Observation of the Singly Cabibbo-Suppressed Decay
D
þ→ ωπ
þand Evidence for
D
0→ ωπ
0M. Ablikim,1M. N. Achasov,9,fX. C. Ai,1O. Albayrak,5M. Albrecht,4D. J. Ambrose,44A. Amoroso,49a,49cF. F. An,1Q. An,46,a J. Z. Bai,1R. Baldini Ferroli,20aY. Ban,31D. W. Bennett,19J. V. Bennett,5M. Bertani,20aD. Bettoni,21aJ. M. Bian,43 F. Bianchi,49a,49cE. Boger,23,dI. Boyko,23R. A. Briere,5H. Cai,51X. Cai,1,aO. Cakir,40a,bA. Calcaterra,20aG. F. Cao,1 S. A. Cetin,40bJ. F. Chang,1,aG. Chelkov,23,d,eG. Chen,1H. S. Chen,1H. Y. Chen,2J. C. Chen,1M. L. Chen,1,aS. Chen,41 S. J. Chen,29X. Chen,1,aX. R. Chen,26Y. B. Chen,1,aH. P. Cheng,17X. K. Chu,31G. Cibinetto,21aH. L. Dai,1,aJ. P. Dai,34 A. Dbeyssi,14D. Dedovich,23Z. Y. Deng,1A. Denig,22I. Denysenko,23M. Destefanis,49a,49cF. De Mori,49a,49cY. Ding,27 C. Dong,30J. Dong,1,aL. Y. Dong,1M. Y. Dong,1,aZ. L. Dou,29S. X. Du,53P. F. Duan,1J. Z. Fan,39J. Fang,1,aS. S. Fang,1 X. Fang,46,aY. Fang,1L. Fava,49b,49cF. Feldbauer,22G. Felici,20aC. Q. Feng,46,aE. Fioravanti,21aM. Fritsch,14,22C. D. Fu,1 Q. Gao,1X. L. Gao,46,aX. Y. Gao,2Y. Gao,39Z. Gao,46,aI. Garzia,21aK. Goetzen,10W. X. Gong,1,aW. Gradl,22M. Greco,49a,49c M. H. Gu,1,aY. T. Gu,12Y. H. Guan,1A. Q. Guo,1L. B. Guo,28R. P. Guo,1Y. Guo,1Y. P. Guo,22Z. Haddadi,25A. Hafner,22 S. Han,51F. A. Harris,42K. L. He,1T. Held,4Y. K. Heng,1,aZ. L. Hou,1C. Hu,28H. M. Hu,1J. F. Hu,49a,49cT. Hu,1,aY. Hu,1 G. M. Huang,6G. S. Huang,46,aJ. S. Huang,15X. T. Huang,33X. Z. Huang,29Y. Huang,29T. Hussain,48Q. Ji,1Q. P. Ji,30X. B. Ji,1 X. L. Ji,1,aL. W. Jiang,51X. S. Jiang,1,aX. Y. Jiang,30J. B. Jiao,33Z. Jiao,17D. P. Jin,1,aS. Jin,1T. Johansson,50A. Julin,43
N. Kalantar-Nayestanaki,25X. L. Kang,1X. S. Kang,30M. Kavatsyuk,25B. C. Ke,5P. Kiese,22R. Kliemt,14B. Kloss,22 O. B. Kolcu,40b,iB. Kopf,4M. Kornicer,42W. Kuehn,24A. Kupsc,50J. S. Lange,24M. Lara,19P. Larin,14C. Leng,49cC. Li,50 Cheng Li,46,aD. M. Li,53F. Li,1,aF. Y. Li,31G. Li,1H. B. Li,1H. J. Li,1J. C. Li,1Jin Li,32K. Li,33K. Li,13Lei Li,3P. R. Li,41T. Li,33
W. D. Li,1W. G. Li,1X. L. Li,33X. M. Li,12X. N. Li,1,aX. Q. Li,30Z. B. Li,38H. Liang,46,aJ. J. Liang,12Y. F. Liang,36 Y. T. Liang,24G. R. Liao,11D. X. Lin,14B. J. Liu,1C. X. Liu,1D. Liu,46,aF. H. Liu,35Fang Liu,1Feng Liu,6H. B. Liu,12 H. H. Liu,16H. H. Liu,1H. M. Liu,1J. Liu,1J. B. Liu,46,aJ. P. Liu,51J. Y. Liu,1K. Liu,39K. Y. Liu,27L. D. Liu,31P. L. Liu,1,a Q. Liu,41S. B. Liu,46,aX. Liu,26Y. B. Liu,30Z. A. Liu,1,aZhiqing Liu,22H. Loehner,25X. C. Lou,1,a,hH. J. Lu,17J. G. Lu,1,a Y. Lu,1Y. P. Lu,1,aC. L. Luo,28M. X. Luo,52T. Luo,42X. L. Luo,1,aX. R. Lyu,41F. C. Ma,27H. L. Ma,1L. L. Ma,33M. M. Ma,1 Q. M. Ma,1T. Ma,1X. N. Ma,30X. Y. Ma,1,aF. E. Maas,14M. Maggiora,49a,49cY. J. Mao,31Z. P. Mao,1S. Marcello,49a,49c J. G. Messchendorp,25J. Min,1,aR. E. Mitchell,19X. H. Mo,1,aY. J. Mo,6C. Morales Morales,14K. Moriya,19N. Yu. Muchnoi,9,f
H. Muramatsu,43Y. Nefedov,23F. Nerling,14I. B. Nikolaev,9,fZ. Ning,1,aS. Nisar,8S. L. Niu,1,aX. Y. Niu,1S. L. Olsen,32 Q. Ouyang,1,aS. Pacetti,20bY. Pan,46,aP. Patteri,20aM. Pelizaeus,4H. P. Peng,46,aK. Peters,10J. Pettersson,50J. L. Ping,28 R. G. Ping,1R. Poling,43V. Prasad,1M. Qi,29S. Qian,1,aC. F. Qiao,41L. Q. Qin,33N. Qin,51X. S. Qin,1Z. H. Qin,1,aJ. F. Qiu,1
