Observation of the Doubly Cabibbo-Suppressed Decay D + → K + π + π − π 0 and Evidence for D + → K + ω

Using 2 . 93 fb − 1 of e + e − collision data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the ﬁrst observation of the doubly Cabibbo-suppressed decay D + → K + π + π − π 0 is reported. After removing decays that contain narrow intermediate resonances, including D + → K + η , D + → K + ω , and D + → K + φ , the branching fraction of the decay D + → K + π + π − π 0 is measured to be (1 . 13 ± 0 . 08 stat ± 0 . 03 syst ) × 10 − 3 . The ratio of branching fractions of D + → K + π + π − π 0 over D + → K − π + π + π 0 is found to be (1 . 81 ± 0 . 15)%, which corresponds to (6 . 28 ± 0 . 52) tan 4 θ C , where θ C is the Cabibbo mixing angle. This ratio is signiﬁcantly larger than the corresponding ratios for other doubly Cabibbo-suppressed decays. The asymmetry of the branching fractions of charge-conjugated decays D ± → K ± π ± π ∓ π 0 is also determined, and no evidence of CP violation is found. In addition, the ﬁrst evidence of the D + → K + ω decay, with a statistical signiﬁcance of 3.3 σ , is presented and its decay branching fraction is determined to be (5 . 7 +2 . 5 − 2 . 1stat ± 0 . 2 syst ) × 10 − 5 .

a Also at Bogazici University, 34342 Istanbul, Turkey b Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia c Also at the Novosibirsk State University, Novosibirsk, 630090, Russia d Also at the NRC "Kurchatov Institute", PNPI, 188300, Gatchina, Russia e Also at Istanbul Arel University, 34295 Istanbul, Turkey f Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germany Using 2.93 fb −1 of e + e − collision data collected at a center-of-mass energy of 3.773 GeV with the BESIII detector, the first observation of the doubly Cabibbo-suppressed decay D + → K + π + π − π 0 is reported.After removing decays that contain narrow intermediate resonances, including D + → K + η, D + → K + ω, and D + → K + φ, the branching fraction of the decay D + → K + π + π − π 0 is measured to be (1.13 ± 0.08stat ± 0.03syst) × 10 −3 .The ratio of branching fractions of D + → K + π + π − π 0 over D + → K − π + π + π 0 is found to be (1.81 ± 0.15)%, which corresponds to (6.28 ± 0.52) tan 4 θC, where θC is the Cabibbo mixing angle.This ratio is significantly larger than the corresponding ratios for other doubly Cabibbo-suppressed decays.The asymmetry of the branching fractions of charge-conjugated decays D ± → K ± π ± π ∓ π 0 is also determined, and no evidence of CP violation is found.In addition, the first evidence of the D + → K + ω decay, with a statistical significance of 3.3σ, is presented and its decay branching fraction is determined to be (5.7 +2.5 −2.1 stat ± 0.2syst) × 10 −5 .
PACS numbers: 13.20.Fc, 14.40.Lb Doubly Cabibbo-suppressed (DCS) decays of D mesons can provide unique insight into charmed hadron dynamics.To date, DCS decays of charmed hadrons remain relatively unexplored [1].The naive expectation for the DCS decay rate relative to its Cabibbo-favored (CF) counterpart [2,3] is of the order tan 4 θ C ∼ 0.29%, where θ C is the Cabibbo mixing angle.The known ratios of DCS and CF decay rates [4] roughly support this expectation, with the exception of D + → K − π + π + [5] where the ratio is doubled due to identical particles in the final state.A measurement of the BF of D + → K + π + π − π 0 and a comparison with its CF counterpart provides a crucial test of this model.
In the Standard Model, CP violation in the weak decays of hadrons arises due to a single irreducible phase in the Cabibbo-Kobayashi-Maskawa matrix [13].CP violation in charmed-hadron decays is expected to be small, up to a few 10 −3 for singly Cabibbosuppressed processes, and much smaller for CF and DCS processes [12,14].In the past two decades, CP violation of charmed hadrons has been extensively explored [15].In 2019, the LHCb collaboration reported an observation of CP violation in neutral D decays [16].Searching for CP violation in other DCS decays offers complementary information about CP violation in the charm sector.
