Contents lists available atScienceDirect
Physics
Letters
B
www.elsevier.com/locate/physletb
Measurement
of
singly
Cabibbo-suppressed
decays
D
0
→
π
0
π
0
π
0
,
π
0
π
0
η
,
π
0
ηη
and
ηηη
BESIII
Collaboration
M. Ablikim
a,
M.N. Achasov
i,
4,
S. Ahmed
n,
M. Albrecht
d,
A. Amoroso
bf,
bh,
F.F. An
a,
Q. An
bc,
ap,
J.Z. Bai
a,
Y. Bai
ao,
O. Bakina
z,
R. Baldini Ferroli
t,
Y. Ban
ah,
D.W. Bennett
s,
J.V. Bennett
e,
N. Berger
y,
M. Bertani
t,
D. Bettoni
v,
J.M. Bian
az,
F. Bianchi
bf,
bh,
E. Boger
z,
2,
I. Boyko
z,
R.A. Briere
e,
H. Cai
bj,
X. Cai
a,
ap,
O. Cakir
as,
A. Calcaterra
t,
G.F. Cao
a,
aw,
S.A. Cetin
at,
J. Chai
bh,
J.F. Chang
a,
ap,
G. Chelkov
z,
2,
3,
G. Chen
a,
H.S. Chen
a,
aw,
J.C. Chen
a,
M.L. Chen
a,
ap,
P.L. Chen
bd,
S.J. Chen
af,
X.R. Chen
ac,
Y.B. Chen
a,
ap,
X.K. Chu
ah,
G. Cibinetto
v,
H.L. Dai
a,
ap,
J.P. Dai
ak,
8,
A. Dbeyssi
n,
D. Dedovich
z,
Z.Y. Deng
a,
A. Denig
y,
I. Denysenko
z,
M. Destefanis
bf,
bh,
F. De Mori
bf,
bh,
Y. Ding
ad,
C. Dong
ag,
J. Dong
a,
ap,
L.Y. Dong
a,
aw,
M.Y. Dong
a,
ap,
aw,
Z.L. Dou
af,
S.X. Du
bl,
P.F. Duan
a,
J. Fang
a,
ap,
S.S. Fang
a,
aw,
Y. Fang
a,
R. Farinelli
v,
w,
L. Fava
bg,
bh,
S. Fegan
y,
F. Feldbauer
y,
G. Felici
t,
C.Q. Feng
bc,
ap,
E. Fioravanti
v,
M. Fritsch
y,
n,
C.D. Fu
a,
Q. Gao
a,
X.L. Gao
bc,
ap,
Y. Gao
ar,
Y.G. Gao
f,
Z. Gao
bc,
ap,
B. Garillon
y,
I. Garzia
v,
K. Goetzen
j,
L. Gong
ag,
W.X. Gong
a,
ap,
W. Gradl
y,
M. Greco
bf,
bh,
M.H. Gu
a,
ap,
Y.T. Gu
l,
A.Q. Guo
a,
R.P. Guo
a,
aw,
Y.P. Guo
y,
Z. Haddadi
ab,
S. Han
bj,
X.Q. Hao
o,
F.A. Harris
ax,
K.L. He
a,
aw,
X.Q. He
bb,
F.H. Heinsius
d,
T. Held
d,
Y.K. Heng
a,
ap,
aw,
T. Holtmann
d,
Z.L. Hou
a,
H.M. Hu
a,
aw,
T. Hu
a,
ap,
aw,
Y. Hu
a,
G.S. Huang
bc,
ap,
J.S. Huang
o,
X.T. Huang
aj,
X.Z. Huang
af,
Z.L. Huang
ad,
T. Hussain
be,
W. Ikegami Andersson
bi,
Q. Ji
a,
Q.P. Ji
o,
X.B. Ji
a,
aw,
X.L. Ji
a,
ap,
X.S. Jiang
a,
ap,
aw,
X.Y. Jiang
ag,
J.B. Jiao
aj,
Z. Jiao
q,
D.P. Jin
a,
ap,
aw,
S. Jin
a,