K. H. Rashid,48C. F. Redmer,22M. Ripka,22G. Rong,1Ch. Rosner,14X. D. Ruan,12A. Sarantsev,23,gM. Savrié,21b K. Schoenning,50S. Schumann,22W. Shan,31M. Shao,46,aC. P. Shen,2P. X. Shen,30X. Y. Shen,1H. Y. Sheng,1M. Shi,1
W. M. Song,1X. Y. Song,1S. Sosio,49a,49cS. Spataro,49a,49cG. X. Sun,1J. F. Sun,15S. S. Sun,1X. H. Sun,1Y. J. Sun,46,a Y. Z. Sun,1Z. J. Sun,1,aZ. T. Sun,19C. J. Tang,36X. Tang,1I. Tapan,40cE. H. Thorndike,44M. Tiemens,25M. Ullrich,24 I. Uman,40bG. S. Varner,42B. Wang,30B. L. Wang,41D. Wang,31D. Y. Wang,31K. Wang,1,aL. L. Wang,1L. S. Wang,1 M. Wang,33P. Wang,1P. L. Wang,1S. G. Wang,31W. Wang,1,aW. P. Wang,46,aX. F. Wang,39Y. Wang,37Y. D. Wang,14 Y. F. Wang,1,aY. Q. Wang,22Z. Wang,1,aZ. G. Wang,1,aZ. H. Wang,46,aZ. Y. Wang,1Z. Y. Wang,1T. Weber,22D. H. Wei,11
J. B. Wei,31P. Weidenkaff,22S. P. Wen,1U. Wiedner,4M. Wolke,50L. H. Wu,1L. J. Wu,1Z. Wu,1,aL. Xia,46,aL. G. Xia,39 Y. Xia,18D. Xiao,1H. Xiao,47Z. J. Xiao,28Y. G. Xie,1,aQ. L. Xiu,1,aG. F. Xu,1J. J. Xu,1L. Xu,1Q. J. Xu,13X. P. Xu,37 L. Yan,49a,49cW. B. Yan,46,aW. C. Yan,46,aY. H. Yan,18H. J. Yang,34H. X. Yang,1L. Yang,51Y. Yang,6Y. Y. Yang,11M. Ye,1,a M. H. Ye,7J. H. Yin,1B. X. Yu,1,aC. X. Yu,30J. S. Yu,26C. Z. Yuan,1W. L. Yuan,29Y. Yuan,1A. Yuncu,40b,cA. A. Zafar,48 A. Zallo,20aY. Zeng,18Z. Zeng,46,aB. X. Zhang,1B. Y. Zhang,1,aC. Zhang,29C. C. Zhang,1D. H. Zhang,1H. H. Zhang,38 H. Y. Zhang,1,aJ. Zhang,1J. J. Zhang,1J. L. Zhang,1J. Q. Zhang,1J. W. Zhang,1,aJ. Y. Zhang,1J. Z. Zhang,1K. Zhang,1 L. Zhang,1X. Y. Zhang,33Y. Zhang,1Y. H. Zhang,1,aY. N. Zhang,41Y. T. Zhang,46,aYu Zhang,41Z. H. Zhang,6Z. P. Zhang,46 Z. Y. Zhang,51G. Zhao,1J. W. Zhao,1,aJ. Y. Zhao,1J. Z. Zhao,1,aLei Zhao,46,aLing Zhao,1M. G. Zhao,30Q. Zhao,1Q. W. Zhao,1
S. J. Zhao,53T. C. Zhao,1Y. B. Zhao,1,aZ. G. Zhao,46,aA. Zhemchugov,23,dB. Zheng,47J. P. Zheng,1,aW. J. Zheng,33 Y. H. Zheng,41B. Zhong,28L. Zhou,1,aX. Zhou,51X. K. Zhou,46,aX. R. Zhou,46,aX. Y. Zhou,1K. Zhu,1K. J. Zhu,1,aS. Zhu,1
S. H. Zhu,45X. L. Zhu,39Y. C. Zhu,46,aY. S. Zhu,1Z. A. Zhu,1J. Zhuang,1,aL. Zotti,49a,49cB. S. Zou,1and J. H. Zou1 (BESIII Collaboration)
1Institute of High Energy Physics, Beijing 100049, People’s Republic of China 2
Beihang University, Beijing 100191, People’s Republic of China
3Beijing Institute of Petrochemical Technology, Beijing 102617, People’s Republic of China 4
Bochum Ruhr-University, D-44780 Bochum, Germany 5Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA 6
Central China Normal University, Wuhan 430079, People’s Republic of China
7China Center of Advanced Science and Technology, Beijing 100190, People’s Republic of China 8
COMSATS Institute of Information Technology, Lahore, Defence Road, Off Raiwind Road, 54000 Lahore, Pakistan 9G.I. Budker Institute of Nuclear Physics SB RAS (BINP), Novosibirsk 630090, Russia
10
GSI Helmholtzcentre for Heavy Ion Research GmbH, D-64291 Darmstadt, Germany 11Guangxi Normal University, Guilin 541004, People’s Republic of China
12
GuangXi University, Nanning 530004, People’s Republic of China 13Hangzhou Normal University, Hangzhou 310036, People’s Republic of China 14
Helmholtz Institute Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany 15Henan Normal University, Xinxiang 453007, People’s Republic of China 16
Henan University of Science and Technology, Luoyang 471003, People’s Republic of China 17Huangshan College, Huangshan 245000, People’s Republic of China
