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Measurement of e+ e− → DD cross sections at theψ(3770) resonanceTo cite this article: M. Ablikim et al 2018 Chinese Phys. C 42 083001

 

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Chinese Physics C Vol. 42, No. 8 (2018) 083001

Measurement of e+e−→DD cross sections at the ψ(3770) resonance *

M. Ablikim(ð&A)1 M. N. Achasov9,d S. Ahmed14 M. Albrecht4 M. Alekseev55A,55C A. Amoroso55A,55C F. F. An(S¥¥)1 Q. An(Sj)42,52 Y. Bai(x�)41 O. Bakina26 R. Baldini Ferroli22A Y. Ban(�])34 K. Begzsuren24 D. W. Bennett21

J. V. Bennett5 N. Berger25 M. Bertani22A D. Bettoni23A J. M. Bian(>ì´)49 F. Bianchi55A,55C E. Boger26,b I. Boyko26

R. A. Briere5 H. Cai(éÓ)57 X. Cai(é�)1,42 O. Cakir45A A. Calcaterra22A G. F. Cao(ùIL)1,46 S. A. Cetin45B J. Chai55C

J. F. Chang(~§~)1,42 W. L. Chang1,46 G. Chelkov26,b,c G. Chen(�f)1 H. S. Chen(�Ú))1,46 J. C. Chen(�ôA)1

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N. Yu. Muchnoi9,d H. Muramatsu(~t�)49 A. Mustafa4 S. Nakhoul10,g Y. Nefedov26 F. Nerling10 I. B. Nikolaev9,d Z. Ning(wó)1,42 S. Nisar8 S. L. Niu(Ú^|)1,42 X. Y. Niu(ÚÕ�)1,46 S. L. Olsen(29)35,j Q. Ouyang(î�+)1 S. Pacetti22B Y. Pan(�

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Received 17 March 2018, Published online 20 June 2018

∗ Supported by National Key Basic Research Program of China (2015CB856700), National Natural Science Foundation of China(NSFC) (11235011, 11335008, 11425524, 11625523, 11635010), the Chinese Academy of Sciences (CAS) Large-Scale Scientific FacilityProgram, the CAS Center for Excellence in Particle Physics (CCEPP), Joint Large-Scale Scientific Facility Funds of the NSFC and CAS(U1332201, U1532257, U1532258), CAS Key Research Program of Frontier Sciences (QYZDJ-SSW-SLH003, QYZDJ-SSW-SLH040), 100Talents Program of CAS, National 1000 Talents Program of China, INPAC and Shanghai Key Laboratory for Particle Physics and Cosmol-ogy, German Research Foundation DFG under Contracts Nos. Collaborative Research Center CRC 1044, FOR 2359, Istituto Nazionaledi Fisica Nucleare, Italy, Koninklijke Nederlandse Akademie van Wetenschappen (KNAW) (530-4CDP03), Ministry of Development ofTurkey (DPT2006K-120470), National Science and Technology fund, The Swedish Research Council, U. S. Department of Energy (DE-FG02-05ER41374, DE-SC-0010118, DE-SC-0010504, DE-SC-0012069), University of Groningen (RuG) and the Helmholtzzentrum fuerSchwerionenforschung GmbH (GSI), Darmstadt, WCU Program of National Research Foundation of Korea (R32-2008-000-10155-0)

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distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article fundedby SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academyof Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd

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(BESIII Collaboration)1 Institute of High Energy Physics, Beijing 100049, China

2 Beihang University, Beijing 100191, China3 Beijing Institute of Petrochemical Technology, Beijing 102617, China

4 Bochum Ruhr-University, D-44780 Bochum, Germany5 Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

6 Central China Normal University, Wuhan 430079, China7 China Center of Advanced Science and Technology, Beijing 100190, China

8 COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan9 G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia10 GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany

11 Guangxi Normal University, Guilin 541004, China12 Guangxi University, Nanning 530004, China

13 Hangzhou Normal University, Hangzhou 310036, China14 Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany

15 Henan Normal University, Xinxiang 453007, China16 Henan University of Science and Technology, Luoyang 471003, China

17 Huangshan College, Huangshan 245000, China18 Hunan Normal University, Changsha 410081, China

19 Hunan University, Changsha 410082, China20 Indian Institute of Technology Madras, Chennai 600036, India

21 Indiana University, Bloomington, Indiana 47405, USA22 (A)INFN Laboratori Nazionali di Frascati, I-00044, Frascati, Italy; (B)INFN and University of Perugia, I-06100, Perugia, Italy

23 (A)INFN Sezione di Ferrara, I-44122, Ferrara, Italy; (B)University of Ferrara, I-44122, Ferrara, Italy24 Institute of Physics and Technology, Peace Ave. 54B, Ulaanbaatar 13330, Mongolia

25 Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany26 Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia

27 Justus-Liebig-Universitaet Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany28 KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands

29 Lanzhou University, Lanzhou 730000, China30 Liaoning University, Shenyang 110036, China

31 Nanjing Normal University, Nanjing 210023, China

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32 Nanjing University, Nanjing 210093, China33 Nankai University, Tianjin 300071, China34 Peking University, Beijing 100871, China

35 Seoul National University, Seoul, 151-747, Korea36 Shandong University, Jinan 250100, China

37 Shanghai Jiao Tong University, Shanghai 200240, China38 Shanxi University, Taiyuan 030006, China

39 Sichuan University, Chengdu 610064, China40 Soochow University, Suzhou 215006, China

41 Southeast University, Nanjing 211100, China42 State Key Laboratory of Particle Detection and Electronics, Beijing 100049, Hefei 230026, China

43 Sun Yat-Sen University, Guangzhou 510275, China44 Tsinghua University, Beijing 100084, China

45 (A)Ankara University, 06100 Tandogan, Ankara, Turkey; (B)Istanbul Bilgi University, 34060 Eyup, Istanbul, Turkey; (C)UludagUniversity, 16059 Bursa, Turkey; (D)Near East University, Nicosia, North Cyprus, Mersin 10, Turkey

46 University of Chinese Academy of Sciences, Beijing 100049, China47 University of Hawaii, Honolulu, Hawaii 96822, USA

48 University of Jinan, Jinan 250022, China49 University of Minnesota, Minneapolis, Minnesota 55455, USA

50 University of Muenster, Wilhelm-Klemm-Str. 9, 48149 Muenster, Germany51 University of Science and Technology Liaoning, Anshan 114051, China52 University of Science and Technology of China, Hefei 230026, China