aw,
Y. Jin
ay,
T. Johansson
bi,
A. Julin
az,
N. Kalantar-Nayestanaki
ab,
X.L. Kang
a,
X.S. Kang
ag,
M. Kavatsyuk
ab,
B.C. Ke
e,
T. Khan
bc,
ap,
A. Khoukaz
ba,
P. Kiese
y,
R. Kliemt
j,
L. Koch
aa,
O.B. Kolcu
at,
6,
B. Kopf
d,
M. Kornicer
ax,
M. Kuemmel
d,
M. Kuessner
d,
M. Kuhlmann
d,
A. Kupsc
bi,
W. Kühn
aa,
J.S. Lange
aa,
M. Lara
s,
P. Larin
n,
L. Lavezzi
bh,
H. Leithoff
y,
C. Leng
bh,
C. Li
bi,
Cheng Li
bc,
ap,
D.M. Li
bl,
F. Li
a,
ap,
F.Y. Li
ah,
G. Li
a,
H.B. Li
a,
aw,
H.J. Li
a,
aw,
J.C. Li
a,
Jin Li
ai,
K.J. Li
aq,
Kang Li
m,
Ke Li
aj,
Lei Li
c,
P.L. Li
bc,
ap,
P.R. Li
aw,
g,
Q.Y. Li
aj,
W.D. Li
a,
aw,
W.G. Li
a,
X.L. Li
aj,
X.N. Li
a,
ap,
X.Q. Li
ag,
Z.B. Li
aq,
H. Liang
bc,
ap,
Y.F. Liang
am,
Y.T. Liang
aa,
G.R. Liao
k,
D.X. Lin
n,
B. Liu
ak,
8,
B.J. Liu
a,
C.X. Liu
a,
D. Liu
bc,
ap,
F.H. Liu
al,
Fang Liu
a,
Feng Liu
f,
H.B. Liu
l,
H.M. Liu
a,
aw,
Huanhuan Liu
a,
Huihui Liu
p,
J.B. Liu
bc,
ap,
J.Y. Liu
a,
aw,
K. Liu
ar,
K.Y. Liu
ad,
Ke Liu
f,
L.D. Liu
ah,
P.L. Liu
a,
ap,
Q. Liu
aw,
S.B. Liu
bc,
ap,
X. Liu
ac,
Y.B. Liu
ag,
Z.A. Liu
a,
ap,
aw,
Zhiqing Liu
y,
Y.F. Long
ah,
X.C. Lou
a,
ap,
aw,
H.J. Lu
q,
J.G. Lu
a,
ap,
Y. Lu
a,
Y.P. Lu
a,
ap,
C.L. Luo
ae,
M.X. Luo
bk,
X.L. Luo
a,
ap,
X.R. Lyu
aw,
F.C. Ma
ad,
H.L. Ma
a,
L.L. Ma
aj,
M.M. Ma
a,
aw,
Q.M. Ma
a,
T. Ma
a,
X.N. Ma
ag,
X.Y. Ma
a,
ap,
Y.M. Ma
aj,
F.E. Maas
n,
M. Maggiora
bf,
bh,
Q.A. Malik
be,
Y.J. Mao
ah,
Z.P. Mao
a,
S. Marcello
bf,
bh,
Z.X. Meng
ay,
J.G. Messchendorp
ab,
G. Mezzadri
w,
J. Min
a,
ap,
T.J. Min
a,
R.E. Mitchell
s,
X.H. Mo
a,
ap,
aw,
Y.J. Mo
f,
C. Morales Morales
n,
N.Yu. Muchnoi
i,
4,
H. Muramatsu
az,
A. Mustafa
d,
Y. Nefedov
z,
F. Nerling
j,
I.B. Nikolaev
i,
4,
Z. Ning
a,
ap,
S. Nisar
h,
S.L. Niu
a,
ap,
X.Y. Niu
a,
aw,
S.L. Olsen
ai,
10,
Q. Ouyang
a,
ap,
aw,
S. Pacetti
u,
Y. Pan
bc,
ap,
∗
,
M. Papenbrock
bi,
P. Patteri
t,
https://doi.org/10.1016/j.physletb.2018.04.0170370-2693/©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3.