18
Hunan University, Changsha 410082, People’s Republic of China 19Indiana University, Bloomington, Indiana 47405, USA 20a
INFN Laboratori Nazionali di Frascati, I-00044 Frascati, Italy 20bINFN and University of Perugia, I-06100 Perugia, Italy
21a
INFN Sezione di Ferrara, I-44122 Ferrara, Italy 21bUniversity of Ferrara, I-44122 Ferrara, Italy 22
Johannes Gutenberg University of Mainz, Johann-Joachim-Becher-Weg 45, D-55099 Mainz, Germany 23Joint Institute for Nuclear Research, 141980 Dubna, Moscow region, Russia
24
Justus Liebig University Giessen, II. Physikalisches Institut, Heinrich-Buff-Ring 16, D-35392 Giessen, Germany 25KVI-CART, University of Groningen, NL-9747 AA Groningen, The Netherlands
26
Lanzhou University, Lanzhou 730000, People’s Republic of China 27Liaoning University, Shenyang 110036, People’s Republic of China 28
Nanjing Normal University, Nanjing 210023, People’s Republic of China 29Nanjing University, Nanjing 210093, People’s Republic of China
30
Nankai University, Tianjin 300071, People’s Republic of China 31Peking University, Beijing 100871, People’s Republic of China
32
Seoul National University, Seoul, 151-747 Korea 33Shandong University, Jinan 250100, People’s Republic of China 34
Shanghai Jiao Tong University, Shanghai 200240, People’s Republic of China 35Shanxi University, Taiyuan 030006, People’s Republic of China 36
Sichuan University, Chengdu 610064, People’s Republic of China 37Soochow University, Suzhou 215006, People’s Republic of China 38
Sun Yat-Sen University, Guangzhou 510275, People’s Republic of China 39Tsinghua University, Beijing 100084, People’s Republic of China
40a
Istanbul Aydin University, 34295 Sefakoy, Istanbul, Turkey 40bIstanbul Bilgi University, 34060 Eyup, Istanbul, Turkey
40c
Uludag University, 16059 Bursa, Turkey
41University of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 42
University of Hawaii, Honolulu, Hawaii 96822, USA 43University of Minnesota, Minneapolis, Minnesota 55455, USA
44
University of Rochester, Rochester, New York 14627, USA
45University of Science and Technology Liaoning, Anshan 114051, People’s Republic of China 46
University of Science and Technology of China, Hefei 230026, People’s Republic of China 47University of South China, Hengyang 421001, People’s Republic of China
48
University of the Punjab, Lahore-54590, Pakistan 49aUniversity of Turin, I-10125, Turin, Italy 49b
University of Eastern Piedmont, I-15121, Alessandria, Italy 49cINFN, I-10125, Turin, Italy
50
Uppsala University, Box 516, SE-75120 Uppsala, Sweden 51Wuhan University, Wuhan 430072, People’s Republic of China 52
Zhejiang University, Hangzhou 310027, People’s Republic of China 53Zhengzhou University, Zhengzhou 450001, People’s Republic of China
Based on 2.93 fb−1 eþe− collision data taken at center-of-mass energy of 3.773 GeV by the BESIII detector, we report searches for the singly Cabibbo-suppressed decays Dþ→ ωπþ and D0→ ωπ0. A double tag technique is used to measure the absolute branching fractionsBðDþ→ ωπþÞ ¼ ð2.79 0.57 0.16Þ × 10−4 and BðD0→ ωπ0Þ ¼ ð1.17 0.34 0.07Þ × 10−4, with statistical significances of 5.5σ and 4.1σ, where the first and second uncertainties are statistical and systematic, respectively.