This Letter reports the first measurement of the absolute BFs of the DCS decays D + → K + π + π − π 0 and D + → K + ω.Charge-conjugated decays are always implied unless otherwise stated.The CP asymmetry of The data sample was collected with the BESIII detector at the center-of-mass energy of √ s = 3.773 GeV and has an integrated luminosity of 2.93 fb −1 [17].Details about the design and performance of the BESIII detector are given in Refs.[18,19].Simulated samples produced with a Geant4-based [20] 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 backgrounds.The simulation includes the beam energy spread and initial state radiation (ISR) in the e + e − annihilations modeled with the generator kkmc [21].The signal of D + → K + π + π − π 0 is simulated using an MC generator that incorporates the resonant decays D + → K * (892) 0 ρ(770) + , K * (892) + ρ(770) 0 , K + η, K + ω, the phase space decay D + → K + π + π − π 0 , and possible interferences.The parameters of the generator have been tuned to reach a good data-MC agreement in distributions over the momenta of the daughter particles and the invariant masses of each two-and three-body particle combinations.The signal of D + → K + ω is simulated using an MC generator which simulates pseudoscalar meson decays into vector meson and scalar meson [22].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.The known decay modes are modeled with evtgen [22] using the known BFs taken from the Particle Data Group [1], while the remaining unknown decays from the charmonium states are modeled with lundcharm [23].Final state radiation (FSR) from charged final state particles is incorporated with the photos package [24].This analysis employs a double-tag technique, pioneered by the Mark III Collaboration [25].We obtain the BFs by reconstructing signal D + decays in events with D − decays reconstructed in one of the three decay modes is found, it is referred to as a single-tag (ST) candidate.An event in which a signal D + decay and a ST D − are simultaneously found is referred as a double-tag (DT) event.The BF of the signal decay is given by where N DT is the number of events with any D − tag and a signal candidate, ǫ i DT is the signal selection efficiency for an event with a D − in the i-th tag mode, and N i ST and ǫ i ST are the number of tags and reconstruction efficiency for D − candidates in mode i.
For the reconstruction and identification of K ± , π ± , K 0 S , and π 0 we use the same criteria as in Refs.[26][27][28][29][30][31][32][33].The tagged D − mesons are selected using two variables, the energy difference and the beam-constrained mass  The signal D + candidates are reconstructed from the particles that have not been used for the tagged D − reconstruction.To select D + → K + π + π − π 0 candidates, the invariant mass of the π + π − pair must satisfy the condition |M π + π − − M K 0 S | > 20 MeV/c 2 to reject the dominant peaking background from D + → K 0 S K + π 0 .This requirement corresponds to about ±5σ of the experimental resolution.The signal D + mesons are identified using the energy difference and the beamconstrained mass of the signal side, ∆E sig and M sig BC , calculated similarly to Eqs. ( 2) and ( 3), respectively, with D − replaced by D + .The signal D + candidates are required to be within ∆E sig ∈ (−58, 45) MeV.To suppress non-D + D − events, the opening angle between the D + and D − candidates is required to be greater than 160 • , which results in a loss of 6% of the signal but rejects 34% of the background contributions.The top-left figure of Fig. 2 shows the M tag BC vs. M sig BC distribution of the accepted candidates for Furthermore, the D + → K + ω candidates are selected from events with π + π − π 0 invariant mass within where M ω is the nominal mass of the ω meson [1].This requirement is set by taking into account both the natural width of the ω meson and the invariant mass resolution.To suppress non-ω backgrounds, the ω helicity angle is required to satisfy | cos θ ω | > 0.57, where θ ω is the opening angle between the normal to the ω → π + π − π 0 decay plane and the direction of the D + meson in the ω rest frame.Moreover, the normalized slope parameter λ/λ max , introduced in Ref. [34], is required to be greater than 0.21, where the criterion is based on an optimization using the inclusive MC sample.The middle-left and bottom-left figures of Fig. 2 show the M tag BC vs. M sig BC distributions of the accepted candidates for D + → K + π + π − π 0 in data, with M π + π − π 0 in the ω signal region and the ω sideband region defined as M π + π − π 0 ∈ (0.60, 0.70) ∪ (0.85, 0.95) GeV/c 2 , respectively.Figure 3 shows the definitions of the ω signal and sideband regions.