53 University of South China, Hengyang 421001, China54 University of the Punjab, Lahore-54590, Pakistan

55 (A)University of Turin, I-10125, Turin, Italy; (B)University of Eastern Piedmont, I-15121, Alessandria, Italy; (C)INFN, I-10125,Turin, Italy

56 Uppsala University, Box 516, SE-75120 Uppsala, Sweden57 Wuhan University, Wuhan 430072, China

58 Xinyang Normal University, Xinyang 464000, China59 Zhejiang University, Hangzhou 310027, China

60 Zhengzhou University, Zhengzhou 450001, China

a Also at Bogazici University, 34342 Istanbul, Turkeyb Also at the Moscow Institute of Physics and Technology, Moscow 141700, Russia

c Also at the Functional Electronics Laboratory, Tomsk State University, Tomsk, 634050, Russiad Also at the Novosibirsk State University, Novosibirsk, 630090, Russia

e Also at the NRC ”Kurchatov Institute”, PNPI, 188300, Gatchina, Russiaf Also at Istanbul Arel University, 34295 Istanbul, Turkey

g Also at Goethe University Frankfurt, 60323 Frankfurt am Main, Germanyh 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, Chinai Also at Government College Women University, Sialkot - 51310. Punjab, Pakistan.

j Currently at: Center for Underground Physics, Institute for Basic Science, Daejeon 34126, Korea

Abstract: We report new measurements of the cross sections for the production of DD final states at the ψ(3770)

resonance. Our data sample consists of an integrated luminosity of 2.93 fb−1 of e+e− annihilation data produced by

the BEPCII collider and collected and analyzed with the BESIII detector. We exclusively reconstruct three D0 and six

D+ hadronic decay modes and use the ratio of the yield of fully reconstructed DD events (“double tags”) to the yield of

all reconstructed D or D mesons (“single tags”) to determine the number of D0D0 and D+D− events, benefiting from

the cancellation of many systematic uncertainties. Combining these yields with an independent determination of the

integrated luminosity of the data sample, we find the cross sections to be σ(e+e−→D0D0)=(3.615±0.010±0.038) nb

and σ(e+e−→D+D−)=(2.830±0.011±0.026) nb, where the uncertainties are statistical and systematic, respectively.

Keywords: charm mesons, cross sections, BESIII/BEPCII

PACS: 13.25.Ft, 13.25.Gv, 13.66.Bc DOI: 10.1088/1674-1137/42/8/083001

1 Introduction

The ψ(3770) resonance is the lowest-energy charmo-nium state above the threshold for decay to charmedmeson pairs. The expectation that the ψ(3770) shoulddecay predominantly to D0D0 and D+D− has been val-idated by experiment [1], although inconsistent results

for the branching fraction of ψ(3770) to non-DD finalstates have been reported [2, 3]. The cross sectionsσ(e+e−→D0D0) and σ(e+e−→D+D−) at center-of-massenergy Ecm =3.773 GeV, the peak of the ψ(3770) res-onance, can be measured precisely and are necessaryinput for normalizing some measurements of charmedmeson properties in ψ(3770) decays. The most precise

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determinations to date are from the CLEO-c Collabora-tion [4] using 818 pb−1 of e+e− annihilation data at Ecm=3774±1 MeV, σ(e+e−→D0D0)=(3.607±0.017±0.056) nband σ(e+e− → D+D−) = (2.882±0.018±0.042) nb. Inthis paper we report measurements of the DD cross sec-tions using fully reconstructed D0 and D+ mesons in aψ(3770) data sample that is approximately 3.6 timeslarger than CLEO-c’s. Here and throughout this pa-per, charge-conjugate modes are implied unless explicitlystated.

Our procedure is an application of the D-taggingtechnique developed by the MARK III Collaboration [5],exploiting the kinematics of DD production just abovethreshold at the ψ(3770) resonance. We use ratios offully reconstructed D mesons (“single tags”) and DDevents (“double tags”) to determine the total numbersof DD pairs. This procedure benefits from the cancella-tion of systematic uncertainties associated with efficien-cies and input branching fractions, giving better overallprecision than measurements based on single tags. Theproduction of D0D0 pairs in a pure C=−1 state compli-cates the interpretation of measurements at ψ(3770) byintroducing correlations between the D0 and D0 decays.We apply corrections derived by Asner and Sun [6] toremove the bias introduced by these correlations.

2 BESIII detector

Our measurement has been made with the BESIIIdetector at the BEPCII collider of the Institute for HighEnergy Physics in Beijing. Data were collected at theψ(3770) peak, with Ecm = 3.773 GeV. The integratedluminosity of this sample has previously been deter-mined with large-angle Bhabha scattering events to be2.93 fb−1 [7, 8], with an uncertainty of 0.5% dominatedby systematic effects. An additional data sample of44.9 pb−1 at Ecm = 3.650 GeV has been used to assesspotential background from continuum production underthe ψ(3770).

BESIII is a general-purpose magnetic spectrometerwith a geometrical acceptance of 93% of 4π. Chargedparticles are reconstructed in a 43-layer helium-gas-baseddrift chamber (MDC), which has an average single-wireresolution of 135 µm. A uniform axial magnetic fieldof 1 T is provided by a superconducting solenoid, allow-ing the precise measurement of charged particle trajecto-ries. The resolution varies as a function of momentum,and is 0.5% at 1.0 GeV/c. The MDC is also instru-mented to measure the specific ionization (dE/dx) ofcharged particles for particle identification. Additionalparticle identification is provided by a time-of-flight sys-tem (TOF) constructed as a cylindrical (“barrel”) struc-ture with two 5-cm-thick plastic-scintillator layers andtwo “end caps” with one 5-cm layer. The time resolu-

tion in the barrel is approximately 80 ps, and in the endcaps it is 110 ps. Just beyond the TOF is an electro-magnetic calorimeter (EMC) consisting of 6240 CsI(Tl)crystals, also configured as a barrel and two end caps.For 1.0-GeV photons, the energy resolution is 2.5% inthe barrel and it is 5% in the end caps. This entire innerdetector resides in the solenoidal magnet, which is sup-ported by an octagonal flux-return yoke instrumentedwith resistive-plate counters interleaved with steel formuon identification (MUC). More detailed informationon the design and performance of the BESIII detectorcan be found in Ref. [9].

