Study of the doubly Cabibbo-suppressed decays $D^+_s\to K^+K^+\pi^-$ and $D^+_s\to K^+K^+\pi^-\pi^0$

Based on 7.33 fb$^{-1}$ of $e^+e^-$ collision data collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector, the experimental studies of the doubly Cabibbo-suppressed decays $D^+_s\to K^+K^+\pi^-$ and $D^+_s\to K^+K^+\pi^-\pi^0$ are reported. We determine the absolute branching fraction of $D^+_s\to K^+K^+\pi^-$ to be (${1.23^{+0.28}_{-0.25}}({\rm stat})\pm0.06({\rm syst})$) $\times 10^{-4}$. No significant signal of $D^+_s\to K^+K^+\pi^-\pi^0$ is observed and the upper limit on its decay branching fraction at 90\% confidence level is set to be $1.7\times10^{-4}$.

In the D + s sector, only the DCS decay D + s → K + K + π − was previously reported [12].
Its decay branching fraction was measured relative to the CF decay of D + s → K + K − π + by LHCb, BaBar, Belle and FOCUS [13][14][15][16].In this article, we present the first measurement of absolute branching fraction of D + s → K + K + π − and search for D + s → K + K + π − π 0 for the first time.This analysis uses the e + e − collision data samples collected at center-of-mass energies (E cm ) between 4.128 and 4.226 GeV with the BESIII detector, corresponding to an integrated luminosity of 7.33 fb −1 .

II. BESIII DETECTOR AND MONTE CARLO SIMULATION
The BESIII detector [17] is a magnetic spectrometer located at the Beijing Electron Positron Collider (BEPCII) [18].The cylindrical core of the BESIII detector consists of a helium-based multilayer drift chamber (MDC), a plastic scintillator time-of-flight system (TOF), and a CsI(Tl) electromagnetic calorimeter (EMC), which are all enclosed in a superconducting solenoidal magnet providing a 1.0 T magnetic field.The solenoid is supported by an octagonal flux-return yoke with resistive plate counter muon identifier modules interleaved with steel.
The acceptance of charged particles and photons is 93% over 4π solid angle.The charged particle momentum resolution at 1 GeV/c is 0.5%, and the specific ionization energy loss dE/dx resolution is 6% for the electrons from Bhabha scattering.The EMC measures photon energies with a resolution of 2.5% (5%) at 1 GeV in the barrel (end cap) region.The time resolution of the TOF barrel section is 68 ps, while that of the end cap portion is 110 ps.The end cap TOF system was upgraded in 2015 using multi-gap resistive plate chamber technology, providing a time resolution of 60 ps [19], which benefits 83% of the data used in this analysis [20,21].
Simulated samples produced with the geant4based [22] Monte-Carlo (MC) package which includes the geometric description of the BESIII detector and the detector response, are used to determine the detection efficiency and to estimate the backgrounds.
The simulation includes the beam energy spread and initial state radiation (ISR) of the e + e − annihilations modeled with the generator kkmc [23].
The inclusive MC samples consist of the production of D ( * ) s

D( * )
(s) pairs (with consideration of quantum coherence for all D 0 D0 pair decays), the non-D D decays of the ψ(3770), the ISR production of the J/ψ and ψ(3686) states, and the continuum processes.The known decay modes are modeled with evtgen [24] using the branching fractions taken from the Particle Data Group (PDG) [12], and the remaining unknown decays of the charmonium states with lundcharm [25].Final state radiation from charged final state particles is incorporated with the photos package [26].The signal MC sample of , while the unknown sub-channels are generated according to the phase space.The signal MC sample of D + s → K + K + π − π 0 is also generated uniformly over the phase space.

III. MEASUREMENT METHOD
In the e + e − collision data taken at E cm between 4.128 and 4.226 GeV, the D ± s mesons are produced mainly via the e + e − → D * ± s D ∓ s → γ(π 0 )D + s D − s process.This analysis is performed by using the double-tag (DT) method pioneered by the MARKIII Collaboration [27].A D − s meson which is fully reconstructed via one of the eleven hadronic decay modes is referred to as a single-tag (ST) D − s meson.The event, in which the γ(π 0 ) emitted from D * + s and the signal decay can be successfully reconstructed in the presence of ST D − s meson, is called as a DT event.The branching fraction of the signal decay is determined as where N DT and N ST are the yields of the DT events and ST D − s mesons in data, respectively; ǫ sig is the efficiency of detecting the signal decay in the presence of the ST D − s mesons, averaged over the D * s → D s γ and D * s → D s π 0 transitions weighted by their branching fractions.