In the M tag BC vs. M sig BC distributions, as shown in the left column of Fig. 2, signal events concentrate around M tag BC = M sig BC = M D , where M D is the nominal mass of the D + meson [1].Background events are divided into three categories.The first (BKGI) is from events with correctly reconstructed D + (D − ) and incorrectly reconstructed D − (D + ).This background is distributed along the bands M tag BC = M D and M sig BC = M D .The second (BKGII) describes events found along the diagonal, which are mainly from the e + e − → q q processes.The third (BKGIII) consists of uniformly distributed events in which both the tagged D − and the signal D + are reconstructed incorrectly.For the decay D + → K + π + π − π 0 the peaking backgrounds from D + → K + K − (→ π − π 0 )π + decays and from the residual D + → K 0 S (→ π + π − )K + π 0 events are evaluated using the MC simulations.For the decay D + → K + ω the peaking background contributions are dominated by the non-ω decays from D + → K + π + π − π 0 .This peaking background has the same event topology as the signal and is estimated using data events in the ω sideband region defined above.
To extract the DT yields, a two-dimensional (2D) unbinned maximum likelihood fit is performed on the corresponding M tag BC vs. M sig BC distribution.The 2D probability density function (PDF) for the signal is taken from the MC simulation.The PDFs of background contributions are constructed as • BKGIII: Here, x = M tag BC , y = M sig BC , z = (x + y)/ √ 2, and k = (x − y)/ √ 2. The functions b(x) and b(y) are the onedimensional signal shapes taken from the MC simulation.The function c f is the ARGUS function [35] defined as where f denotes x, y, or z, E b is fixed at 1.8865 GeV, A f is a normalization factor, and ξ f is a fit parameter.The function g(k; σ k ) is a Gaussian distribution with a mean of zero and a standard deviation , where σ 0 and p are parameters determined by the fit.For the decay D + → K + π + π − π 0 the yields and shapes of the peaking background contributions are fixed to the expectation from the MC simulations.All other parameters are left free.
To extract the signal yield of D + → K + ω, simultaneous 2D fits are performed on the events in the ω signal and sideband regions.The background PDFs are fixed to the shapes obtained from the D + → K + π + π − π 0 fit.The ratio of the background yield in the ω sideband region and in the ω signal region is fixed to the value f ω = 4.12 ± 0.08 obtained using the D + → K + π + π − π 0 MC simulation.The reliability of the choice and normalization of the nominal ω sideband region has been further verified by using those events with M π + π − π 0 ∈ (0.85, 1.35) GeV/c 2 arbitrarily.
The spectra in the middle and right columns in Fig. 2 show the projections on M tag BC and M sig BC of the 2D fits to data.For both signal decay modes the statistical significance is evaluated as −2ln(L 0 /L max ), where L max is the maximum likelihood of the nominal fit and L 0 is the likelihood of the fit excluding the signal PDF.The statistical significance is found to be 23.3σ for D + → K + π + π − π 0 and 3.3σ for D + → K + ω.For D + → K + ω, the effect of the fluctuation of the ω sideband events has been considered in the simultaneous fit.Fig. 2. Distributions of (left column) M tag BC vs. M sig BC , and the projections of the corresponding 2D fits on (middle column) M tag BC and (right column) M sig BC , for the DT candidate events of D − → all tags vs. D + → K + π + π − π 0 .The top, middle, and bottom rows correspond to all events, events lying in ω signal region, and those falling in ω sideband region, respectively.In the figures of the middle and right columns, data are shown as dots with error bars; the blue solid, black dashed, blue dot-dashed, red dot-long-dashed, pink longdashed, and green dashed curves denote the overall fit results, signal, BKGI, BKGII, BKGIII, and peaking background components, respectively.
The numbers of N DT and ǫ sig as well as the obtained BFs of the two decays are summarized in the first two rows of Table 1.With the DT method, most of the uncertainties related to the ST selection are negligible.The systematic uncertainties arise from the following sources and are Table 1.The ST and DT yields in data (NST and NDT), the signal efficiencies (ǫsig), and the obtained BFs before (Bsig) and after (B * sig ) removing the contributions from D + → K + η, K + ω, and K + φ.The uncertainties are statistical only.estimated relative to the measured BFs.The uncertainty on the total ST D − yield is due to the fit to the M tag BC distributions and is estimated to be 0.5% [26][27][28].The tracking and PID efficiencies of K ± and π ± are studied with DT D D hadronic events.A small difference between the K ± tracking efficiency in data and in MC simulation is found, but those for the efficiencies of K ± PID, π ± tracking and π ± PID are negligible.The averaged data-MC difference of K ± tracking efficiency weighted by the momentum spectrum of signal MC events is 1.8%.After correcting the MC efficiencies by this averaged data-MC difference, the systematic uncertainties of tracking efficiencies are estimated to be 0.3% per K ± or π ± .The systematic uncertainties originating from PID efficiencies are assigned as 0.3% per K ± or π ± .The efficiency of reconstructing a π 0 meson is investigated by using the DT D D hadronic decay samples of 26,27].