3 Technique

To select a DD event, we fully reconstruct a D us-ing tag modes that have sizable branching fractions andcan be reconstructed with good efficiency and reasonablebackground. We use three D0 and six D+ tag modes:D0 → K−π+, D0 → K−π+π0, D0 → K−π+π+π−, D+ →K−π+π+, D+→K−π+π+π0, D+→K0

Sπ+, D+→K0

Sπ+π0,

D+→K0Sπ

+π+π−, and D+→K−K+π+.When both the D and D in an event decay to tag

modes we can fully reconstruct the entire event. Thesedouble-tag events are selected when the event has twosingle tags and satisfies the additional requirements thatthe reconstructed single tags have opposite net charge,opposite-charm D parents and no shared tracks. Theyield Xi for single-tag mode i is given by Eq. (1):

Xi=NDD·B(D→i)·εi, (1)

where NDD is the total number of DD events, B(D→ i)is the branching fraction for decay mode i, and εi is thereconstruction efficiency for the mode, determined withMonte Carlo (MC) simulation. Extending this reasoning,the yields for D decaying to mode j and for ij double-tag events, in which the D decays to mode i and the Ddecays to mode j, are given as follows:

Yj =NDD·B(D→j)·εj , (2)

andZij =NDD·B(D→i)·B(D→j)·εij . (3)

In these equations, Zij is the yield for the double-tagmode ij, and εij is the efficiency for reconstructing bothtags in the same event. Combining Eqs. (1), (2) and (3),NDD can be expressed as

NDD=Xi·Yj ·εijZij ·εi·εj

. (4)

The cancellation of systematic uncertainties occursthrough the ratio of efficiencies εij/(εi·εj). The measuredNDD from each combinations of i and j are then aver-aged, weighted by their statistical uncertainties. Finally,to determine cross sections we divide NDD by the inte-

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grated luminosity L of the ψ(3770) sample, σ(e+e− →DD)=NDD/L.

4 Particle reconstruction

Detection efficiencies and backgrounds for this anal-ysis have been studied with detailed simulations of theBESIII detector based on GEANT4 [10]. High-statisticsMC samples were produced for generic D0D0 and D+D−

decays from ψ(3770), qq→ light hadrons (q=u,d or s),τ+τ−, and radiative return to J/ψ and ψ(3686). TheD0D0, D+D−, qq, and τ+τ− states were generated us-ing KKMC [11, 12], while the γJ/ψ and γψ(3686) weregenerated with EvtGen [13]. All were then decayed withEvtGen, except for the qq and τ+τ−, which were modeledwith the LUNDCHARM [14] and the TAUOLA [11, 15]generators, respectively.

Data and MC samples are treated identically for theselection of D tags. All particles used to reconstruct acandidate must pass requirements specific to the parti-cle type. Charged particles are required to be within thefiducial region for reliable tracking (|cosθ|<0.93, whereθ is the polar angle relative to the beam direction) andto pass within 1 cm (10 cm) of the interaction point inthe plane transverse to the beam direction (along thebeam direction). Particle identification is based on TOFand dE/dx measurements, with the identity as a pion orkaon assigned based on which hypothesis has the higherprobability. To be selected as a photon, an EMC showermust not be associated with any charged track [16], musthave an EMC hit time between 0 and 700 ns to suppressactivity that is not consistent with originating from thecollision event, must have an energy of at least 25 MeV ifit is in the barrel region of the detector (|cosθ|<0.8), and50 MeV if it is in the end cap region (0.84<|cosθ|<0.92)to suppress noise in the EMC as a potential backgroundto real photons. Showers in the transition region betweenthe barrel and end cap are excluded.

K0S mesons are reconstructed from the decay into

π+π−. Because of the cleanliness of the selection andthe possibility of a measurably displaced decay vertex,the pions are not required to pass the usual particleidentification or interaction-point requirements. A fit isperformed with the pions constrained to a common ver-tex and the K0

S candidate is accepted if the fit satisfiesχ2 < 100 and the candidate mass is within ∼ 3σ of thenominal K0

S mass (487−511 MeV/c2). The momentum ofthe K0

S that is obtained from the constrained-vertex fitis used for the subsequent reconstruction of D-tag can-didates. π0 mesons are reconstructed through the de-cay into two photons. Both photons for a π0 candidatemust pass the above selection criteria, and at least oneof them must be in the barrel region of the detector. Tobe accepted a π0 candidate must have an invariant mass

between 115 MeV/c2 and 150 MeV/c2. The photons arethen refitted with a π0 mass constraint and the result-ing π0 momentum is used for the reconstruction of D-tagcandidates.

5 Event selection

In addition to the requirements on the final-state par-ticles, the reconstructed D-tag candidates must pass sev-eral additional requirements that ensure the measuredcandidate energy and momentum are close to the ex-pected values for production via ψ(3770) → DD. Thefirst of these requirements is ∆E=ED−Ebeam'0, whereED is the energy of the reconstructed D candidate andEbeam is the beam energy. In calculating ∆E we use thebeam energy calibrated with D0 and D+ decays, combin-ing groups of nearby runs to obtain sufficient statistics.Selection requirements on ∆E are determined separatelyfor each tag mode for data and MC to account for differ-ing resolutions. As shown in Table 1, for modes decayinginto all charged tracks, the requirements are set to ±3σabout the mean, while for modes with a π0, the require-ments are asymmetric about the mean, extending on thelow side to −4σ to accommodate the tail from the photonenergy resolution.

Figure 1 shows the data and MC overlays of the ∆Edistributions by mode.

Table 1. The selected range on ∆E is ±3σ aboutthe mean, except that for modes with a π0 anextended lower bound of −4σ is used. The reso-lutions and means are extracted by fitting with adouble Gaussian, weighted by the two Gaussianyields, and determined separately for data andMC.

Tag modeMC data

σ/MeV mean/MeV σ/MeV mean/MeV

D0→K−π+ 7.6 −0.4 9.4 −0.8

D0→K−π+π0 14.1 −7.6 15.4 −7.6

D0→K−π+π+π− 8.2 −1.4 9.8 −2.0

D+→K−π+π+ 7.2 −0.9 8.6 −1.2

D+→K−π+π+π0 12.8 −6.9 13.7 −6.9

D+→K0Sπ

+ 6.7 0.4 8.4 −0.1

D+→K0Sπ

+π0 14.6 −7.7 16.2 −7.9

D+→K0Sπ

+π+π− 8.2 −1.1 10.4 −1.7

D+→K+K−π+ 6.2 −1.1 7.2 −1.5

The second variable used in selecting D tags isthe beam-constrained mass MBCc

2 =√E2

beam−|ptagc|2,where ptag is the 3-momentum of the candidate D. Weuse MBC rather than the invariant mass because of theexcellent precision with which the beam energy is known.The requirement that MBC be close to the known D massensures that the D tag has the expected momentum.After application of the ∆E requirement to single-tagcandidates of a given mode, we construct an MBC dis-