DOI:10.1103/PhysRevLett.116.082001
Hadronic decays of charm mesons provide important input for beauty physics and also open a window into the study of strong final state interactions. For Cabibbo-sup-pressed charm decays, precise measurements are challeng-ing due to low statistics and high backgrounds. Among them, the singly Cabibbo-suppressed (SCS) decaysDþ;0→ ωπþ;0have not yet been observed, and only upper limits on
the branching fractions were set to be3.4 × 10−4and2.6 × 10−4at the 90% confidence level (C.L.) forDþ→ ωπþand
D0→ ωπ0, respectively, by the CLEO-c Collaboration[1].
Following the diagrammatic approach, the small decay rates may be caused by the destructive interference between the color-suppressed quark diagrams CV and CP [2]. Numerically, ifW-annihilation contributions are neglected, the branching fractions of theD → ωπ decays should be at about the 1.0 × 10−4 level[2,3].
Besides searching for Dþ;0→ ωπþ;0, we also report measurements of the branching fractions for the decays Dþ;0→ ηπþ;0. Precise measurements of these decay rates
can improve understanding of U-spin and SUð3Þ-flavor symmetry breaking effects in D decays, benefiting theo-retical predictions of CP violation in D decays [4].
The data used have an integrated luminosity of2.93 fb−1
[5] and were collected with the BESIII detector at the ψð3770Þ resonance (pffiffiffis≈ 3.773 GeV). Details on the features and capabilities of the BESIII detector can be found in Ref. [6]. The response of the experimental apparatus is studied with a detailed GEANT-based [7]
Monte Carlo (MC) simulation of the BESIII detector for particle trajectories generated by the generator KKMC
[8] using EVTGEN [9], with initial state radiation (ISR)
effects[10]and final state radiation effects [11]included. Simulated events are processed in a fashion similar to data. At the ψð3770Þ resonance, DD pairs are produced in a coherent 1−− final state with no additional particles. To suppress huge non-DD backgrounds [1], we employ the “double tag” (DT) technique first developed by the MARK-III Collaboration [12,13] to perform absolute measurements of the branching fractions. We select“single tag” (ST) events in which either a D or D is fully reconstructed. We then look for the D decays of interest in the remainder of each event, namely, in DT events where both the D and D are fully reconstructed. The absolute branching fractions forD meson decays are calculated by the general formula
Bsig¼
P
αNobs;αsig
P
αNobs;αtag ϵαtag;sig=ϵαtag
; ð1Þ
whereα denotes different ST modes, Nobs;αtag is the yield of ST events for the tag modeα, Nobs;αsig is the corresponding yield of DT events, andϵαtag andϵαtag;sigare the ST and DT
efficiencies for the tag mode α. Correlation between the reconstructions ofD and D in an event has been considered in the efficiency determination.
