Search for $B_{s}^{0} \rightarrow \eta^{\prime} X_{s\bar{s}}$ at Belle using a semi-inclusive method

We report the first search for the penguin-dominated process $B_{s}^{0} \rightarrow \eta^{\prime} X_{s\bar{s}}$ using a semi-inclusive method. A 121.4 $\mathrm{fb}^{-1}$ integrated luminosity $\Upsilon(5S)$ data set collected by the Belle experiment, at the KEKB asymmetric-energy $e^+e^-$ collider, is used. We observe no statistically significant signal and including all uncertainties, we set a 90\% confidence level upper limit on the partial branching fraction at 1.4 $\times$ 10$^{-3}$ for $M(X_{s\bar{s}})$ $\leq$ 2.4 GeV/$c^{2}$.

We report the first search for the penguin-dominated process B 0 s → η Xss using a semi-inclusive method.A 121.4 fb −1 integrated luminosity Υ(5S) data set collected by the Belle experiment, at the KEKB asymmetric-energy e + e − collider, is used.We observe no statistically significant signal and, including all uncertainties, we set a 90% confidence level upper limit on the partial branching fraction at 1.4 × 10 −3 for M (Xss) ≤ 2.4 GeV/c 2 .
The study of the decay of B mesons -bound states of a b antiquark and either a u, d, s, or c quark -has been fruitful for the interrogation of rare processes, elucidating the strong and weak interactions of the Standard Model (SM) of particle physics.According to the SM flavorchanging neutral currents are forbidden in B decays at leading-order, but may effectively occur at higher-order in "penguin" ∆B = 1 processes, where B is the beauty quantum number [1].
Inclusive b → sg processes have not yet been investigated using the B 0 s meson.We report the first search for the decay B 0 s → η X ss using a semi-inclusive method [15] with data collected at the Υ(5S) resonance by the Belle detector at the KEKB asymmetric-energy e + e − collider in Japan [16].
To lowest order, the amplitude for B 0 s → η X ss contains contributions from QCD penguin diagrams [17], the anomalous gη coupling, the tree-level color-suppressed b → u diagram, and the b → s(γ, Z) electroweak penguin diagrams, shown in Fig. 1.Contributions from penguin annihilation diagrams are typically omitted as they are suppressed by a factor of Λ QCD /m b , where Λ QCD is the quantum chromodynamic scale and m b is the mass of the beauty quark [18].
The Belle detector is a large-solid-angle magnetic spectrometer that consists of a silicon vertex detector (SVD), a 50-layer central drift chamber (CDC), an array of aero- The rates are 87.0%,7.3%, and 5.7%, respectively [20].This corresponds to (7.11 ± 1.30) × 10 6 B 0 s B0 s pairs, the world's largest Υ(5S) sample in e + e − collisions.A blind analysis is performed, whereby the selection criteria are first optimized on Monte Carlo (MC) simulations before being applied to the data.A signal MC sample for B 0 s → η X ss is generated using EvtGen [21] and the detector response is simulated using GEANT3 [22], with PHOTOS describ-ing final-state radiation [23].The MC-generated mass of the X ss system is bounded below by the two-(charged) kaon mass 0.987 GeV/c 2 and has an upper bound of 3.0 GeV/c 2 .The X ss mass is generated as a flat distribution and is fragmented by Pythia 6 [24].The flat distribution reduces model dependence and allows for an analysis that does not depend on the X ss mass distribution.The B 0 s ( bs) and B0 s (bs) candidates are reconstructed using a semi-inclusive method in which the X ss is reconstructed as a system of two kaons, either K + K − or K ± K 0 S (→ π + π − ), and up to four pions with at most one π 0 , where the π 0 decays via the channel π 0 → γγ.The η is reconstructed in the channel η → η(→ γγ)π + π − .The experimental signature is divided into two classes of decay modes: without (B 0 s → η K + K − + nπ) and with (B 0 s → η K ± K 0 S + nπ) a K 0 S .These classes are analyzed separately, with the weighted average BFs taken at the end.Charge-conjugate decays are included unless explicitly stated otherwise.
Charged particle tracks are required to satisfy loose impact parameter requirements to remove mismeasured tracks [15], and have transverse momenta p T greater than 50 MeV/c.Separation of the charged kaons and charged pions is provided by the CDC [25], ACC [26], and the TOF [27] systems.Information from these subdetectors is combined to form a likelihood ratio for the charged kaon hypothesis: For this analysis, the selections P K ± > 0.6 for K ± and P K ± < 0.6 for π ± are applied.The efficiency to correctly identify a pion (kaon) is 98% (88)%, with a misidentification rate of 4% (12)% [5].
The π 0 candidate mass range is M (γγ) ∈ [0.089, 0.180] GeV/c 2 (±5σ window).The π 0 candidates are kinematically constrained to the nominal mass [28].In the ECL, the photons constituting the π 0 are required to have energies greater than 50 MeV in the barrel region, greater than 100 MeV in the endcaps, and the ratio of their energy depositions in a 3×3 ECL crystal array to that in a 5×5 crystal array around the central crystal, is required to be greater than 0.9.To further reduce combinatorial background, a requirement on the π 0 laboratory-frame momentum to be greater than 0.2 GeV/c is imposed.