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-0.1 -0.04 0 0.04 0.1ΔE (GeV)

Fig. 1. (color online) ∆E line shape for various single-tag mode (arbitrarily scaled). Starting from the top left, themodes are: (a) D0→K−π+, (b) D0→K−π+π0, (c) D0→K−π+π+π−, (d) D+→K−π+π+, (e) D+→K−π+π+π0,(f) D+ → K0

Sπ+, (g) D+ → K0

Sπ+π0, (h) D+ → K0

Sπ+π+π−, and (i) D+ → K+K−π+. These plots overlay the

3.773 GeV data (blue dashed histograms) and the corresponding narrower-width MC (red solid histograms). Onlyrequirements on the constituent particles and a very loose MBC requirement (1.83 GeV/c2 6MBC61.89 GeV/c2)have been applied.

tribution in the region of the known masses of charmedmesons (1.83−1.89 GeV/c2). For the MC a small upwardshift of just under 1 MeV/c is applied to the measuredD momentum for the calculation of MBC to compensatefor input parameters that do not precisely match data.Initial inspection of the distribution in data for the two-body mode D0→K−π+ exhibited peaking near the highend of the MBC range not seen in MC. We demonstratedthis to be background from cosmic ray and QED events.To eliminate it from the distribution, additional require-ments are applied in selecting D0 → K−π+ candidateswith exactly two charged tracks. We veto these events ifthey satisfy at least one of the following conditions: TOFinformation consistent with a cosmic ray event, particleidentification information consistent with an e+e− hy-pothesis, two tracks with EMC energy deposits consis-tent with an e+e− hypothesis, or either track with parti-cle identification and MUC information consistent withbeing a muon.

6 Yields and efficiencies

The MBC distribution for single-tag candidates foreach mode is fitted with a MC-derived signal shape andan ARGUS function background [17]. The signal shape isconvolved with a double Gaussian with a common meanto allow for differences in MBC resolution between data

and MC. Charge-conjugate modes are fitted simultane-ously with the double-Gaussian signal-shape parametersconstrained to be the same and the normalizations andbackground parameters allowed to vary independentlyin the fit. Peaking backgrounds contributed by decaymodes that have similar final states to the signal modeare included in the signal shape, although the yields arecorrected after the fit to count only true signal events.

An example MBC fit is shown in Fig. 2. (The full setof fits is provided in Appendix A.) In events with mul-tiple single-tag candidates, the best candidate is chosenper mode and per charm to be the one with the small-est |∆E|. Based on the fit results tight mode-dependentrequirements on ∆E are applied. To determine the tagyield, the MBC histogram is integrated within the signalregion, 1.8580 GeV/c2 6 MBC 6 1.8740 GeV/c2 for D0

modes and 1.8628 GeV/c2 6MBC 6 1.8788 GeV/c2 forD+ modes, and then the analytic integral of the ARGUSfunction in this region is subtracted. The efficiency foreach of the 18 single-tag modes is found by using MCtruth information to determine the total number gener-ated for the denominator and using the same cut-and-count method as used for data to determine the numer-ator. The single-tag yields and efficiencies are summa-rized in Table 2, where the efficiencies include branchingfractions for π0→γγ and K0

S→π+π− decays.

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1.83 1.85 1.87 1.89

1

2345678

M (GeV/c ) BC2

Even

ts/0

.000

24 G

eV/c

2

(×10 )3

9

Fig. 2. (color online) MBC fit for single-tag modeD+ → K−π+π+π0, from data. Blue dash-dot(green dashed) line represents the total fit (thefitted background shape) and the red solid curvecorresponds to the fitted signal shape.

Table 2. Single-tag yields after subtracting theircorresponding peaking backgrounds from dataand efficiencies from MC, as described in the text.The uncertainties are statistical only.

tag mode yield efficiency(%)

D0→K−π+ 260,915 ± 520 63.125 ± 0.007

D0→K+π− 262,356 ± 522 64.272 ± 0.006

D0→K−π+π0 537,923 ± 845 35.253 ± 0.007

D0→K+π−π0 544,252 ± 852 35.761 ± 0.007

D0→K−π+π+π− 346,583 ± 679 38.321 ± 0.007

D0→K+π+π−π− 351,573 ± 687 39.082 ± 0.007

D+→K−π+π+ 391,786 ± 653 50.346 ± 0.005

D−→K+π−π− 394,749 ± 656 51.316 ± 0.005

D+→K−π+π+π0 124,619 ± 529 26.138 ± 0.014

D−→K+π−π−π0 128,203 ± 539 26.586 ± 0.015

D+→K0Sπ

+ 48,185 ± 229 36.726 ± 0.008

D−→K0Sπ

− 47,952 ± 228 36.891 ± 0.008

D+→K0Sπ

+π0 114,919 ± 471 20.687 ± 0.011

D−→K0Sπ

−π0 116,540 ± 472 20.690 ± 0.011

D+→K0Sπ

+π+π− 63,018 ± 421 21.966 ± 0.019

D−→K0Sπ

+π−π− 62,982 ± 421 21.988 ± 0.019

D+→K+K−π+ 34,416 ± 258 41.525 ± 0.042

D−→K+K−π− 34,434 ± 257 41.892 ± 0.042

Double tags are fully reconstructed events in whichboth the D and the D pass the selection criteria for one ofthe tag modes. In events with multiple double-tag can-didates, the best candidate per mode combination perevent is chosen with the [MBC(D)+MBC(D)]/2 closest tothe known D mass. Following a procedure similar to thesingle-tag counting, we fit the two-dimensional distribu-tion of MBC(D) vs. MBC(D) for the selected single-tagmodes to define the signal region for a cut-and-countdetermination of the double-tag yield. A more sophisti-cated treatment of the background is required because

of the correlations between the tags. The signal shape isagain derived from MC, using truth information and in-cluding peaking backgrounds with the signal. We foundthat convolving the MC shape with smearing functions toaccount for the small data/MC resolution difference didnot appreciably improve the accuracy of the tag yields,so no signal smearing is included in the double-tag fits.