The ST candidate events are selected by reconstructing a D− or D0 in the following hadronic final states:
D−→ Kþπ−π−, Kþπ−π−π0, K0
Sπ−, K0Sπ−π0, K0Sπþπ−π−,
KþK−π−, and D0→ Kþπ−, Kþπ−π0, Kþπ−πþπ−,
Kþπ−π0π0, Kþπ−πþπ−π0, comprising approximately
28.0% and 38.0%[14] of all D− andD0 decays, respec-tively. For the signal side, we reconstructDþ → ωπþðηπþÞ and D0→ ωπ0ðηπ0Þ, with ωðηÞ → πþπ−π0. Throughout
1 84 1 86 1 88 1 84 1 86 1 88 (a) 0 50 1 84 1 86 1 88 1 841 84 1 861 86 1 881 88 (b) 0 20 1 84 1 86 1 88 1 841 84 1 861 86 1 881 88 (c) 0 10 1 84 1 86 1 88 (d) 0 10 (e) 0 10 (f) 0 5 8 8 1 6 8 186 188 1 (g) 0 50 8 8 1 6 8 1 118866 118888 (h) 0 50 8 8 1 6 8 1 (i) 0 50 (j) 0 10 (k) 0 10 ) 2 Events/(0.00025GeV/c ) 2 (GeV/c BC M 1.84 1.86 1.88 1.84 1.86 1.88 1.84 1.86 1.88 1.86 1.88 1.86 1.88 1.86 1.88 ) 3 (x10 ) 3 (x10 ) 3 (x10 ) 3 (x10 ) 3 (x10 ) 3 (x10
FIG. 1. MBC distributions of ST samples for different tag modes. The first two rows show charged D decays: (a) Kþπ−π−, (b) Kþπ−π−π0, (c) K0Sπ−, (d) K0Sπ−π0, (e) K0Sπþπ−π−, (f) KþK−π−, the latter two rows show neutral D decays: (g) Kþπ−, (h)Kþπ−π0, (i)Kþπ−πþπ−, (j)Kþπ−π0π0, (k)Kþπ−πþπ−π0. Data are shown as points, the (red) solid lines are the total fits and the (blue) dashed lines are the background shapes.D and ¯D candidates are combined.
the Letter, charge-conjugate modes are implicitly implied, unless otherwise noted.
The reconstruction ofD mesons uses charged particles, π0’s and K0
S’s reconstructed with standard selection
require-ments [15]. To identify the reconstructed D candidates, we use two variables, the beam-constrained mass, MBC,
and the energy difference, ΔE, which are defined as MBC≡
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E2
beam=c4− j~pDj2=c2
p
, ΔE ≡ ED− Ebeam. Here,
~pD andED are the reconstructed momentum and energy
of theD candidate in the eþe− center-of-mass system, and Ebeamis the beam energy. We acceptD candidates with MBC
greater than 1.83 GeV=c2 and with mode-dependent ΔE requirements of approximately 3 standard deviations. For the ST modes, we accept at most one candidate per mode per event; the candidate with the smallestjΔEj is chosen[16]. To obtain ST yields, we fit theMBC distributions of the
acceptedD candidates, as shown in Fig.1. The signal shape, which is modeled by the MC shape convoluted with a Gaussian function, includes the effects of beam energy spread, ISR, the ψð3770Þ line shape, and resolution. The combinatorial background is modeled by an ARGUS func-tion[17]. With requirement of1.866<MtagBC<1.874GeV=c2 forDþcase or1.859<MtagBC<1.871GeV=c2forD0case, ST yields are calculated by subtracting the integrated ARGUS background yields within the signal region from the total event counts in this region. The tag efficiency is studied using MC samples following the same procedure. The ST yields in data and corresponding tag efficiencies are listed in TableI.
On the signal side we search forDþ → πþπ−π0πþ and D0→ πþπ−π0π0 modes containing an ωðηÞ → πþπ−π0
decay. For both Dþ and D0 decays, two possible ωðηÞ combinations exist. Combinations with 3π mass in the intervalð0.4; 1.0Þ GeV=c2are considered. The chance that bothωðηÞ candidates combinations lie in this region is only about 0.3%, rendering this source of multiple candidates negligible.
With the DT technique, the continuum background eþe− → qq is highly suppressed. The remaining
back-ground dominantly comes fromDD events broadly populat-ing the3π mass window. To suppress the non-ω background, we require that the helicity,Hω≡ cos θH, of theω have an absolute value larger than 0.54 (0.51) forDþ(D0). The angle θH is the opening angle between the direction of the normal
to theω → 3π decay plane and the direction of the D meson in the ω rest frame. True ω signal from D decays is longitudinally polarized so we expect a cos2θH≡ H2ω distribution. To further suppress background fromDþ;0→ K0
Sπþπ0;−withK0S→ πþπ−, we apply aK0Sveto by requiring
jMπþπ−− mPDG
K0
S j > 12ð9Þ MeV=c
2for theDþ ðD0Þ
analy-sis. Here, mPDG
K0
S is the known K
0
S mass and Mπþπ− is calculated at the interaction point for simplicity.