M. Pelizaeus
d,
J. Pellegrino
bf,
bh,
H.P. Peng
bc,
ap,
K. Peters
j,
7,
J. Pettersson
bi,
J.L. Ping
ae,
R.G. Ping
a,
aw,
A. Pitka
y,
R. Poling
az,
V. Prasad
bc,
ap,
H.R. Qi
b,
M. Qi
af,
S. Qian
a,
ap,
C.F. Qiao
aw,
N. Qin
bj,
X.S. Qin
d,
Z.H. Qin
a,
ap,
J.F. Qiu
a,
K.H. Rashid
be,
9,
C.F. Redmer
y,
M. Richter
d,
M. Ripka
y,
M. Rolo
bh,
G. Rong
a,
aw,
Ch. Rosner
n,
A. Sarantsev
z,
5,
M. Savrié
w,
C. Schnier
d,
K. Schoenning
bi,
W. Shan
ah,
M. Shao
bc,
ap,
C.P. Shen
b,
P.X. Shen
ag,
X.Y. Shen
a,
aw,
H.Y. Sheng
a,
J.J. Song
aj,
W.M. Song
aj,
X.Y. Song
a,
S. Sosio
bf,
bh,
C. Sowa
d,
S. Spataro
bf,
bh,
G.X. Sun
a,
J.F. Sun
o,
L. Sun
bj,
S.S. Sun
a,
aw,
X.H. Sun
a,
Y.J. Sun
bc,
ap,
Y.K. Sun
bc,
ap,
Y.Z. Sun
a,
Z.J. Sun
a,
ap,
Z.T. Sun
s,
C.J. Tang
am,
G.Y. Tang
a,
X. Tang
a,
I. Tapan
au,
M. Tiemens
ab,
B. Tsednee
x,
I. Uman
av,
G.S. Varner
ax,
B. Wang
a,
B.L. Wang
aw,
D. Wang
ah,
D.Y. Wang
ah,
Dan Wang
aw,
K. Wang
a,
ap,
L.L. Wang
a,
L.S. Wang
a,
M. Wang
aj,
Meng Wang
a,
aw,
P. Wang
a,
P.L. Wang
a,
W.P. Wang
bc,
ap,
X.F. Wang
ar,
Y. Wang
an,
Y.D. Wang
n,
Y.F. Wang
a,
ap,
aw,
Y.Q. Wang
y,
Z. Wang
a,
ap,
Z.G. Wang
a,
ap,
Z.Y. Wang
a,
Zongyuan Wang
a,
aw,
T. Weber
y,
D.H. Wei
k,
P. Weidenkaff
y,
S.P. Wen
a,
U. Wiedner
d,
M. Wolke
bi,
L.H. Wu
a,
L.J. Wu
a,
aw,
Z. Wu
a,
ap,
L. Xia
bc,
ap,
Y. Xia
r,
D. Xiao
a,
H. Xiao
bd,
Y.J. Xiao
a,
aw,
Z.J. Xiao
ae,
Y.G. Xie
a,
ap,
Y.H. Xie
f,
X.A. Xiong
a,
aw,
Q.L. Xiu
a,
ap,
G.F. Xu
a,
J.J. Xu
a,
aw,
L. Xu
a,
Q.J. Xu
m,
Q.N. Xu
aw,
X.P. Xu
an,
L. Yan
bf,
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W.B. Yan
bc,
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W.C. Yan
b,
Y.H. Yan
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H.J. Yang
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H.X. Yang
a,
L. Yang
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Y.H. Yang
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Y.X. Yang
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M. Ye
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M.H. Ye
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C.Z. Yuan
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aaInstituteofHighEnergyPhysics,Beijing100049,People’sRepublicofChina bBeihangUniversity,Beijing100191,People’sRepublicofChina
cBeijingInstituteofPetrochemicalTechnology,Beijing102617,People’sRepublicofChina dBochumRuhr-University,D-44780Bochum,Germany
eCarnegieMellonUniversity,Pittsburgh,PA 15213,USA
fCentralChinaNormalUniversity,Wuhan430079,People’sRepublicofChina
gChinaCenterofAdvancedScienceandTechnology,Beijing100190,People’sRepublicofChina
hCOMSATSInstituteofInformationTechnology,Lahore,DefenceRoad,OffRaiwindRoad,54000Lahore,Pakistan iG.I.BudkerInstituteofNuclearPhysicsSBRAS(BINP),Novosibirsk630090,Russia
jGSIHelmholtzcentreforHeavyIonResearchGmbH,D-64291Darmstadt,Germany kGuangxiNormalUniversity,Guilin541004,People’sRepublicofChina
lGuangxiUniversity,Nanning530004,People’sRepublicofChina
mHangzhouNormalUniversity,Hangzhou310036,People’sRepublicofChina nHelmholtzInstituteMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany oHenanNormalUniversity,Xinxiang453007,People’sRepublicofChina
pHenanUniversityofScienceandTechnology,Luoyang471003,People’sRepublicofChina qHuangshanCollege,Huangshan245000,People’sRepublicofChina
rHunanUniversity,Changsha410082,People’sRepublicofChina sIndianaUniversity,Bloomington,IN 47405,USA
tINFNLaboratoriNazionalidiFrascati,I-00044,Frascati,Italy uINFNandUniversityofPerugia,I-06100,Perugia,Italy vINFNSezionediFerrara,I-44122,Ferrara,Italy wUniversityofFerrara,I-44122,Ferrara,Italy