The background shapes in the double-tag fits cor-respond to four possible ways of mis-reconstructing anevent, as shown in Fig. 3. A direct product of a MC-derived signal shape with an analytic ARGUS functionbackground, with shape parameters fixed to those ofthe corresponding single-tag fit, is used to represent thebackground contributed by events with a correctly re-constructed D and incorrectly reconstructed D. Thebackground shape for the charm-conjugate case is sim-ilarly constructed. For completely reconstructed con-tinuum events or fully reconstructed but mispartitionedDD events (with particles assigned incorrectly to the Dand D), a direct product of a double-Gaussian functionand an ARGUS function rotated by 45◦ is used. Thekinematic limit and exponent parameters of the rotatedARGUS function are fixed, while the slope parameteris allowed to be free in the fit. Finally, the remainingbackground events with neither D nor D correctly recon-structed are modeled with a direct product of two AR-GUS functions, with parameters taken from the corre-sponding single-tag fits. An example fit to data is shownin Fig. 4. (The full set of fits is provided in AppendixA.)

BC )2 (GeV/cM (D1.83 1.84 1.85 1.86 1.87 1.88 1.89

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)

)

Fig. 3. (color online) The two-dimensional MBC

plane divided into regions dominated by signaland various backgrounds. These regions representthe shapes used in the double-tag fitting methodand sideband corrections described in the text.

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Chinese Physics C Vol. 42, No. 8 (2018) 083001

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Fig. 4. (color online) Example two-dimensional MBC double-tag fit from data as described in the text, for tag modeK+π−π− vs. K−π+π+π0. The top left figure is a scatter plot of the data and the top right is a scatter plot ofthe fit to the data. The bottom two plots are overlays of data and the fit projected onto the positive and negativecharm MBC axes. The red dashed (blue solid) lines represent the total fits (the fitted signal shapes) and the solidgreen curves are the fitted background shapes. The magenta curve corresponds to the case when D−→K+π−π−

is reconstructed correctly, while D+→K−π+π+π0 is not.

After the two-dimensional fit is performed, the MBC

histogram is integrated within the same signal region asthe single-tag fits, and the integrals of the four back-ground shapes are subtracted from this total. The re-sultant double-tag yields and efficiencies, which includebranching fractions for π0→γγ and K0

S→π+π− decays,are summarized in Tables 3 and 4.

We must correct the yields determined with the MBC

fits (data and MC) for contributions from backgroundprocesses that peak in the signal region. Such back-grounds come from other D decays with similar kine-matics and particle compositions as the specific signalmode. We rely on MC, generated with world-averagebranching fractions [1], to determine the fraction of peak-ing background events, as well as to calculate their se-lection efficiencies. We apply MC-determined correc-tions for these in every case where more than 0.01% ofthe fitted yield is attributable to peaking background.The largest contribution of peaking background is forD+ → K0

Sπ+π+π−, approximately 2.5% of the fitted

yield. D0 →K−π+π+π− and D+ →K0Sπ

+π0 both have∼2.0% of their fitted yields from peaking backgrounds,

and all other modes have less than 1.0%. Because thepeaking backgrounds come from well understood pro-cesses, like doubly Cabibbo-suppressed modes, simulta-neous misidentification of both a pion and a kaon in anevent, and charged pion pairs not from K0

S decays thatpass the K0

S invariant mass requirement, we are confidentthat they are well modeled by the MC.

The analysis described above results in a set of mea-sured values of NDDij, the number of DD events deter-mined with the single- and double-tag yields of positivetag mode i and negative tag mode j. The uncertaintiesare highly mode dependent because of branching frac-tions, efficiencies and backgrounds, so these measure-ments must be combined into an uncertainty-weightedmean taking into account correlations within and be-tween the mode-specific measurements. We use an ana-lytic procedure for this and demonstrated its reliabilitywith a toy MC study.

For our full 2.93 fb−1 ψ(3770) data sample we findND0D0 =(10,621±29)×103 and ND+D−=(8,296±31)×103.Using the integrated luminosity from Ref. [8], we ob-tain observed cross sections for DD production at the

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Table 3. D0D0 double-tag yields from data and efficiencies from MC, as described in the text. The uncertaintiesare statistical only.

tag mode yield efficiency(%)

D0→K−π+ vs. D0→K+π− 6,545 ± 81 42.58 ± 0.13

D0→K−π+ vs. D0→K+π−π0 14,701 ± 122 24.90 ± 0.06

D0→K−π+ vs. D0→K+π+π−π− 9,096 ± 96 25.54 ± 0.08

D0→K−π+π0 vs. D0→K+π− 14,526 ± 122 24.94 ± 0.06

D0→K−π+π0 vs. D0→K+π−π0 30,311 ± 176 13.94 ± 0.03

D0→K−π+π0 vs. D0→K+π+π−π− 18,651 ± 139 14.35 ± 0.03

D0→K−π+π+π− vs. D0→K+π− 8,988 ± 96 25.77 ± 0.08

D0→K−π+π+π− vs. D0→K+π−π0 18,635 ± 139 14.32 ± 0.03

D0→K−π+π+π− vs. D0→K+π+π−π− 11,572 ± 110 14.86 ± 0.04

Table 4. D+D− double-tag yields from data and efficiencies from MC, as described in the text. The uncertaintiesare statistical only.

tag mode yield efficiency(%)