After the above selection criteria, the signal region S for the DT candidates is defined as 1.866 < MBC<
1.874 GeV=c2for theDþ(1.859 < M
BC< 1.871 GeV=c2
for the D0) in the two-dimensional (2D) MsigBC vs MtagBC plane, as illustrated in Fig.2. We also define sideband box regions to estimate potential background[18]. SidebandsA andB contain candidates where either the D or the D is TABLE I. ST data yields (Nobs
tag), ST (ϵtag), and DT (ϵωtag;sig and ϵηtag;sig) efficiencies, and their statistical uncertainties. Branching fractions of theK0S and π0 are not included in the efficiencies, but are included in the branching fraction calculations. The first six rows are forD−and the last five are for ¯D0.
Mode ST yields ϵtagð%Þ ϵωtag;sigð%Þ ϵηtag;sigð%Þ
Kþπ−π− 772711895 48.760.02 11.010.15 12.640.17 Kþπ−π−π0 226969608 23.190.02 4.470.10 5.260.11 K0 Sπ− 95974315 52.350.07 11.690.18 13.990.21 K0 Sπ−π0 211872572 26.680.03 5.350.13 6.440.14 K0 Sπ−πþπ− 121801459 30.530.04 6.160.13 7.170.15 KþK−π− 65955306 38.720.07 8.500.13 9.760.14 Kþπ− 529558745 64.790.03 12.440.16 14.170.17 Kþπ−π0 10449631164 34.130.01 5.730.11 6.870.12 Kþπ−πþπ− 708523946 38.330.02 6.040.11 7.000.13 Kþπ−π0π0 236719747 13.870.02 1.780.06 2.100.07 Kþπ−πþπ−π0 152025684 15.550.03 1.930.06 2.080.07 ) 2 (GeV/c tag BC M 1.84 1.86 1.88 ) 2 (GeV/c sig BC M 1.84 1.86 1.88 S A B D D C (a) ) 2 (GeV/c tag BC M 1.84 1.86 1.88 ) 2 (GeV/c sig BC M 1.84 1.86 1.88 S A B D D C (b)
FIG. 2. 2D MBC distributions for (a) Dþ→ ωπþ and (b) D0→ ωπ0 with the signal (S) and sideband (A, B, C, D) regions used for background estimation indicated.
misreconstructed. Sidebands C and D contain candidates where both D and D are misreconstructed, either in a correlated way (C), by assigning daughter particles to the wrong parent, or in an uncorrelated way (D).
To obtain theωðηÞ yield, we perform a fit to the πþπ−π0 invariant massðM3πÞ distribution with events in the signal region S. The ωðηÞ shape is modeled by the signal MC shape convoluted with a Gaussian function to describe the difference in theM3π resolution between MC calculations and data. Because of high statistics, the width ση of the Gaussian for the η case is determined by the fit, while the width σω for the ω case is constrained by the MC-determined ratio R ¼ σMC
ω =σMCη , giving the relative
M3π resolution for η and ω final states. For Dþ, the
background shape is described by a third-order Chebychev polynomial, while for D0 we use a shape of a0M1=23π þ a1M3=23π þ a2M5=23π þ a3M7=23π þ a4M9=23π , where
ai (i ¼ 0; …; 4) are free parameters. The fit results are
shown in Fig.3, and the totalω yields Nω forDþ andD0 cases are listed in TableII.
To estimate the ωðηÞ yield in the signal region S from background processes, event counts in sidebandsA, B, and C are projected into the signal region S using scale factors determined from integrating the background shape in the STMBCfits. Contributions to sidebandD are assumed to be
uniformly distributed across the other regions [18]. For
these events from the sideband regions, we perform similar fits to the3π mass spectra, and find the peaking background yields NbkgωðηÞ for Dþ and D0, respectively, as listed in TableII. By subtracting theω peaking background extend-ing underneath the signal region, the DT signal yields,Nobssig, are obtained. The statistical significances for Dþ → ωπþ andD0→ ωπ0are found to be5.5σ and 4.1σ, respectively. We now remove theω helicity requirement, and inves-tigate the helicity dependence of our signal yields. By following procedures similar to those described above, we obtain the signal yield in each jHωj bin. The efficiency corrected yields are shown in Fig.4, demonstrating agree-ment with expected cos2θHbehavior, further validating this analysis.
As shown in Fig.3, the background level in theη signal region of the 3π invariant mass distribution is small compared to that near theω mass. Therefore, to improve statistics, we remove the K0S veto requirements and also make no helicity requirement since Hη≡ cos θH for the signal is flat. Following a similar fit procedure, with results shown in Fig.5, we determineηπþ andηπ0 DT yields as listed in TableII.