xInstituteofPhysicsandTechnology,PeaceAve.54B,Ulaanbaatar13330,Mongolia
yJohannesGutenbergUniversityofMainz,Johann-Joachim-Becher-Weg45,D-55099Mainz,Germany zJointInstituteforNuclearResearch,141980Dubna,Moscowregion,Russia
aaJustus-Liebig-UniversitaetGiessen,II.PhysikalischesInstitut,Heinrich-Buff-Ring16,D-35392Giessen,Germany abKVI-CART,UniversityofGroningen,NL-9747AAGroningen,theNetherlands
ac
LanzhouUniversity,Lanzhou730000,People’sRepublicofChina adLiaoningUniversity,Shenyang110036,People’sRepublicofChina aeNanjingNormalUniversity,Nanjing210023,People’sRepublicofChina afNanjingUniversity,Nanjing210093,People’sRepublicofChina agNankaiUniversity,Tianjin300071,People’sRepublicofChina ahPekingUniversity,Beijing100871,People’sRepublicofChina aiSeoulNationalUniversity,Seoul,151-747, RepublicofKorea ajShandongUniversity,Jinan250100,People’sRepublicofChina
akShanghaiJiaoTongUniversity,Shanghai200240,People’sRepublicofChina alShanxiUniversity,Taiyuan030006,People’sRepublicofChina
amSichuanUniversity,Chengdu610064,People’sRepublicofChina anSoochowUniversity,Suzhou215006,People’sRepublicofChina aoSoutheastUniversity,Nanjing211100,People’sRepublicofChina
apStateKeyLaboratoryofParticleDetectionandElectronics,Beijing100049,Hefei230026,People’sRepublicofChina aqSunYat-SenUniversity,Guangzhou510275,People’sRepublicofChina
arTsinghuaUniversity,Beijing100084,People’sRepublicofChina asAnkaraUniversity,06100Tandogan,Ankara,Turkey atIstanbulBilgiUniversity,34060Eyup,Istanbul,Turkey auUludagUniversity,16059Bursa,Turkey
avNearEastUniversity,Nicosia,NorthCyprus,Mersin10,Turkey
awUniversityofChineseAcademyofSciences,Beijing100049,People’sRepublicofChina axUniversityofHawaii,Honolulu,HI 96822,USA
ayUniversityofJinan,Jinan250022,People’sRepublicofChina azUniversityofMinnesota,Minneapolis,MN 55455,USA
baUniversityofMuenster,Wilhelm-Klemm-Str.9,48149Muenster,Germany
bbUniversityofScienceandTechnologyLiaoning,Anshan114051,People’sRepublicofChina bcUniversityofScienceandTechnologyofChina,Hefei230026,People’sRepublicofChina bd
UniversityofSouthChina,Hengyang421001,People’sRepublicofChina beUniversityofthePunjab,Lahore54590,Pakistan
bfUniversityofTurin,I-10125,Turin,Italy
bgUniversityofEasternPiedmont,I-15121,Alessandria,Italy bhINFN,I-10125,Turin,Italy
biUppsalaUniversity,Box516,SE-75120Uppsala,Sweden bjWuhanUniversity,Wuhan430072,People’sRepublicofChina bkZhejiangUniversity,Hangzhou310027,People’sRepublicofChina blZhengzhouUniversity,Zhengzhou450001,People’sRepublicofChina
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Articlehistory:
Received16March2018
Receivedinrevisedform5April2018 Accepted8April2018
Availableonline10April2018 Editor:W.-D.Schlatter Keywords: BESIII D0meson Hadronicdecays Branchingfractions
Using adata sample of e+e− collision data corresponding to an integrated luminosity of 2.93 fb−1
collected with the BESIII detector ata center-of-mass energy of √s=3.773 GeV, we search for the singlyCabibbo-suppresseddecaysD0→
π
0π
0π
0,π
0π
0η
,π
0ηη
andηηη
usingthedoubletagmethod.The absolute branching fractions are measured to be B(D0→
π
0π
0π
0) = (2.0±0.4±0.3) ×10−4,B(D0→
π
0π
0η
) = (3.8±1.1±0.7) ×10−4 and B(D0→π
0ηη
) = (7.3±1.6±1.5) ×10−4with thestatisticalsignificancesof4.8
σ
,3.8σ
and5.5σ
,respectively,wherethefirstuncertaintiesarestatistical andthesecondonessystematic.NosignificantsignalofD0→ηηη
isfound,andtheupperlimitonitsdecaybranchingfractionissettobeB(D0→
ηηη
) <1.3×10−4atthe90%confidencelevel.©2018TheAuthor(s).PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.