D+→K−π+π+ vs. D−→K+π−π− 18,800 ± 138 26.02 ± 0.05

D+→K−π+π+ vs. D−→K+π−π−π0 5,981 ± 80 13.62 ± 0.05

D+→K−π+π+ vs. D−→K0Sπ

− 2,368 ± 49 18.45 ± 0.12

D+→K−π+π+ vs. D−→K0Sπ

−π0 5,592 ± 75 10.51 ± 0.04

D+→K−π+π+ vs. D−→K0Sπ

+π−π− 2,826 ± 53 10.82 ± 0.06

D+→K−π+π+ vs. D−→K+K−π− 1,597 ± 40 20.87 ± 0.15

D+→K−π+π+π0 vs. D−→K+π−π− 6,067 ± 80 13.48 ± 0.05

D+→K−π+π+π0 vs. D−→K+π−π−π0 1,895 ± 53 6.79 ± 0.06

D+→K−π+π+π0 vs. D−→K0Sπ

− 693 ± 26 9.82 ± 0.11

D+→K−π+π+π0 vs. D−→K0Sπ

−π0 1,726 ± 44 5.22 ± 0.04

D+→K−π+π+π0 vs. D−→K0Sπ

+π−π− 857 ± 33 5.41 ± 0.06

D+→K−π+π+π0 vs. D−→K+K−π− 549 ± 24 10.78 ± 0.15

D+→K0Sπ

+ vs. D−→K+π−π− 2,352 ± 48 18.96 ± 0.12

D+→K0Sπ

+ vs. D−→K+π−π−π0 722 ± 27 9.80 ± 0.12

D+→K0Sπ

+ vs. D−→K0Sπ

− 269 ± 16 13.95 ± 0.27

D+→K0Sπ

+ vs. D−→K0Sπ

−π0 678 ± 26 7.67 ± 0.10

D+→K0Sπ

+ vs. D−→K0Sπ

+π−π− 383 ± 20 7.90 ± 0.13

D+→K0Sπ

+ vs. D−→K+K−π− 191 ± 14 15.2 ± 0.34

D+→K0Sπ

+π0 vs. D−→K+π−π− 5,627 ± 75 10.64 ± 0.04

D+→K0Sπ

+π0 vs. D−→K+π−π−π0 1,708 ± 43 5.28 ± 0.04

D+→K0Sπ

+π0 vs. D−→K0Sπ

− 624 ± 25 7.67 ± 0.10

D+→K0Sπ

+π0 vs. D−→K0Sπ

−π0 1,557 ± 40 4.08 ± 0.03

D+→K0Sπ

+π0 vs. D−→K0Sπ

+π−π− 747 ± 28 4.26 ± 0.05

D+→K0Sπ

+π0 vs. D−→K+K−π− 503 ± 23 8.51 ± 0.13

D+→K0Sπ

+π+π− vs. D−→K+π−π− 2,857 ± 53 11.01 ± 0.06

D+→K0Sπ

+π+π− vs. D−→K+π−π−π0 924 ± 34 5.44 ± 0.06

D+→K0Sπ

+π+π− vs. D−→K0Sπ

− 313 ± 18 7.72 ± 0.13

D+→K0Sπ

+π+π− vs. D−→K0Sπ

−π0 778 ± 29 4.17 ± 0.05

D+→K0Sπ

+π+π− vs. D−→K0Sπ

+π−π− 468 ± 24 4.28 ± 0.06

D+→K0Sπ

+π+π− vs. D−→K+K−π− 246 ± 18 8.96 ± 0.19

D+→K+K−π+ vs. D−→K+π−π− 1,576 ± 40 21.31 ± 0.16

D+→K+K−π+ vs. D−→K+π−π−π0 509 ± 23 10.41 ± 0.15

D+→K+K−π+ vs. D−→K0Sπ

− 185 ± 14 14.48 ± 0.33

D+→K+K−π+ vs. D−→K0Sπ

−π0 468 ± 22 8.23 ± 0.13

D+→K+K−π+ vs. D−→K0Sπ

+π−π− 232 ± 18 8.62 ± 0.19

D+→K+K−π+ vs. D−→K+K−π− 156 ± 16 16.46 ± 0.53

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ψ(3770) of σ(e+e− → D0D0) = (3.623±0.010) nb andσ(e+e− → D+D−) = (2.830±0.011) nb. Here, the un-certainties are statistical only. The summed χ2 valuesrelative to the mean for all pairs of tag modes are 13.2for D0D0 (9 modes) and 53.6 for D+D− (36 modes).

We verified the reliability of our yield measurementswith an “In vs. Out” test with MC by randomly parti-tioning our MC (signal and background) into ten statisti-cally independent data-sized sets. We determined single-and double-tag yields for these subsamples, calculatedthe NDD and compared these to the true values for each.The overall χ2 for these ten tests was 10.7 for ND0D0 and12.4 for ND+D− , demonstrating that our procedure reli-ably determines both NDD and its statistical uncertainty.In a second test, the data sample was partitioned in timeinto five subsamples of approximately 0.5 fb−1 each andmeasured σ(e+e− → D0D0) and σ(e+e− → D+D−) foreach. The values of χ2 for the hypothesis of equal valuesfor all intervals were 5.4 and 6.0, respectively.

7 Effects of quantum correlations

As mentioned earlier in this paper, the D0D0 yieldand cross section must be corrected for correlations in-troduced by production through a pure C=−1 state atthe ψ(3770). Asner and Sun [6] provide correction fac-tors that can be applied directly to our measured yieldswith Eq. 5 for D0→f and D0→f ′ and Eq. 6 for the casef=f ′.

NmeasuredD0D0 =N true

D0D0×(1+rf yf+rf ′ yf ′+rfrf ′v−ff ′) (5)

NmeasuredD0D0 =N true

D0D0×(1+2rf yf−r2f (2−z2

f )) (6)

The quantities appearing in these equations can be ex-pressed in terms of measured parameters of D0 decaysand D0D0 mixing, with v−jk=(zjzk−wjwk)/2, zj =2cosδj

and wj =2sinδj . rj and δj are defined by 〈j|D0〉/〈j|D0〉=rje

iδj , where rj = |〈j|D0〉/〈j|D0〉|, and δj is the aver-age strong phase difference for the Cabibbo-favored tagmode. The usual mixing parameters x and y, which arerelated to the differences in masses and lifetimes of thetwo mass eigenstates, enter through yj =ycosδj+xsinδj .The D0 →K−π+π0 and K−π+π+π− tag modes requirea slightly more complicated treatment because they aremixtures of modes with different phases. This requiresintroducing coherence factors Rj to characterize the vari-ation of δj over phase space, with zj and wj being rede-fined as zj =2Rj cosδj and wj =2Rj sinδj [18].

Table 5 shows the input parameters that are used toobtain the correction factors and Fig. 5 shows the correc-tions to σ(e+e−→D0D0) for each of the nine double-tagmodes, along with the average. The overall effect is arelative change in ND0D0 of approximately −0.2%, withfinal corrected values of ND0D0 =(10,597±28)×103 andσ(e+e−→D0D0)=(3.615±0.010) nb. The uncertainties

are statistical only. The summed χ2 value relative tothe mean for all pairs of tag modes is 11.8 for D0D0 (9modes).

Table 5. Input parameters for the quantum corre-lation corrections.

x=0.0037±0.0016 [19]

y=0.0066+0.0007−0.0010 [19]

r2Kπ=0.00349±0.00004 [19]

δKπ=(11.8+9.5−14.7)◦ [19]

rKππ0 =0.0447±0.0012 [20]

δKππ0 =(198+14−15)◦ (*) [20]

RKππ0 =0.81±0.06 [20]

rK3π=0.0549±0.0006 [20]

δK3π=(128+28−17)◦ (*) [20]

RK3π=0.43+0.17−0.13 [20]

(*) 180◦ difference in phase convention from Ref. [19].

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Fig. 5. (color online) σ(e+e−→D0D0) for the ninedouble-tag modes, as labeled on the horizontalaxis. The red (black) points show the D0D0 crosssection values with (without) the quantum cor-relation correction. The light red (black shaded)band denotes the one-standard-deviation boundof the weighted average of the corrected (uncor-rected) measurements.

