Observation of the Doubly Cabibbo-Suppressed Decays D + → K + π 0 π 0 and D + → K + π 0 η

: By analyzing e + e − annihilation data corresponding to an integrated luminosity of 2 . 93 fb − 1 collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we report the ﬁrst observations of the doubly Cabibbo-suppressed decays D + → K + π 0 π 0 and D + → K + π 0 η . The branching fractions of D + → K + π 0 π 0 and D + → K + π 0 η are measured to be (2 . 1 ± 0 . 4 stat ± 0 . 1 syst ) × 10 − 4 and (2 . 1 ± 0 . 5 stat ± 0 . 1 syst ) × 10 − 4 with statistical signiﬁcances of 8.8 σ and 5.5 σ , respectively. In addition, we search for the subprocesses D + → K ∗ (892) + π 0 and D + → K ∗ (892) + η with K ∗ (892) + → K + π 0 . The branching fraction of D + → K ∗ (892) + η is determined to be (4 . 4 +1 . 8 − 1 . 5stat ± 0 . 2 syst ) × 10 − 4 , with a statistical signiﬁcance of 3.2 σ . No signiﬁcant signal for D + → K ∗ (892) + π 0 is found and we set an upper limit on the branching fraction of this decay at the 90% conﬁdence level to be 5 . 4 × 10 − 4 .

a Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia b Also at the Novosibirsk State University, Novosibirsk, 630090, Russia c Also at the NRC "Kurchatov Institute", PNPI, 188300, Gatchina, Russia d Currently at Istanbul Arel University, 34295 Istanbul, Turkey e Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany f Also at Key Laboratory for Particle Physics, Astrophysics and Cosmology, Ministry of Education; Shanghai Key Laboratory for Particle Physics and Cosmology; Institute of Nuclear and Particle Physics, Shanghai 200240, People's Republic of China g Also at Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443, People's Republic of China h Also at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People's Republic of China i Also at School of Physics and Electronics, Hunan University, Changsha 410082, China j Also at Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China k Also at Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, People's Republic of China l Also at Lanzhou Center for Theoretical Physics, Lanzhou University, Lanzhou 730000, People's Republic of China m Also at the Department of Mathematical Sciences, IBA, Karachi , Pakistan Abstract: By analyzing e + e − annihilation data corresponding to an integrated luminosity of 2.93 fb −1 collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we report the first observations of the doubly Cabibbo-suppressed decays D + → K + π 0 π 0 and D + → K + π 0 η.The branching fractions of D + → K + π 0 π 0 and D + → K + π 0 η are measured to be (2.1 ± 0.4 stat ± 0.1 syst ) × 10 −4 and (2.1 ± 0.5 stat ± 0.1 syst ) × 10 −4 with statistical significances of 8.8σ and 5.5σ, respectively.In addition, we search for the subprocesses D + → K * (892) + π 0 and D + → K * (892) + η with K * (892) + → K + π 0 .The branching fraction of D + → K * (892) + η is determined to be (4.4 +1.8 −1.5 stat ± 0.2 syst ) × 10 −4 , with a statistical significance of 3.2σ.No significant signal for D + → K * (892) + π 0 is found and we set an upper limit on the branching fraction of this decay at the 90% confidence level to be 5.4 × 10 −4 .

INTRODUCTION
Hadronic D decays open an important window to explore weak D decay mechanisms.Based on SU(3)-flavor symmetry, the branching fractions (BFs) of two-body hadronic D → V P decays, where V and P denote vector and pseudoscalar mesons, have been calculated with various approaches [1][2][3].The effect of SU(3)-flavor symmetry breaking has been validated in Cabbibo-favored (CF) and singly Cabibbo-suppressed D → V P decays.However, experimental information related to doubly Cabibbo-suppressed (DCS) D → V P decays is rare, due to their small BFs coupled with large backgrounds.The BFs of the DCS decays D + → K * + π 0 and D + → K * + η are predicted to be ∼ 10 −4 , and the ratio of these branching ratios is estimated to be either 2.86 ± 0.76 [1] or 4 [2].Improved understanding of U-spin and SU(3)-flavor symmetry breaking effects can be derived from these decays, which can lead to more precise theoretical predictions of CP violation in the charm sector [1][2][3][4][5][6][7][8].
This energy point is above the threshold to produce D D and below that to produce D * D, where D and D * denote charged or neutral charmed meson and their excited states, respectively.Therefore, the D and D mesons are produced exclusively in pairs, with no additional hadrons accompanying them.This sample corresponds to an integrated luminosity of 2.93 fb −1 .