IV. ST CANDIDATES
To reconstruct ST D − s candidates, we use eleven hadronic decay modes of and η π + π − π 0 ρ − .Throughout this article, ρ denotes ρ(770) and the subscripts of η (′) denote individual decay modes adopted for η (′)  reconstruction.The MBC distributions of the ST candidates in data and inclusive MC samples at 4.178 GeV.The candidates between the two red arrows are accepted.
The K ± , π ± , K 0 S , γ, π 0 , and η candidates are selected with the same criteria as in Refs.[28][29][30].All charged tracks, except for those from K 0 S , are required to originate from a region defined as |V xy | < 1 cm and |V z | < 10 cm, where |V z | and |V xy | are the distances of the closest approach relative to the interaction point along the MDC axis and in the transverse plane, respectively.The track polar angle θ with respect to the MDC axis must satisfy |cos θ| < 0.93.Charged particles are identified by using the combined dE/dx and TOF information.A particle is assigned to be a pion (kaon) candidate if the confidence level for the corresponding hypothesis is greater than for the kaon (pion) hypothesis.
Candidates for K 0 S are selected via the decay K 0 S → π + π − .The two charged pions are required to satisfy |V z | < 20 cm and |cos θ| < 0.93.They are assumed to be π + π − without particle identification (PID) requirements.The two pions are required to have a common vertex point via a secondary vertex fit; the fit χ 2 must be less than 200 and their invariant mass is required to be within (0.487, 0.511) GeV/c 2 .The decay length of any K 0 S candidate, measured from the interaction point, is required to be greater than twice the vertex resolution.
Photon candidates are reconstructed by using shower information measured by the EMC.To suppress backgrounds from electronic noise or bremsstrahlung, candidate showers are required to start within [0, 700] ns from the event start time and the energy of each shower the barrel (end cap) region of the EMC [17] is required to be greater than 25 (50) MeV.To suppress backgrounds associated with charged tracks, the angle subtended by the EMC shower and the closest charged track extrapolation to the EMC must be greater than 10 degrees as measured from the interaction point.
The transition pions from D decays are suppressed by requiring the momentum of any pion which is not from a K 0 S , η, or η ′ decay to be greater than 0.1 GeV/c.In order to reject peaking background from the D − s → K 0 S π − final state in the selection of the D − s → π + π − π − tag mode, the invariant mass of each π + π − combination is required to be outside the mass window of (0.468, 0.528) GeV/c 2 .
The backgrounds from non-D ± s D * ∓ s processes are suppressed by using the beam-constrained mass of the ST D − s candidate, defined as where E beam is the beam energy and p tag is the momentum of the ST D − s candidate in the e + e − rest frame.Figure 1 closest to the D * + s nominal mass [12] is kept for further analysis.When the D − s tag meson is from a D * − decay, the recoil mass distribution is not sharply peaked, but overall the correct tag is selected about 94% of the time.The distributions of the invariant masses (M tag ) of the accepted ST candidates for various tag modes are shown in Fig. 2. The yields of ST D − s mesons reconstructed in various tag modes are derived from fits to their individual M tag distributions.In the fits, the signal is described by the simulated shape convolved with a Gaussian function to take into account the resolution difference between data and simulation.In the fit to the D − s → K 0 S K − tag mode, the shape of the peaking background of D − → K 0 S π − is modeled by the simulated shape convolved with the same Gaussian resolution function as used for the signal.The combinatorial background is described by first, second or third-order Chebychev polynomial functions.The order of the polynomial is chosen by analyzing the inclusive MC sample.Figure 2 shows the fit results of different tag modes for the combined data sample from all energy points.In each sub-figure, the black arrows show the chosen M tag signal regions.The candidates located in these signal regions are kept for further analysis.
Based on simulation, the e + e − → (γ  M BC requirement and are negligible.The second and third columns of Table 2 summarize the yields of ST D − s mesons (N ST ) for various tag modes obtained from the combined data sample and the corresponding detection efficiencies (ǫ ST ), respectively.