Decay mode
The averaged data-MC difference of the π 0 reconstruction efficiencies, weighted by the momentum spectra of signal MC events, is 0.7% per π 0 .After correcting the MC efficiencies by this averaged data-MC difference the systematic uncertainty arising from π 0 reconstruction is estimated as 0.8% per π 0 .The uncertainties of the quoted BFs of ω → π + π − π 0 and π 0 → γγ decays are 0.8% and 0.03% [1], respectively.
To estimate the systematic uncertainty from the 2D fit, the measurements are repeated by varying the signal shape, the endpoint of the ARGUS function, and the fixed number of peaking background events (by varying ±1σ of the quoted BFs of the dominant peaking backgrounds of D + → K 0 S (→ π + π − )K + π 0 and D + → K + K − (→ π − π 0 )π + ).Quadratically summing over the changes of the BFs gives the systematic uncertainties, which are 0.9% for D + → K + π + π − π 0 and negligible for D + → K + ω.The systematic uncertainty of the D + D − opening angle requirement is assigned as 0.5% based on DT events where the signal decays are replaced by the CF D + → K − π + π + π 0 channel.The systematic uncertainty associated with the ∆E sig requirement is evaluated to be 0.2%, estimated by smearing the ∆E sig distribution for signal MC events.The systematic uncertainty due to K 0 S rejection is negligible since the mass resolution is well reproduced by the MC simulation.The boundaries of the ω sideband regions were varied by ±5 MeV/c 2 and the corresponding uncertainty was found to be negligible.The limited statistics of the signal MC simulation contributes 0.5% uncertainty for D + → K + π + π − π 0 and 0.6% for D + → K + ω.The systematic uncertainty related to the MC modeling for D + → K + π + π − π 0 is assigned to be 1.3%, which is the difference of the DT efficiencies with and without involving the less significant decays of D + → K + η, K + ω, and K + φ, and the effect of high excited states are negligible.
For D + → K + ω, the systematic uncertainties of the MC modeling are mainly from the imperfect simulations on cos θ ω and λ/λ max .They are estimated using the DT events D 0 → K 0 S ω vs. D0 → K + π − , K + π − π 0 , and K + π − π − π + .The differences of the acceptance efficiencies of the cos θ ω and λ/λ max requirements between data and MC simulations, 3.0% and 1.2%, are assigned as the corresponding systematic uncertainties, respectively.The uncertainty on the scale factor f sid/sig ω results in 0.6% uncertainty on the D + → K + ω signal.
The total systematic uncertainty of the BF measurement is 2.3% for D + → K + π + π − π 0 and 3.8% for D + → K + ω, obtained by adding the above effects quadratically.
The BFs of the charge-conjugated decays are measured separately.The asymmetry of these two BFs is determined as (5) The corresponding ST yields, DT yields, signal efficiencies, and the obtained BFs are summarized in the last two rows of Table 1.The asymmetry is determined to be A D ± →K ± π ± π ∓ π 0 CP = (−0.04±0.06stat ±0.01 syst ), where the systematic uncertainties of tracking and PID of the π + π − pair, π 0 reconstruction, quoted BFs, and MC modeling cancel.Other systematic uncertainties are estimated separately as above.No evidence for CP violation is found.

g
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 h 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 i Also at Harvard University, Department of Physics, Cambridge, MA, 02138, USA j Currently at: Institute of Physics and Technology, Peace Ave.54B, Ulaanbaatar 13330, Mongolia k Also at State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, People's Republic of China l School of Physics and Electronics, Hunan University, Changsha 410082, China where E b is the beam energy, and p D − and E D − are the momentum and the energy of the D − candidate in the e + e − rest frame.For each tag mode, if there are multiple combinations, the one giving the minimum |∆E tag | is retained for further analysis.The tagged D − are required to satisfy ∆E tag ∈ (−55, 40) MeV for the decay mode containing a π 0 , and ∆E tag ∈ (−25, 25) MeV for the other decay modes.The yields of ST D − mesons were obtained from maximum likelihood fits to the M tag BC distributions of the accepted ST candidates [26-31].The fit results are shown in Fig. 1.The total ST D − yield is N ST =1150287 ± 1484 stat .

Fig. 1 .
Fig. 1.Fits to the MBC distributions of the ST D − candidates.Data are shown as dots with error bars.The blue solid and red dashed curves are the fit results and the fitted backgrounds, respectively.