BESIII DETECTOR AND MONTE CARLO SIMULATION
The BESIII detector is a magnetic spectrometer [17] located at the Beijing Electron Positron Collider (BEPCII) [16].The cylindrical core of the BESIII detector consists of a heliumbased 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 resolution of the specific ionization energy loss (dE/dx) 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 part is 68 ps, while that of the end cap part is 110 ps.Details about the design and performance of the BESIII detector are given in Refs.[17].Simulated samples produced with a Geant4-based [18][19][20] Monte Carlo (MC) simulation, which includes the geometric description of the BESIII detector and the detector response, are used to determine the detection efficiency and to estimate backgrounds.The simulation includes the beam energy spread and initial state radiation (ISR) in the e + e − annihilations modeled with the generator kkmc [21,22].The signal of D + → K + π 0 π 0 (η) is simulated using an MC generator that incorporates the resonant decay D + → K * + π 0 (η) and the phase space decay D + → K + π 0 π 0 (η).The background is studied using an inclusive MC sample that consists of the production of D D pairs with consideration of quantum coherence for all neutral D modes, the non-D D decays of the ψ(3770), the ISR production of the J/ψ and ψ(3686) states, and the continuum processes incorporated in kkmc [21,22].The known decay modes are modeled with evtgen [23,24] using the corresponding BFs taken from the Particle Data Group [13], while the remaining unknown decays from the charmonium states are modeled with lundcharm [25,26].Final state radiation from charged final state particles is incorporated using photos [27][28][29].

MEASUREMENT METHOD AND SINGLE TAG YIELDS
The BFs of the signal decays are measured with a double-tag technique that was first developed by the Mark III Collaboration [30].The signal D + decays are reconstructed alongside hadronic Here, S is the signal yield expected based on the known BFs of , which are isospin symmetric decays of the DCS decays of interest; and B is the scaled background yield estimated by the inclusive MC sample.The fully reconstructed D − is called the single-tag (ST) meson.Events in which both the signal D + meson and the ST D − meson are found are called double-tag (DT) events.For a given signal decay, the decay BF is determined by where N ST and N DT are the yields of ST and DT candidates in data, is the signal efficiency in the presence of the ST candidate, in which ǫ ST and ǫ DT are the efficiencies of selecting ST and DT candidates, and i stands for tag modes.The B sub is the product of branching fractions of the subdecays of K * + , π 0 and η.
The ST D − mesons are distinguished from combinatorial background using two kinematic variables: the energy difference ∆E tag ≡ E D − − E b and the beam-constrained mass Here, E b is the beam energy, and p D − and E D − are the momentum and energy, respectively, of the D − candidate in the rest frame of the e + e − system.If more than one candidate survives the selection criteria of a given tag mode, the combination with the minimum |∆E tag | is chosen.Tagged D − candidates are selected with a requirement of ∆E tag ∈ (−25, 25) MeV to suppress combinatorial backgrounds in the M tag BC distributions.To extract the number of ST D − mesons for each tag mode, maximum likelihood fits have been performed on the individual M tag BC distributions [31,32].The ST yields and efficiencies for various tag modes are summarized in Table 1.The number of ST D − mesons summed over the three tag modes is N ST = (1150.3± 1.5 stat ) × 10 3 .