With the DT technique, the branching fraction measure-ments are insensitive to systematics coming from the ST side since they mostly cancel. For the signal side, system-atic uncertainties mainly come from imperfect knowledge ) 2 (GeV/c π 3 M 0.5 0.6 0.7 0.8 0.9 ) 2 Events/(0.005GeV/c 0 20 40 60 80 20 (a) ) 2 (GeV/c π 3 M 0.5 0.6 0.7 0.8 0.9 ) 2 Events/(0.01GeV/c 0 10 20 30 40 (b)
FIG. 3. Fits to the3π mass spectra for (a) Dþ→ πþπ−π0πþand (b)D0→ πþπ−π0π0 in the signal regionS as defined in Fig.2. Points are data, the (red) solid lines are the total fits, the (blue) dashed lines are the background shapes, and the hatched histo-grams are peaking background estimated from 2DMBCsidebands.
TABLE II. Summary for the total ω (η) yields (NωðηÞ), ωðηÞ peaking background yields (NbkgωðηÞ), and net DT yields (Nobs
sig) in the signal regionS as defined in Fig.2.Nobssig is estimated from the defined sidebands. The errors are statistical.
ModeH NωðηÞ Nbkg ωðηÞ N obs sig Dþ→ ωπþ 100 16 21 4 79 16 D0→ ωπ0 50 12 5 5 45 13 Dþ→ ηπþ 264 17 6 2 258 18 D0→ ηπ0 78 10 3 2 75 10 | ω H | 0 0.2 0.4 0.6 0.8 1 (corr.)± π ω N 0 200 400 600 (a) /ndf = 9.7/4 2 χ | ω H | 0 0.2 0.4 0.6 0.8 1 (corr.)0π ω N 0 200 400 (b) /ndf = 5.6/3 2 χ
FIG. 4. Efficiency corrected yields versus jHωj for (a) Dþ→ ωπþ and (b)D0→ ωπ0. Both are consistent with a distribution like cos2θH(black line).
) 2 (GeV/c π 3 M 0.52 0.54 0.56 0.58 ) 2 Events/(0.002GeV/c 0 20 40 60 80 π (a) ) 2 (GeV/c π 3 M 0.52 0.54 0.56 0.58 ) 2 Events/(0.002GeV/c 0 5 10 15 20 ) 2 π Events/(0.002GeV/c (b)
FIG. 5. Fits to the3π mass spectra for (a) Dþ→ πþπ−π0πþand (b)D0→ πþπ−π0π0in theη mass region for the signal region S as defined in Fig.2. Points are data; the (red) solid lines are the total fits; the (blue) dashed lines are the background shapes, and the hatched histograms are the peaking background estimated from 2DMBC sidebands.
of the efficiencies for tracking finding, PID criteria, theK0S veto, and theHω requirement; additional uncertainties are related to the fit procedures.
Possible differences in tracking, PID, and π0 reconstruction efficiencies between data and the MC simulations are investigated using a partial-reconstruction technique based on the control samplesD0→ K−πþπ0and D0→ K−πþ. We assign uncertainties of 1.0% and 0.5%
per track for track finding and PID, respectively, and 1.0% per reconstructed π0.
Uncertainty due to the 2D signal region definition is investigated via the relative change in signal yields for different signal region definitions based on the control samplesDþ → K0Sπþπ0andD0→ K0Sπ0π0which have the same pions in the final state as our signal modes. With the same control samples, uncertainties due to theΔE require-ments are also studied. The relative data-MC efficiency differences are taken as systematic uncertainties, as listed in Table III.
Uncertainty due to thejHωj requirement is studied using the control sample D0→ K0Sω. The data-MC efficiency difference with or without this requirement is taken as our systematic. Uncertainty due to the K0S veto is similarly obtained with this control sample.
The ω peaking background is estimated from 2D MBC sidebands. We change the sideband ranges by 2 MeV=c2 for both sides and investigate the fluctuation on the signal yields, which is taken as a systematic uncertainty.
In the nominal fit to the M3π distribution, the ratio R, which is the relative difference on the M3π resolution between η and ω positions, is determined by MC simu-lations. With control samples D0→ K0Sη and K0Sω, the difference between data and MC defined as δR ¼ Rdata=RMC− 1 is obtained. We vary the nominal R value
by1σ and take the relative change of signal yields as a systematic uncertainty.
Uncertainties due to the background shapes are investigated by changing the orders of the polynomials employed. Uncertainties due to the M3π fitting range are investigated by changing the range from ð0.50; 0.95Þ GeV=c2 to ð0.48; 0.97Þ GeV=c2 in the fits,
yielding relative differences which are taken as systematic uncertainties.