The η is reconstructed in a two-photon asymmetric invariant mass window M η ∈ [0.476, 0.617] GeV/c 2 (4.5σL , 9.2σ R , from signal MC samples, after all final selections are applied), where L and R refer to the left and right sides of the mean of the mass distribution.The asymmetry is due to energy leakage in the ECL, causing the η mass distribution to be asymmetric.Each photon is required to have E γ > 0.1 GeV.A requirement on the photon-energy asymmetry ratio |E γ1 − E γ2 |/(E γ1 + E γ2 ) < 0.6 is applied to further suppress the background.The η mesons are reconstructed in a maximally efficient mass window M η ∈ [0.933, 0.982] GeV/c 2 (approximately ±7.0σ, from signal MC samples, after all final selections are applied).The η and η masses are kinematically fit to the world average [28].The mass range of the K 0 S is M K 0 S ∈ [0.487, 0.508] GeV/c 2 (±3σ window).The X ss system is reconstructed as a system of kaons and pions, which is in turn combined with the η to form B s candidates.Two variables important in extracting the signal are the energy difference ∆E, defined as ∆E = E Bs − E beam and the beam-energy-constrained mass, defined as M bc = E 2 beam /c 4 − p 2 Bs /c 2 , where E beam = √ s/2, E Bs is the energy of the B s , and p Bs is the magnitude of the B s three-momentum in the CM frame of the colliding e + e − beams.
The dominant nonpeaking background is from continuum with others coming from generic B 0( * ) s B0( * ) s and B BX decays.An initial reduction in continuum background (e + e − → q q, q = u, d, s, c) is done with a selection on the ratio of the second to the zeroth order Fox-Wolfram moments R 2 ≤ 0.6 [29].A neural network (NN), NeuroBayes [30], is used to further suppress continuum background, with other backgrounds being reduced as well.The NN is trained to primarily discriminate between event topologies using event shape variables [31].Signal events have a spherical topology, while continuum background events are jetlike.The NN is trained using these variables on independent signal and continuum background MC simulations.The NN output variable O NN describes, effectively, the probability that a B 0 s candidate came from an event whose topology is spherical or jetlike.
To obtain a specific O NN selection, the figure-of-merit (FOM) S/ √ S + B is optimized as a function of O NN , where S and B are the fitted signal and background yields from an MC sample that is passed through the trained network.This MC contains an approximately dataequivalent background and an enhanced signal.This was done assuming B(B 0 s → η X ss ) = 2×10 −4 ; this is 1.6 standard deviations below the BABAR central value for B → η X s .The value of O NN corresponding to the maximum value of the FOM is selected.Events having O NN values below this selection are rejected.Separate optimizations are done for B 0 s → η K + K − + nπ and B 0 s → η K ± K 0 S + nπ, which have substantially different background levels and efficiencies.The NN requirement reduces continuum background by more than 97% in both cases, while preserving 39% and 53% of signal events for After an initial requirement of M bc > 5.30 GeV/c 2 , |∆E| < 0.35 GeV, and M (X ss ) ≤ 2.4 GeV/c 2 , and after all final selections are applied, there are an average of 6.4 candidates per event for B 0 s → η K + K − + nπ and 26.0 for B 0 s → η K ± K 0 S + nπ.To select the best candidate per event, the candidate with the smallest χ 2 given by , where ∆E is calculated on a candidate-by-candidate basis, and µ ∆E is the mean energy difference of the ∆E distribution, obtained through studies of signal MC of individual exclusive B 0 s → η X ss decay modes; σ ∆E is the width of these distributions.Here χ 2 vtx /ndf is the reduced χ 2 from a successful vertex fit of the primary charged daughter particles of the X ss .From signal MC, the efficiency of the best candidate selection is 85.5% for B 0 s → η K + K − +nπ and 43.2% for B 0 s → η K ± K 0 S + nπ, in the signal region.The fraction of B 0 s candidates passing best candidate selection that are correctly reconstructed is 94.0% for B 0 s → η K + K − +nπ and 60.4% for B 0 s → η K ± K 0 S +nπ.These numbers are obtained after all final selections are applied.
Other backgrounds were studied as sources of potential peaking background.Due to the signal final state, it is difficult to have backgrounds that will be equivalent in topology and strangeness, and that are not highly suppressed.However, one such unmeasured mode is Reconstruction efficiency is estimated using MC events and an expected number of peaking events is determined.For B 0 s → η D s π the BF is assumed to be similar to B 0 → D − π + ρ 0 , for which the world average is [1.1 ± 1.0] ×10 −3 [28].After applying all final selections, the total number of expected peaking events is less than one.There is a negligible amount of peaking background based on studies of B 0 (s)