V. DT CANDIDATES
The transition photon (or π 0 ) and the signal D + s decay candidate are reconstructed from the particles recoiling against the selected D − s tag.We define the energy difference or tag] are the energy and momentum of γ(π 0 ) or D − s tag, respectively.A loop is performed over all γ and π 0 candidates which were not used in the ST reconstruction, under the two assumptions of D * s → π 0 D s and D * + s → γD + s .If more than one combination satisfies the selection criteria, the one with the minimum |∆E| is chosen.
The selection criteria of π − , K + , and π 0 for D + s → K + K + π − and D + s → K + K + π − π 0 reconstruction are the same as those used to choose the ST candidates.We require that there are exactly three good charged tracks which are not used to form the ST candidate; one track is identified as a π − and the others are required to be identified as K + s.For D + s → K + K + π − π 0 , if there are multiple π 0 s on the signal side, only the π 0 with the smallest χ 2 of the mass-constrained kinematic fit is selected.
Figure 3 shows the distributions of the invariant masses, M sig , of the accepted signal candidates.The DT efficiencies and the signal efficiencies of detecting for different tag modes, weighted over different energy points, are summarized in Table 2.The average signal efficiencies of D + s → K + K + π − and D + s → K + K + π − π 0 , weighted over different tag modes, are (35.57±0.18)%and (10.32± 0.10)%, respectively, where the uncertainties are due to the limited MC statistics.
The signal yields are extracted from unbinned maximum likelihood fits to the M sig spectra in Fig. 3.In the fit, the signal is modeled by the MC-simulated signal shape smeared with an additional Gaussian resolution function (with parameters obtained from a fit to the corresponding CF decays).The background is described by the simulated shape from the inclusive MC sample, and the yields of the signal and background are floating.The fitted yields of ST D − s mesons from the combined data sample, NST (in units of ×10 3 ), the efficiencies of detecting ST D − s mesons, DT events and signal events (ǫST, ǫDT, ǫsig = ǫDT/ǫST, all %) for various tag modes.For all numbers, the uncertainties are statistical only.The listed efficiencies do not include the branching fractions of any daughter particle decays.For each signal channel, the efficiencies have been weighted over different energy points.

Tag mode
Mtag(GeV/c 2 ) The statistical significance of D + s → K + K + π − is estimated to be 6.2σ, by −2ln(L 0 /L max ), where L max and L 0 are the maximal likelihoods of the fits with and without the signal contribution, respectively.The signal yield of D + s → K + K + π − is obtained to be 32.9 +7.6 −6.8 .For D + s → K + K + π − π 0 , no significant signal is observed, and an upper limit on the decay branching fraction is set.

VI. SYSTEMATIC UNCERTAINTIES
Table 3 summarizes the sources of systematic uncertainty in the branching fraction measurements; details are given below.
The systematic uncertainties on the fitted yields of the ST D − s mesons are estimated by using alternative signal and background shapes.First, alternative signal shapes are obtained by changing from those derived from the inclusive MC sample to those from the signal MC samples.Second, an alternative background shape is obtained by varying the order of the nominal Chebychev function by ±1.For a given ST mode, the differences in the ratio of the yields of ST D − s mesons over the corresponding efficiency for all variations, and the background fluctuation of the fitted yield of ST D − s are re-weighted by the yields of ST D − s mesons in various data samples and are added in quadrature.An additional component to this uncertainty is statistical in nature, and accounts for the contribution of background fluctuations to the fitted yields of ST D − s mesons.The total uncertainty associated with the ST yield N tot ST is estimated to be 0.5%.
The systematic uncertainties from the tracking and PID of K ± and π ± are estimated by using the control sample of e + e − → K + K − π + π − (π 0 ) [31].
The systematic uncertainties in the tracking and PID efficiencies are both assigned as 1.0% per K ± or π ± .The systematic uncertainties in the photon selection and the π 0 reconstruction are studied with the control sample of J/ψ → π + π − π 0 [32].The systematic uncertainty in the photon selection is assigned as 1.0% per photon, and the systematic uncertainty in the π 0 reconstruction, including the photon finding algorithm, the π 0 mass window and the 1C kinematic fit, is assigned as 2.0% per π 0 .
The systematic uncertainty related to the M sig fit has two sources.Firstly, an alternative signal shape is obtained by varying the parameters of the smeared Gaussian function by ±1σ.Secondly, an alternative background shape is obtained by varying the q q component in the inclusive MC sample by its uncertainty due to the limited MC statistics.For D + s → K + K + π − , the systematic uncertainty is evaluated as 0.4%.For the upper limit determination of D + s → K + K + π − π 0 , the signal shape and background shape affect the likelihood function directly.Changing the signal (background) shape shifts the signal yield from the fit by 0.1 (0.2), and we take the larger value as the additive systematic uncertainty.
Varying the D * s branching fractions [12] by ±1σ changes the efficiency by 0.3%; this is taken as the associated uncertainty.
The systematic uncertainty related to the MC model is estimated using alternative signal MC samples.For D + s → K + K + π − , the branching fraction of the D + s → K + K * 0 sub-channel is varied by its uncertainty.For D + s → K + K + π − π 0 , the average signal efficiency of D + s → K * 0 K + π 0 , K * + K + π − , K + K + ρ − , and D + s → K + K + π − π 0 (phase space) is used in place of the phase space efficiency.The maximum changes of the signal efficiencies, 0.7% and 5.3%, are assigned as the systematic uncertainties for D + s → K + K + π − and D + s → K + K + π − π 0 , respectively.