8 Systematic uncertainties

The sources of systematic uncertainty that have beenconsidered for the D0D0 and D+D− cross section mea-surements are listed in Table 6.

The double-tag technique used to determine the eventyields and cross sections σ(e+e−→D0D0) and σ(e+e−→D+D−) has the benefit of substantial cancellation of sys-tematic uncertainties. Detector effects including track-ing, particle identification, and π0 and K0

S reconstruc-tion, along with tag-mode resonant substructure and the∆E requirement, all affect both single and double tags.

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There are, however, event-dependent effects that donot cancel in the efficiency ratio εij/(εi ·εj). The eventenvironment in which D mesons are tagged affects theefficiency because higher multiplicities of charged tracksor π0s lower the tagging efficiency. This can arise dueto three possible sources: (1) differences in multiplicity-dependent efficiencies between data and MC, (2) differ-ences between the other-side multiplicities in data andMC due to imperfect knowledge of D meson decay modesand rates, and (3) sensitivity of the best candidate selec-tion to the number of fake-tag background events.

Table 6. Systematic uncertainties in the cross sec-tion measurements in %.

source σ(e+e−→D0D0) σ(e+e−→D+D−)

multiplicity-dependent efficiency 0.4 0.1

other-side multiplicity <0.01 0.22

best-candidate selection 0.45 0.07

single tag fit background shape 0.54 0.64

single tag fit signal shape 0.26 0.19

double tag fit 0.28 0.19

cosmic/lepton veto 0.06 n/a

ψ(3770) line shape for isr 0.15 0.25

fsr simulation 0.11 0.10

quantum correlation correction 0.2 n/a

integrated luminosity 0.5 0.5

total 1.05 0.93

To assess a possible uncertainty due to the firstsource, we study efficiencies of tracking and particle iden-tification for charged pions and kaons, as well as π0 re-construction, based on doubly tagged D0D0 and D+D−

samples. We estimate uncertainties while observing howwell our MC simulates these efficiencies in data with dif-ferent particle multiplicities.

We evaluate the effect of the second source for bothtracks and π0s by reweighting the MC to better matchthe multiplicities in data. In this we assume that dataand MC are consistent in the single track and π0 re-construction efficiencies. We obtain corrected efficienciesseparately for each tag mode, and the difference with thenominal efficiency is used as the systematic uncertainty.The effect is larger for tag modes with greater multiplic-ity, and so the overall effect on D+D− is greater thanthat on D0D0.

The third source arises due to the fact that we re-solve multiple-candidate events when choosing singletags based on the smallest |∆E|. This selection isimperfect and sometimes the wrong candidate is cho-sen, lowering the efficiency for multiple-candidate eventsrelative to single-candidate events. Although a best-candidate selection is also applied to double tags, thenumber of multiple candidates in this case is small andthe selection based on two beam-constrained masses ismore reliable, so only the systematic uncertainty of best-

candidate selection for single tags is considered. Such un-certainty only arises when both the multiple-candidaterate is different between data and MC and the single-and multiple-candidate efficiencies are different. Thesequantities can be measured both in data and MC, andthe observed differences are propagated through to thesystematic uncertainties in the cross sections.

Even though we fit both single and double tags toobtain the yields and efficiencies, the differences be-tween one- and two-dimensional fits and the much lowerbackground levels of the double-tag MBC distributionslimit the cancellation. We consider several variations ofthe fitting procedures and use the changes in efficiency-corrected yields to estimate the systematic uncertainties.

The uncertainty due to the single-tag backgroundshape is probed by substituting a MC-derived back-ground for the ARGUS function. The uncertainty dueto the signal shape is assessed by altering the smear-ing of the MC-derived shape (single-Gaussian-convolvedinstead of the double-Gaussian-convolved). To assessthe uncertainty in the double-tag fitting procedure, weobtain double-tag yields and efficiencies with an alter-native sideband-subtraction method, dividing the two-dimensional MBC plane into sections representing thesignal and various background components, as shown inFig. 3. The signal area is the same as that used whenfitting. Horizontal and vertical bands are used to repre-sent combinations with one correctly and one incorrectlyreconstructed D; a diagonal band represents the back-ground from completely reconstructed continuum eventsor mispartitioned DD events; and two triangles are usedto represent the remaining background, which is mostlyflat. An estimate of the flat background is scaled by theratios of the sizes of each of the other background re-gions and subtracted to obtain estimates of the non-flatbackgrounds. These backgrounds are then scaled witharea and ARGUS background parameters obtained fromsingle-tag fits to determine the overall background sub-traction and yield for the signal region for a specific tagmode. The difference in efficiency-corrected double-tagyields for each mode between this method and the stan-dard procedure is taken as the systematic uncertaintyassociated with the double-tag fitting method.

The cosmic and lepton veto suppresses cosmic rayand QED background in the single-tag selection for theD0 → K−π+ mode. A cosmic ray background event isproduced by a single particle that is incorrectly recon-structed as two oppositely charged tracks. The net mo-mentum of the two tracks is therefore close to zero, andtypical QED events also have small net momentum. Thissmall momentum produces MBC values close to the beamenergy, so that residual cosmic ray and QED events pass-ing the veto distort the MBC distribution. Because theprocesses responsible are not included in our MC samples

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or well described by the ARGUS background function,the fit results may be affected. To assess this effect, weperformed alternative single-tag fits for D0→K−π+ witha cut-off in MBC at 1.88 GeV/c2, excluding the rangewhere cosmic and QED events can contribute. We foundthe resulting difference from the standard fit procedureto be 0.18%, which we take as the systematic uncertaintydue to this effect.

The line shape of the ψ(3770) affects our analysisthrough the modeling of initial-state radiation (ISR) atthe peak of the resonance. The cross section for ψ(3770)production in radiative events depends on the cross sec-tion value at the lower effective Ecm that results fromISR. While this may partially cancel in the ratio, wetreat it separately for single and double tags becauseyields and efficiencies are affected with opposite signs,and because correlations are introduced for the double-tag fits that are not present in the single-tag fits. TheMC-determined efficiencies are affected through the ∆Erequirements, which select against large ISR because the∆E calculation assumes that the energy available to theD is the full beam energy. The data yields are affectedvia the MBC fit shape, which acquires an asymmetrichigh-side tail through the contribution of ψ(3770) pro-duction via ISR. More ISR causes a larger high-side tailin both the single- and double-tag signal shapes. Addi-tionally, because both D mesons lose energy when ISRoccurs, double-tag events that include ISR will have acorrelated shift in MBC, causing such events to align withthe diagonal to the high-side of the signal region in thetwo-dimensional MBC plane. We use a preliminary BE-SIII measurement of the ψ(3770) line shape to re-weightthe MC and repeat the D-counting procedure. Combin-ing the mode-by-mode variations in NDD leads to thesystematic uncertainty associated with the ψ(3770) lineshape given in Table 6.