B0
(s) MC samples.The decay B → η K * 0 can contribute to peaking background if the pion from K * 0 → K − π + is misidentified.The world average BF is [2.8 ± 0.6] ×10 −6 [28].From this and the pion misidentification rate, we expect the background contribution from this mode to be negligible.
The Υ(5S) has three channels for B 0 s decays: Υ(5S) s .The corresponding rates are 87.0%,7.3%, and 5.7%, respectively [20].The low-energy photon from B 0 * s → B 0 s γ is not reconstructed.This has the effect of shifting the mean of the ∆E distribution to a value of approximately −50 MeV.As a result, there are three signal peaks in the beam-energy-constrained mass distribution.
The signal in beam-energy-constrained mass is modeled as the sum of three Gaussian probability density functions (PDFs) that correspond to the three Υ(5S) decays described above.Their shape parameters (means and widths of the signal Gaussians) are determined from a B 0 s → D − s ρ + data control sample and are fixed in the fit to data.The nonpeaking background fit component is an ARGUS PDF [32] with a fixed shape parameter, determined from fits to Υ(5S) data NN sidebands.The ARGUS endpoint is fixed at 5.434 GeV/c 2 , the kinematic limit of M bc .The full model is the sum of the signal and background PDFs, with the signal and background yields allowed to float.
The signal reconstruction efficiency, defined as i = N rec i /N gen i , is determined from fitting signal MC sample, in each X ss mass bin i after all selections are applied.Here, , is the number of generated B 0 s mesons in the signal MC sample.The quantity N other i is the number of generated B 0 s mesons that do not belong to either of the two classes of signal modes: is the number of events found from the Gaussian signal fit in the ith X ss mass bin.
The BF is calculated as , where i denotes the mass bins of X ss , the i are the bin-by-bin MC signal reconstruction efficiencies i , corrected for data-MC discrepancies in NN selection, best candidate selection, particle identification, tracking efficiency, η → γγ reconstruction, π 0 → γγ reconstruction, and K 0 S → π + π − reconstruction.The quantity N sig i is the number of fitted signal events and the quantity s pairs.Figures 2 and 3 show the sum of the fits, whose results are listed in Tables I and II, respectively, overlaid on the data.The central value for B(B 0 s → η X ss ) is estimated to be the weighted average of the total BF central values for B 0 s → η K + K − +nπ and B 0 s → η K ± K 0 +nπ.These are obtained by summing the BFs listed in Tables I and II, for B 0 s → η K + K − + nπ and B 0 s → η K ± K 0 + nπ, respectively.The weights for the average central value are obtained from the statistical uncertainties.
The dominant uncertainties are due to the X ss fragmentation.Other systematic uncertainties include neural network selection, uncertainties related to track finding and identification, best candidate selection, neutral meson reconstruction, subdecay branching fractions, Υ(5S) production models, and the number of B 0 s B0 s pairs.A detailed discussion of the uncertainties is given in the accompanying appendix.Systematic uncertainties are added in quadrature; fragmentation model (FM) [34] uncertainties are added linearly within a class and for the final weighted average, these class sums are added in quadrature.
The statistical significance in each X ss mass bin is calculated as S = −2 ln(L 0 /L max ), where L 0 is the likelihood at zero signal yield and L max is the maximum likelihood.No statistically significant excess of events is observed in any X ss mass bin.We set an upper limit on the partial BF (a BF with the requirement M (X ss ) ≤ 2.4 GeV/c 2 ) at 90% confidence level by integrating a Gaussian likelihood function whose standard deviation is estimated by the sum in quadrature of the positive statistical and systematic uncertainties.The standard deviation, σ, is approximately 8.6 × 10 −4 .The integral is restricted to the physically allowed region above zero, giving an upper limit on B(B 0 s → η X ss ).As a result, 1.68σ is added to the weighted average central value to obtain the 90% confidence level upper limit.FIG. 2. Sum of the fits to all M (Xss) bins overlaid on the M bc distribution, for the decay B 0 s → η (→ ηπ + π − )Xss for B 0 s → η K + K − + nπ submodes and M (Xss) ≤ 2.4 GeV/c 2 and with all selections applied.The light blue shaded region is the sum of the background fits, the red shaded region is the sum of the signal fits, and the black dashed curve is the sum of the two.FIG. 3. Sum of the fits to all M (Xss) bins overlaid on the M bc distribution, for the decay B 0 s → η (→ ηπ + π − )Xss for B 0 s → η K ± K 0 S + nπ submodes and M (Xss) ≤ 2.4 GeV/c 2 and with all selections applied.The light blue shaded region is the sum of the background fits, the red shaded region is the sum of the signal fits, and the black dashed curve is the sum of the two.TABLE I. Results for the B 0 s → η K + K − + nπ submodes, from the 121.4 fb −1 Υ(5S) data set; the table contains the M (Xss) bin in units of GeV/c 2 , corrected reconstruction efficiency ( ), number of fitted signal events Nsig, and B, the central value of the partial BF.)] × 10 −4 for M (X ss ) ≤ 2.4 GeV/c 2 .The FM uncertainty is obtained by considering alternate sets of X ss fragmentation parameter values in Pythia and redetermining the signal reconstruction efficiency [35].
As a by-product of the preceding measurement, we searched for the decay B 0 s → η φ, with φ → K + K − .This decay was searched for in the X ss mass subrange M (X ss ) ∈ [1.006, 1.03] GeV/c 2 (±3σ window).From MC simulations, the reconstruction efficiency is determined to be 7.90 ± 0.03%.No statistically significant signal is found and the upper limit at 90% confidence level is determined to be 3.6×10 −5 .The result from fitting is shown in Fig. 4. LHCb determines the upper limit at 90% confidence level to be 8.2×10 −7 [36].