YIELDS OF DOUBLE-TAG EVENTS
Candidates for the DCS D + decays are selected with the residual neutral and charged particles not used in the D − tag reconstruction.Similar to the tag side, the energy difference and beam-constrained mass of the signal side, ∆E sig and M sig BC , respectively, are calculated.For each signal decay, if there are multiple combinations, the one giving the minimum |∆E sig | is kept.The accepted candidates are required to fall in the intervals ∆E sig ∈ (−78, 36) MeV and ∆E sig ∈ (−52, 31) MeV for D + → K + π 0 π 0 and D + → K + π 0 η, respectively.To reduce background events from non-D + D − processes, the minimum opening angle between the D + and D − must be greater than 167 • .This requirement suppresses 57% (81%) of background for D + → K + π 0 π 0 (η) at the cost of losing 9% of the two signal decays.For D + → K + π 0 π 0 , the invariant mass of the π 0 π 0 combination is required to be outside (0.388, 0.588) GeV/c 2 to reject the dominant background from the singly Cabibbo-suppressed decay D + → K + K 0 S (→ π 0 π 0 ).The resulting distributions of M tag BC versus M sig BC of the accepted DT candidates are shown in the left column of Fig. 1.Signal events cluster around M tag BC = M sig BC = M D + , where M D + is the known D + mass [13].There are three kinds of background events.The events with correctly reconstructed D + (D − ) and incorrectly reconstructed D − (D + ) are called BKGI.These background events are distributed along the horizontal and vertical bands around the known D + mass.The events spreading along the diagonal, which are mainly from the e + e − → q q processes, are named BKGII.The events with incorrectly reconstructed D − and D + are dispersed in the allowed kinematic region and they are ignored in the following analysis due to limited statistics.
The signal yields of the DT events are extracted from a two-dimensional (2D) unbinned maximum likelihood fit to the corresponding distribution of M tag BC versus M sig BC .The signal shape is described by the 2D probability density function (PDF) from the MC simulation after convolving with a Gaussian resolution function with parameters derived from the control sample of D + → π + π 0 π 0 .For various background components, the individual PDFs are constructed as [32,33] • BKGI: b(x) • c y (y; E b , ξ y ), The one-dimensional MC-simulated signal shape is b(x).The c f is an ARGUS function [34] defined as where f ≡ y, or z, A f is a normalization factor, ξ f is a fit parameter, and E end is the endpoint fixed at E b for c y or √ 2E b for c z .The function g(k; 0, σ k ) is a Gaussian function with zero mean and standard deviation , where σ 0 and p are the parameters determined from the fit.All other parameters are free in the fit.The spectra of the middle and right columns in Fig. 1 show the projections on M tag BC and M sig BC of the 2D fits to data.These fits give the signal yields of D + → K + π 0 π 0 and D + → K + π 0 η to be 42.8 ± 7.2 stat and 19.2 ± 5.0 stat , respectively.
To account for the large difference of detection efficiencies between resonant and nonresonant decays, we estimate the resonant component of D + → K * + π 0 (η) under the assumption that the non-resonant component is uniformly distributed and there is no interference between the two kinds of components.The signal yield of the resonant decay D + → K * + π 0 (η) is extracted from a simultaneous 2D fit in the K * + signal and sideband regions.
