S K + ).As an input to the calculations, we used branching fraction numbers from [9].The results of these calculations are summarized in Table I.For the B 0 → D * + s K 0 S π − and B − → D * + s K − K − decay modes, the upper limits are set using a frequentist approach [9] and taking into account the systematic uncertainties.The upper limits are summarized in Table I.
Studies of the invariant mass spectra of the D reveal distributions incompatible with those of three-body phase space.As shown in Figure 3, there are enhancements in the number of events at the lower ends of the m(D ( * )+ s K − ) spectra.These enhancements suggest the presence of charm resonances lying below the D are observed for the first time each with significance greater than 5σ.Evidence for B − → D + s K − K − was found with a significance slightly greater than 3σ.Upper limits are set on the branching fractions of the two decay modes with significances lower than 2σ: this may be due to the W-exchange diagram correction to the neutral mode and the color-suppressed contribution to the charged mode.s K − π − (right) decay modes using the data.A requirement of mES > 5.270 GeV/c 2 is applied to the events shown in the figure, in addition to the signal selection described in the text.Combinatoric background is approximated and then subtracted using events outside the mES signal region (mES < 5.265 GeV/c 2 ).The histogram shows the non-resonant signal MC events distribution, scaled to the number of events in the data signal region.
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.This work is supported by DOE and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG (Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MIST (Russia), MEC (Spain), and STFC (United Kingdom).Individuals have received support from the Marie Curie EIF (European Union) and the A. P. Sloan Foundation.

FIG. 1 :
FIG. 1: Feynman diagram for B − → D ( * )+ s K − π − .In addition to the dominant diagram, B − → D ( * )+ s K − π − can occur via the color-suppressed diagram where the constituent ū's of the K − and π − are switched.Although a color-suppressed contribution does not exist for B0 → D ( * )+ s K0 π − , a sub-dominant contribution from a W -exchange diagram with ss and d d popping may exist instead.Either of these contributions could cause a deviation from the naive expectation of two for the ratio of B − → D ( * )+ s K − π − to B 0 → D ( * )+ s K 0 S π − branching fractions.The D ( * ) s -K pair could come from intermediate charm resonances instead of directly from the B. It has been proposed that these resonances can play a significant role in B− → D + s K − π − decays[3] despite their masses lying below the m(D s K) production threshold[4].In this case, it may be possible to measure the parameters of the res- The D * + s candidates are reconstructed in the mode D * + s → D + s γ.The photons are accepted if their energy is greater than 100 MeV.Photons from D * + s candidates are rejected if, when combined with any other photon having an energy greater than 150 MeV, they belong to a photon pair whose invariant mass lies within ±10 MeV/c 2 of the π 0 mass.The D + s candidates are required to have invariant masses in the interval ±10 MeV/c 2 of the nominal D + s mass while the invariant masses of D * + s candidates lie in the range from m(D * + s ) − 15 MeV/c 2 to m(D * + s ) + 10 MeV/c 2 .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 B 0 → D ( * )+ s D − , D − → K 0 S π − events from the B 0 → D ( * )+ s K 0 S π − samples, the invariant mass of the K 0 S and π − must be outside a 40 MeV/c 2 window around the D − mass.

FIG. 2 :
FIG.2: mES spectra for theB − → D + s K − π − (top left), B − → D * + s K − π − (top right), B 0 → D + s K 0 S π − (middle left), B 0 → D * + s K 0 S π − (middle right), B − → D + s K − K − (bottom left),and B − → D * + s K − K − (bottom right).Solid curves show the fit results, as explained in the text.Dashed lines in the signal regions correspond to the peaking and non-peaking background components of the fit.The data are the points with error bars.
FIG.2: mES spectra for theB − → D + s K − π − (top left), B − → D * + s K − π − (top right), B 0 → D + s K 0 S π − (middle left), B 0 → D * + s K 0 S π − (middle right), B − → D + s K − K − (bottom left),and B − → D * + s K − K − (bottom right).Solid curves show the fit results, as explained in the text.Dashed lines in the signal regions correspond to the peaking and non-peaking background components of the fit.The data are the points with error bars.
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 and in the data (estimated using the control modeB − → D − s D 0 , D → K − π + ) contributeto the systematic uncertainty (5% − 10%) as does the efficiency dependence on the D ( * )+ s K − invariant mass spectrum (7% − 9%).In the m ES fits of the lower statistics modes (D * + s K 0 S π − and D * + s K − K − ) the signal Gaussian parameters and √ s in f (m ES ) are fixed to ensure fit con-vergence.The associated systematic uncertainties are 14% and 9%, respectively.The entries in the cross-feed matrix affecting the D ( * )+ s K − K − modes vary by 8%(5%) when they are calculated with MC events weighted according to the observed spectra of the D ( * )+ s K − invariant mass.

K
FIG. 3:D ( * )+ s K − invariant mass spectra for the B − → D + s K − π − (left) and B − → D * + s K − π −(right) decay modes using the data.A requirement of mES > 5.270 GeV/c 2 is applied to the events shown in the figure, in addition to the signal selection described in the text.Combinatoric background is approximated and then subtracted using events outside the mES signal region (mES < 5.265 GeV/c 2 ).The histogram shows the non-resonant signal MC events distribution, scaled to the number of events in the data signal region.

TABLE I :
Summary of results for the total detection efficiencies ε excluding the subsequent branching fractions of D