decay results for M(Xss) ∈ ±3σ φ mass range
To conclude, we set an upper limit on the partial BF for the decay B 0 s → η X ss , for M (X ss ) ≤ 2.4 GeV/c 2 .Including all uncertainties, the upper limit at 90% confidence level is determined to be 1.4 × 10 −3 .This is the first result for the inclusive decay B 0 s → η X ss and should motivate further studies, both experimental and theoretical, of inclusive B 0 s meson processes and SU (3) symmetries.

Appendix: DISCUSSION OF SYSTEMATIC UNCERTAINTIES
The upper limits at 90% confidence level up to a given X ss mass bin are given in Table III.

TABLE III. B 90%
U L ≤ M (Xss) 90% upper limits.Upper limit per bin corresponds to the upper limit up to and including that bin in units of M (Xss).Additive systematic uncertainties are from the PDF parameterization and fit bias.The parameters of the Gaussian signal PDF are allowed to float within their 1σ errors (determined from the B 0 s → D − s ρ + control fit to the Υ(5S) data) and the Υ(5S) data are refitted for the signal yield.The difference in signal yield between the fixed and floated parameterization is taken as the PDF uncertainty.The same is done for the background ARGUS PDF.
The fit bias uncertainty is determined by generating and fitting 5000 MC pseudoexperiments for several assumptions of the branching fraction.This is done using RooStats [37].The number of fitted signal events versus the number of generated signal events is fitted with a first-order polynomial and the offset from zero of the fit along the y-axis is taken as the uncertainty due to fit bias.The fit bias uncertainty is less than one event.The PDF and fit bias uncertainties are added in quadrature for a total additive systematic uncertainty.This is combined with the statistical errors and quoted as the first uncertainty in Tables I and II in the main report.For B 0 s → η K ± K 0 S + nπ, an uncertainty of 1.1 (26% of the fitted, positive statistical uncertainty) and 1.3 (34%) events are obtained in X ss mass bins 1.8 -2.0 GeV/c 2 and 2.0 -2.2 GeV/c 2 , respectively.All others had uncertainties of less than one event.For B 0 s → η K + K − + nπ, the 1.6 -1.8 GeV/c 2 , 1.8 -2.0 GeV/c 2 , 2.0 -2.2 GeV/c 2 , and 2.2 -2.4 GeV/c 2 bins have uncertainties of 1.0 (55%), 1.2 (54%), 3.1 (156%), and 3.0 (132%) events, respectively.All other mass bins each have an uncertainty of less than one event.Additive systematic uncertainties are added in quadrature with the asymmetric fit errors on the signal yield.
Multiplicative systematic uncertainties due to the fragmentation model (FM) of X ss by Pythia 6 [24] are obtained by varying a group of Jetset parameters -PARJ (1,2,3,4,11,12,13,25,26), described in Table s vs u, d quark suppression PARJ (3) s quark further suppression PARJ (4) spin-1 diquark suppression vs spin-0 diquarks PARJ (11) probability of spin-1 light mesons PARJ (12) probability of spin-1 strange meson PARJ(13) probability of spin-1 meson with c or heavier quark PARJ (25) η suppression factor PARJ (26) η suppression factor IV -which are varied together away from the standard Belle default to reduce and enhance the (uncorrected) reconstruction efficiency, giving two sets of parameters for each X ss bin.These alternative tunings ("AT") are given in Table V.They are motivated by the parameter studies in other inclusive B analyses [5,[38][39][40][41].The uncertainty is determined from the fractional change in efficiency with respect to the Belle default parameters.This procedure includes the effect of the change in the proportion of unreconstructed modes.If no increase or decrease in efficiency is found then an uncertainty of zero is assigned.Values for the FM uncertainty, in each X ss mass bin, are given in Tables VIII and IX, obtained from the (uncorrected) efficiencies in Tables VI and VII.