We summarize the systematic uncertainties in TableIII. The total effect is calculated by combining the uncertainties from all sources in quadrature.
Finally, the measured branching fractions of D → ωπ andηπ are summarized in TableIV, where the first errors are statistical and the second ones are systematic.
In summary, we present the first observation of the SCS decayDþ→ ωπþ with statistical significance of5.5σ. We find the first evidence for the SCS decayD0→ ωπ0with statistical significance of4.1σ. The results are consistent with the theoretical prediction[2], and can improve under-standing of U-spin and SUð3Þ-flavor symmetry breaking effects inD decays[4]. We also present measurements of the branching fractions for Dþ → ηπþ and D0→ ηπ0, which are consistent with the previous measurements[19]. The BESIII Collaboration thanks the staff of BEPCII and the IHEP computing center for their strong support. This work is supported in part by National Key Basic Research Program of China under Contract No. 2015CB856700; National Natural Science Foundation of China (NSFC)
under Contracts No. 11125525, No. 11235011,
No. 11322544, No. 11335008, No. 11425524; the Chinese Academy of Sciences (CAS) Large-Scale Scientific Facility Program; the CAS Center for
Excellence in Particle Physics (CCEPP); the
Collaborative Innovation Center for Particles and Interactions (CICPI); Joint Large-Scale Scientific Facility
Funds of the NSFC and CAS under Contracts
No. 11179007, No. 10975093, No. U1232201,
No. U1332201; CAS under Contracts No. KJCX2-YW-N29, No. KJCX2-YW-N45; 100 Talents Program of CAS; National 1000 Talents Program of China; INPAC and Shanghai Key Laboratory for Particle Physics and Cosmology; German Research Foundation DFG under Contract No. Collaborative Research Center CRC-1044; Istituto Nazionale di Fisica Nucleare, Italy; Joint Funds of the National Science Foundation of China under Contract No. U1232107; Ministry of Development of Turkey under TABLE III. Summary of systematic uncertainties in %.
Uncertainties which are not involved are denoted by“ .”
Source ωπþ ωπ0 ηπþ ηπ0 πtracking 3.0 2.0 3.0 2.0 πPID 1.5 1.0 1.5 1.0 π0 reconstruction 1.0 2.0 1.0 2.0 2DMBC window 0.1 0.2 0.1 0.2 ΔE requirement 0.5 1.6 0.5 1.6 jHωj requirement 3.4 3.4 K0 S veto 0.8 0.8 Sideband regions 1.3 2.2 0.0 0.5 Signal resolution 0.9 0.9 Background shape 2.3 1.3 1.9 3.5 Fit range 0.3 1.9 0.8 1.5 BðωðηÞ → πþπ−π0Þ [14] 0.8 0.8 1.2 1.2 Overall 5.8 6.0 4.3 5.3
TABLE IV. Summary of branching fraction measurements, and comparison with the previous measurements[1,19].
Mode This work Previous measurements
Dþ→ωπþ ð2.790.570.16Þ×10−4 <3.4×10−4 at 90% C.L. D0→ωπ0 ð1.170.340.07Þ×10−4 <2.6×10−4 at 90% C.L. Dþ→ηπþ ð3.070.220.13Þ×10−3 ð3.530.21Þ×10−3 D0→ηπ0 ð0.650.090.04Þ×10−3 ð0.680.07Þ×10−3
Contract No. DPT2006K-120470; Russian Foundation for Basic Research under Contract No. 14-07-91152; The Swedish Research Council; U.S. Department of
Energy under Contracts No. DE-FG02-04ER41291,
No. DE-FG02-05ER41374, No. DE-SC0012069,
No. DESC0010118; U.S. National Science Foundation; University of Groningen (RuG) and the Helmholtzzentrum fuer Schwerionenforschung GmbH (GSI), Darmstadt; WCU Program of National Research Foundation of Korea under Contract No. R32-2008-000-10155-0.
aAlso at State Key Laboratory of Particle Detection and
Electronics, Beijing 100049, Hefei 230026, People’s Re-public of China
b
Also at Ankara University,06100 Tandogan, Ankara, Tur-key
c
Also at Bogazici University, 34342 Istanbul, Turkey
dAlso at the Moscow Institute of Physics and Technology,
Moscow 141700, Russia
eAlso at the Functional Electronics Laboratory, Tomsk State
University, Tomsk, 634050, Russia
fAlso at the Novosibirsk State University, Novosibirsk,
630090, Russia
gAlso at the NRC “Kurchatov Institute, PNPI, 188300,
Gatchina, Russia
hAlso at University of Texas at Dallas, Richardson, Texas
75083, USA
iAlso at Istanbul Arel University, 34295 Istanbul, Turkey
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