The MC modeling of final-state radiation (FSR) maylead to a systematic difference between data and MCtag-reconstruction efficiencies. FSR affects our measure-ment from the tag-side, so any systematic effect will alsohave some cancellation. To assess the uncertainty dueto FSR we created signal MC samples with and withoutmodeling of FSR and measured the changes in tag re-construction efficiencies. The largest difference was forD0→K−π+, where the relative change in single-tag re-construction efficiency was 4%. The D0 →K−π+,D0 →K+π− double-tag reconstruction efficiency also changedwhen FSR was turned off, but the cancellation was notcomplete, with the ratio of efficiencies changing by 1.2%.Because the variation of turning on and off FSR modelingis judged to be too extreme (FSR definitely happens), wetake 25% of this difference as our systematic uncertaintydue to FSR modeling, a 0.3% relative uncertainty on theMC reconstruction efficiency ratio. To be conservative,

we take the largest change, for the D0→K−π+ mode, asthe systematic uncertainty for all modes.

The correction in the D0D0 cross section due to thetreatment of quantum correlations incurs systematic un-certainty associated with the parameters x, y, δKπ, andr2Kπ, for which Ref. [19] provides correlation coefficients.

Ref. [20] provides a similar coefficient table for the rest ofthe variables. In evaluating our systematic uncertainty,we have doubled the reported uncertainties and treatedthem incoherently. Toy MC calculations were used topropagate these uncertainties to ND0D0 , giving a system-atic uncertainty in the D0D0 cross section of 0.2%.

Finally, for the calculation of cross sections, the rel-ative systematic uncertainty due to the integrated lumi-nosity measurement is determined in Ref. [7, 8] to be0.5%.

9 Results and conclusions

The separate sources of systematic uncertainty givenin Table 6 are combined, taking correlations among theminto account, to give overall systematic uncertainties inthe D0D0 and D+D− cross sections of 1.05% and 0.93%,respectively. Including these systematic uncertainties,the final results of our analysis are as follows:

ND0D0 = (10,597±28±98)×103,

ND+D− = (8,296±31±65)×103,

σ(e+e−→D0D0) = (3.615±0.010±0.038) nb,σ(e+e−→D+D−) = (2.830±0.011±0.026) nb,σ(e+e−→DD) = (6.445±0.015±0.048) nb,

andσ(e+e−→D+D−)/σ(e+e−→D0D0)

= (78.29±0.36±0.93)%,

where the uncertainties are statistical and systematic, re-spectively. In the determinations of σ(e+e−→DD) andσ(e+e−→D+D−)/σ(e+e−→D0D0), the uncertainties ofthe charged and neutral cross sections are mostly uncor-related, except the systematic uncertainties due to theassumed ψ(3770) line shape, the FSR simulation, andthe measurement of the integrated luminosity.

In conclusion, we have used 2.93 fb−1 of e+e− anni-hilation data at the ψ(3770) resonance collected by theBESIII detector at the BEPCII collider to measure thecross sections for the production of D0D0 and D+D−.The technique is full reconstruction of three D0 and sixD+ hadronic decay modes and determination of the num-ber of D0D0 and D+D− events using the ratio of single-tag and double-tag yields. We find the cross sectionsto be σ(e+e− → D0D0) = (3.615±0.010±0.038) nb andσ(e+e−→D+D−)= (2.830±0.011±0.026) nb, where theuncertainties are statistical and systematic, respectively.These results are consistent with and more precise than

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the previous best measurement by the CLEO-c Collabo-ration [4] and are necessary input for normalizing somemeasurements of charmed meson properties in ψ(3770)decays.

The authors are grateful to Werner Sun of CornellUniversity for very helpful discussions. The BESIII col-laboration thanks the staff of BEPCII and the computingcenter for their hard efforts.

Appendix A

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+,(d) D−→K+π−π−, (e) D−→K+π−π−π0, (f) D−→K0

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Fig. A8. (color online) Two-dimensional MBC fits projected onto the positive and negative charm MBC axes forvarious double-tag modes; (a) D+→K0

Sπ+π+π− vs. (b) D−→K+π−π−, (c) D+→K0

Sπ+π+π− vs. (d) D−→

K+π−π−π0, (e) D+→K0Sπ

+π+π− vs. (f) D−→K0Sπ

−, (g) D+→K0Sπ

+π+π− vs. (h) D−→K0Sπ

−π0, (i) D+→K0

Sπ+π+π− vs. (j) D−→K0

Sπ+π−π−, (k) D+→K0

Sπ+π+π− vs. (l) D−→K+K−π−. Red solid and blue dotted

curves represent the total fits and the fitted signal shapes, respectively. Green long-dashed and orange solid linescorrespond to the fitted non-peaking background shapes, while cyan and magenta short-dashed curves are thefitted peaking background components.

100

200

300

100

200

300

20

60

100

40

80

10

30

50

10

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20

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1.83 1.86 1.89 1.83 1.86 1.89 1.83 1.86 1.89 1.83 1.86 1.89

M (GeV/c ) BC

2

Eve

nts

/0.0

006 G

eV

/c2

(a) (b) (c)

(e) (f) (g)

(i) (j) (k)

(d)

(h)

(l)

Fig. A9. (color online) Two-dimensional MBC fits projected onto the positive and negative charm MBC axes forvarious double-tag modes; (a) D+→K+K−π+ vs. (b) D−→K+π−π−, (c) D+→K+K−π+ vs. (d) D−→K+π−π−π0,(e) D+→K+K−π+ vs. (f) D−→K0

Sπ−, (g) D+→K+K−π+ vs. (h) D−→K0

Sπ−π0, (i) D+→K+K−π+ vs. (j)

D−→K0Sπ

+π−π−, (k) D+→K+K−π+ vs. (l) D−→K+K−π−. Red solid and blue dotted curves represent the totalfits and the fitted signal shapes, respectively. Green long-dashed and orange solid lines correspond to the fittednon-peaking background shapes, while cyan and magenta short-dashed curves are the fitted peaking backgroundcomponents.

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Chinese Physics C Vol. 42, No. 8 (2018) 083001

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