From the signal MC that is generated and used to determine signal reconstruction efficiency, the proportion of unreconstructed modes is determined by searching in the generated signal MC for modes that contain an X ss decay submode but fall outside the criteria for a reconstructed submode, i.e. submodes that contain more than one π 0 , modes with a K 0 L , or modes with more than six daughter particles (excluding the η ).The proportion of unreconstructed events, defined as N UR /(N UR + N R ), where N UR is the number of generated events from unreconstructed signal modes in signal MC, and N R is the number of generated events from reconstructed modes.For B 0 s → η K + K − + nπ, 1.1% of events are unreconstructed in the 1.4-1.6GeV/c 2 bin, increasing monotonically to 14.5% in the 2.2-2.4GeV/c 2 bin.For B 0 s → η K ± K 0 + nπ modes, as they are only reconstructed as B 0 s → η K ± K 0 S + nπ, there is a corresponding class of modes that involve a K 0 L instead of a K 0 S .This causes the proportion of generated signal events to be higher.In the 1.0-1.2GeV/c 2 bin, 48.1% of reconstructable events are unreconstructed, due to unreconstructed K 0 L modes.This increases monotonically to 59.7% in the 2.2-2.4GeV/c 2 bin, of which 84% is due to unreconstructed K 0 L modes.Using the same signal MC, it is also found that the signal cross-feed efficiency is less than 0.05% in each X ss mass bin and is included in the multiplicative systematic uncertainties.The B 0 s → D − s ρ + control sample is used to determine the systematic uncertainty with respect to the neural network (NN) selection.This uncertainty is obtained by determining the signal yield with and without the neural network selection in both MC and data.The double ratio of these results is determined and its absolute difference from unity is used as the systematic uncertainty.This gives an uncertainty of 6.5% for B 0 s → η K + K − + nπ    and 2.1% for B 0 s → η K ± K 0 S + nπ.The control sample B 0 s → D s ρ is also used to obtain the uncertainty for best candidate selection (BCS).The uncertainty is obtained by determining the signal yield with and without best candidate selection in both MC and data.The double ratio of these results is determined and its absolute difference from unity is used as the systematic uncertainty.This gives an uncertainty of 1.0% for B 0 s → η K + K − +nπ and 4.4% for B 0 s → η K ± K 0 S + nπ, using the neural network selection of these associated classes of signal modes.The uncertainty for the reconstruction of η → γγ and π 0 → γγ is 3.0% [42].
The uncertainty on charged track reconstruction is 0.35% per track [43].The uncertainty on the efficiency to identify charged kaons and pions is a function of their momenta and polar angles.The uncertainty for K ± and π ± identification is 0.95% and 1.8%, respectively.The K 0 S reconstruction uncertainty is 1.6% [44].The total track uncertainty, for each source, per X ss mass bin, is obtained by determining the average charged kaon and charged pion multiplicity (M ) in signal MC and multiplying the uncertainty by that multiplicity, e.g.M (0.182).These uncertainties are added linearly as they are uncertainties of common daughters of a single mother particle (B 0 s ) and are thus correlated.The Υ(5S) production model (PM) uncertainty leads to a fractional change in reconstruction efficiency of B 0 * s B0 * s S-wave (L = 0) states in a B → D s π control sample MC, with and without the model in [45], is im-plemented.The uncertainty is approximately 0.2% for B 0 s → η K ± K 0 + nπ and 1.1% for B 0 s → η K ± K 0 S + nπ.The uncertainty on the subdecay mode branching fractions B(η → γγ) and B(η → ηππ) are 0.2% and 0.7%, respectively [28].Estimates of individual multiplicative systematic uncertainties are given in Table X.Totals of these uncertainties are determined in individual X ss mass bins.