The K * + signal region is defined as the invariant mass M K + π 0 ∈ (0.792, 0.992) GeV/c 2 for D + → K * + η and one of two M K + π 0 combinations lying in M K + π 0 ∈ (0.792, 0.992) GeV/c 2 for D + → K * + π 0 .The sideband region is defined as the K + π 0 combination outside the K * + signal region but within the kinematic region.Definitions of the K * + signal and sideband regions are shown in Fig. 2.
The left columns of Figs.3(a) and 3(b) show the M tag BC versus M sig BC distributions of the accepted DT candidates, where the top and bottom rows correspond to the K * + signal and sideband regions, respectively.In the simultaneous fits, the ratios of the non-resonant background yields between the K * + sideband and signal regions are fixed to the MCdetermined values of f K * + π 0 = 1.40 ± 0.02 for D + → K + π 0 π 0 and f K * + η = 2.25 ± 0.05 for D + → K + π 0 η, respectively, where the efficiency differences have been considered.In addition, the parameters of the ARGUS functions in the 2D fit to the K * + sideband events are constrained to be the same as those for the K * + signal region.The other parameters are left free.These fits give the signal yields of D + → K * + π 0 and D + → K * + η to be 16.6 +6.6 −6.2 stat and 10.9 +4.4 −3.8 stat , respectively.Combining the D + → K + π 0 π 0 and D + → K + π 0 η signal yields, we obtain the fractions of the resonant components to be r K * + π 0 = 0.39 ± 0.17 stat and r K * + η = 0.57 ± 0.28 stat , respectively.
The efficiency of detecting the signal decay D + → K + π 0 π 0 (η) is estimated by using a mixture of the signal MC events for the resonant decay D + → K * + π 0 (η) and the phase space decay D + → K + π 0 π 0 (η) with fractions of r K * + π 0 and r K * + η determined above.The obtained DT efficiencies (ǫ i DT = ǫ i tag,sig ) and signal efficiencies (ǫ i sig ) for individual decays are summarized in Table 1.
Table 1.The ST yields (N i ST ), the ST efficiencies (ǫ i tag ), the DT efficiencies (ǫ i DT = ǫ i tag,sig ), and the signal efficiencies (ǫ i sig ).Compared to the mixed signal MC events, the lower signal efficiencies for the resonant decays are mainly due to that the π 0 s from K * + decays have much lower momenta and an additional K * + mass requirement.For D − → K + π − π − π 0 , the efficiencies are lower than those of the other two tag modes, mainly because of more migrations of low momentum pions between tag and signal sides.The efficiencies do not include the BFs of subresonance decays.The uncertainties are statistical only.
Tag mode i For each signal decay, the statistical significance is evaluated using −2ln(L 0 /L max ), where L max is the maximum likelihood of the nominal fit and L 0 is obtained by refitting the M tag BC versus M sig BC distribution without the signal PDF.Especially, the peaking background of the non-resonant component has been fixed for D + → K * + π 0 and D + → K * + η.The resulting statistical significances are 8.8σ, 5.5σ, 2.7σ, and 3.2σ for K + π 0 η, D + → K * + π 0 , and D + → K * + η, respectively.In addition, 10000 toy MC studies show that the 2D fit is stable and no potential bias is found for each signal decay.
The measured values for N DT , ǫ sig , and B sig are summarized in Table 2.Because there is no significant signal for D + → K * + π 0 , we set an upper limit on its decay BF at the 90% confidence level to be 5.4 × 10 −4 .This is set utilizing the Bayesian approach after incorporating the associated systematic uncertainty [35], as discussed later.
Table 2.The DT yields in data (N DT ), the signal efficiencies (ǫ sig = ǫ i DT /ǫ i ST ) and the obtained BFs.The first and second uncertainties are statistical and systematic, respectively.The efficiencies do not include the BFs of π 0 , η and K * + decays.The lower efficiency for D + → K + π 0 π 0 is mainly due to the K 0 S rejection.