VII. RESULTS
Inserting the numbers of N DT , N ST and ǫ sig of D + s → K + K + π − in Eq. ( 1), we determine the decay branching fraction to be The upper limit on the branching fraction of D + s → Table 3. Systematic uncertainties on the branching fraction measurements.Uncertainties in the square brackets are additive uncertainties on the number of events; all other uncertainties are in %.K + K + π − π 0 is set with the Bayesian approach [33], incorporating the systematic uncertainties.The raw likelihood distribution versus the branching fractions is smeared by a Gaussian function with a mean of zero and a width equal to the systematic uncertainty.The red solid curve in Fig. 4 shows the resulting likelihood distribution.The upper limit on the branching fraction at 90% confidence level is set as  D + s → K + K + π − π 0 < 1.7 D + s → K + K − π + π 0 5.50 ± 0.24 < 3.09 < 1.07 D + s → K + K + π − is determined to be (1.23 +0.28 −0.25 (stat) ± 0.06(syst)) × 10 −4 , which is in good agreement with the world average value of (1.274 ± 0.031) × 10 −4 [12], based on the relative measurements from LHCb, BaBar, Belle and FOCUS [13][14][15][16].No significant signal of D + s → K + K + π − π 0 is observed.The upper limit on the branching fraction of D + s → K + K + π − π 0 is 1.7 × 10 −4 at 90% confidence level.Table 4 summarizes the results obtained in this work and the world average branching fractions of the corresponding CF decays.The DCS/CF branching fraction ratios and the corresponding factors relative to tan 4 θ C are also listed.No significant deviation from native expectation of (0.5 − 2.0) × tan 4 θ C is found.

Source
Fig. 1.The MBC distributions of the ST candidates in data and inclusive MC samples at 4.178 GeV.The candidates between the two red arrows are accepted.

s
process is found to contribute about (0.7-1.1)% in the fitted yields of ST D − s mesons for various tag modes and has been subtracted away from the fitted yields in this analysis.Production of D * + s D * − s pairs occurs only at the highest c.m. energy; candidates are suppressed by the

Fig. 2 .
Fig. 2. Fits to the Mtag distributions of the selected ST candidates for various tag modes.The points with error bars are the data combined from all energy points.The blue solid curves represent the best fit results, and the red dashed curves stand for the fitted backgrounds.For the tag mode of D − s → K 0 S K − , the blue dashed curve is the peaking background from D − → K 0 S π − .The pair of arrows denote the Mtag signal regions.

Fig. 3 .Fig. 4 .
Fig. 3. Fits to the Msig distributions of the accepted DT candidates.The points with error bars are the combined data from all energy points.The blue solid curves are the fit results, the red solid curves are the combinatorial backgrounds, and the histograms filled in colors are from different background sources, derived from the inclusive MC sample and normalized to the fitted background yields in data.

7 × 10 − 4 .
VIII.SUMMARYUsing 7.33 fb −1 of e + e − collision data collected at E cm between 4.128 and 4.226 GeV with the BESIII detector, we investigate the DCS decaysD + s → K + K + π − and D + s → K + K + π − π 0 .The absolute branching fraction of shows the M BC distributions of the ST candidates in data and inclusive MC samples at 4.178 GeV.For the direct D − s mesons which are produced by the e + e − collision, M BC peaks, as shown by the open histogram.For the indirect D − s mesons which are produced from D * − s decays, the M BC distribution is broader, as shown by the red histogram.The M BC value is required to be within the intervals listed in Table 1.This requirement retains about 99% of the D − s and D + s mesons from e + e − → D * ∓ s D ± s .If there are multiple candidates present per tag mode per charge, only the one with the D − s recoil mass