TABLE IV .
Jetset parameter descriptions

TABLE V .
Jetset parameters used to tune the fragmentation of the Xss system in Pythia.Alternative tunings (AT) AT1 and AT2 are used to obtain the systematic uncertainties due to fragmentation.

TABLE VI .
Comparison of uncorrected reconstruction efficiencies and their associated relative systematic uncertainties (%) between Pythia tunings (Standard, AT1, and AT2) given in TableV, used in systematic uncertainty estimation; tuning is done in 0.2 GeV/c 2 Xss mass bins for B 0 s → η K + K − + nπ modes.

TABLE VII .
Comparison of uncorrected reconstruction efficiencies and their associated relative systematic uncertainties (%) between Pythia tunings (Standard, AT1, and AT2) given in TableV, used in systematic uncertainty estimation; tuning is done in 0.2 GeV/c 2 Xss mass bins for B 0 s → η K ± K 0 S + nπ modes.

TABLE VIII .
Summary of FM multiplicative systematic uncertainties for B 0 s → η K + K − + nπ.

TABLE IX .
Summary of FM multiplicative systematic uncertainties for B 0 s

TABLE X .
Summary of multiplicative systematic uncertainties.The uncertainties for particle identification and reconstruction are evaluated per Xss mass bin.
s 18.3