Decay mode
for D + → K + π 0 π 0 candidates (two entries per event for symmetrization).In the kinematic region marked in blue, the regions inside and outside the red band are the K * + signal and sideband regions, respectively.The requirement of |M  Distributions of (left column) M tag BC versus M sig BC and the projections on (middle column) M tag BC and (right column) M sig BC of the constrained 2D fits to the DT candidate events in the K * + signal region (top row) and sideband region (bottom row) for (a) D + → K + π 0 π 0 and (b) D + → K + π 0 η.Points with error bars are data.Blue solid curves are the fit results.Black dotted curves are the signal distributions.For the K * + sideband region, green dotted and red dot-longdashed curves are BKGI and BKGII, respectively.For the K * + signal region, red dot-long-dashed curves are BKGII and green dotted curves are the peaking backgrounds constrained by using the K * + sideband events.

SYSTEMATIC UNCERTAINTY
One of the advantages of the DT method is that most of the uncertainties associated with the ST selection cancel.The systematic uncertainties in the BF measurements are mainly from the following sources.They are reported relative to the measured BFs.
• ST yields (N tag ): The uncertainty of the total ST D − yield, which is mainly due to the fit to the M tag BC distribution, has been previously estimated to be 0.5% in Ref. [31].
• K ± tracking or particle identification (PID): The efficiencies of tracking and PID of the K + are studied with DT D D hadronic events.The systematic uncertainty for K + tracking and PID is 1.0% for each.
• π 0 (η) reconstruction: The efficiency of π 0 reconstruction is investigated using DT D D hadronic decay samples of 36,37].The systematic uncertainty due to π 0 reconstruction is 2.0% per π 0 .Based on the π 0 uncertainty, the systematic uncertainty of η reconstruction is also taken to be 2.0%.The total systematic uncertainty due to π 0 π 0 or π 0 η reconstruction is obtained to be 4.0% by adding each of them linearly.
• 2D fit: The systematic uncertainty of the 2D fit is mainly due to the signal and background shapes.To compensate for the possible data-MC difference of the signal, the MC-simulated signal shapes have been smeared by a Gaussian resolution function with parameters derived from the control sample of D + → π + π 0 π 0 .Therefore, the systematic uncertainty due to the signal shape is ignored.To consider the uncertainty of center-of-mass energy calibration [38], the endpoint of the ARGUS background function is varied by ±0.2 MeV/c 2 .
The changes of the BFs are assigned as the corresponding systematic uncertainties, which are 0.2% for both D + → K + π 0 π 0 and D + → K + π 0 η, but are negligible for D + → K * + π 0 and D + → K * + η.
• D + D − opening angle: The systematic uncertainty arising from the D + D − opening angle requirement is studied by using the control sample of D + → π + π 0 π 0 .The difference of the acceptance efficiencies between data and MC simulation, 1.2%, is assigned as the corresponding systematic uncertainty.
• ∆E sig requirement: The systematic uncertainty of the ∆E sig requirement is estimated by convolving with one Gaussian resolution function obtained from the control sample with the ∆E sig distribution of the signal MC events.The change of the DT efficiency is found to be negligible.Therefore, the corresponding systematic uncertainty is neglected.
• K 0 S rejection: The systematic uncertainty due to the K 0 S rejection is also negligible since the BFs are found to be insensitive to shrinking or enlarging the K 0 S rejection window by 0.02 GeV/c 2 , which is about two standard deviations of the fitted K 0 S (→ π 0 π 0 ) resolution, and taking into account correlations of the two signal samples with the nominal and varied K 0 S signal regions [39].
• K * + signal region: The systematic uncertainty of the K * + signal region is studied using DT events from the processes D 0 → K − π + and K − π + π 0 versus D0 → K * + (→ K + π 0 )e − νe .The change of the DT efficiencies after convolving with the obtained Gaussian resolution function with the M K + π 0 distributions, 0.1%, is assigned as the associated uncertainty.
• Scale factor of K * + sideband: The systematic uncertainties due to the scale factors of K * + sideband are examined by varying f K * + π 0 and f K * + η by ±1σ.The changes of the re-measured BFs, 1.4% and 0.5%, are assigned as the systematic uncertainties for D + → K * + π 0 and D + → K * + η, respectively.
• Multiplicities of tag and signal sides: To verify the smallest |∆E| selection method, we have examined the multiple candidate rates for the tag and signal sides.Due to limited signal statistics, the signal side is examined with the control sample of D + → π + π 0 π 0 , which has similar multiple candidate rates as our signal candidates.The multiple candidate rates of , and D + → π + π 0 π 0 are about 0.4%, 0.2%, 9.9%, and 1.7% with negligible uncertainties, respectively, for both data and MC simulation.Therefore, the relevant effect is ignored in this analysis.

Figure 1 .
Figure 1.Distributions of (left column) M tag BC versus M sig BC and the projections on (middle column) M tag BC and (right column) M sig BC of the 2D fits to the DT candidate events.The top row is for D + → K + π 0 π 0 and the bottom row is for D + → K + π 0 η.Points with error bars are data.Blue solid curves are the fit results.Cyan dotted curves are the fitted signal distributions.Blue longdashed curves are BKGI.Red dot-long-dashed curves are BKGII.
Figure 3.Distributions of (left column) M tag BC versus M sig BC and the projections on (middle column) M tag BC and (right column) M sig BC of the constrained 2D fits to the DT candidate events in the K * + signal region (top row) and sideband region (bottom row) for (a) D + → K + π 0 π 0 and (b) D + → K + π 0 η.Points with error bars are data.Blue solid curves are the fit results.Black dotted curves are the signal distributions.For the K * + sideband region, green dotted and red dot-longdashed curves are BKGI and BKGII, respectively.For the K * + signal region, red dot-long-dashed curves are BKGII and green dotted curves are the peaking backgrounds constrained by using the K * + sideband events.