1. Introduction
Thestudyofcharmedmesondecays,whichinvolvebothstrong and weak interactions, is an interesting and challenging field in particle physics. Experimental measurements of charmed meson decays yield essential information for understanding the intrin-sic decay mechanism and provide inputs to theoretical
calcula-*
Correspondingauthor.E-mailaddress:sa004043@mail.ustc.edu.cn(Y. Pan). 1 AlsoatBogaziciUniversity,34342Istanbul,Turkey.
2 AlsoattheMoscowInstituteofPhysicsandTechnology,Moscow141700,Russia. 3 Alsoatthe FunctionalElectronicsLaboratory,Tomsk StateUniversity,Tomsk, 634050,Russia.
4 AlsoattheNovosibirskStateUniversity,Novosibirsk,630090,Russia. 5 AlsoattheNRC“KurchatovInstitute”,PNPI,188300,Gatchina,Russia. 6 AlsoatIstanbulArelUniversity,34295Istanbul,Turkey.
7 AlsoatGoetheUniversityFrankfurt,60323FrankfurtamMain,Germany. 8 AlsoatKeyLaboratoryforParticlePhysics,AstrophysicsandCosmology, Min-istryofEducation;Shanghai KeyLaboratoryfor ParticlePhysicsand Cosmology; Institute ofNuclearand Particle Physics,Shanghai 200240, People’sRepublic of China.
9 GovernmentCollegeWomenUniversity,Sialkot51310, Punjab,Pakistan. 10 Currentlyat:CenterforUndergroundPhysics,InstituteforBasicScience, Dae-jeon34126,RepublicofKorea.
tionsandpredictions.Forexample,Ref. [1] suggeststhatthe mea-surement of the branching fraction (BF) of the hadronic decay
D0
→
π
0π
0π
0 mayshed light on the understanding ofthe role of isospin symmetryin D0 decays tothree-pion final states,and the isospinnature of thenon-resonant contribution.Additionally, thestudyofthehadronicdecaysofcharmedmesonsprovides im-portantinputsforthestudiesofB physics [2
].The singly Cabibbo-suppressed (SCS) decaysof the D0 meson to three neutral pseudoscalar particles, D0
→
π
0π
0π
0,π
0π
0η
,π
0ηη
andηηη
,proceeddominantlythroughinternal W -emission and W -exchange diagrams. Experimental studies ofthese decays are challenging due to the dominant presence of neutral parti-cles (photons) in thefinal states,low BFsandhigh backgrounds. Until now, only asearch for D0→
π
0π
0π
0 decay hasbeen per-formedbytheCLEO Collaborationwithaψ(3770)
datasampleof 281pb−1 in2006 [3].Usingthe“singletag”(ST)method,inwhich one D0 or D¯
0 mesonis found ineach event, they obtaineda BF upperlimitof3.5×
10−4 atthe90% confidencelevel(C.L.).InthisLetter, wepresentmeasurements oftheBFsoftheSCS decays D0
→
π
0π
0π
0,π
0π
0η
,π
0ηη
andηηη
withthe “double tag” (DT) technique andadata sample corresponding toan inte-grated luminosity of 2.93 fb−1 [4], collected at a center-of-mass energy of√
s=
3.773 GeV withthe BESIII detectoratthe BEPCIIe+e− collider.Throughoutthe Letter,charge conjugatemodesare alwaysimplied,unlessexplicitlymentioned.
2. BESIIIdetectorandMonteCarlosimulation
BESIII [5] isacylindricalspectrometer composedof a helium-gas-based main drift chamber (MDC), a plastic scintillator time-of-flight(TOF)system,aCsI(Tl)electromagneticcalorimeter(EMC), a superconductingsolenoidprovidinga1.0 Tmagneticfield,anda muoncounter.The chargedparticle momentumresolution inthe MDCis0.5%atatransversemomentum of1GeV/c andthe pho-ton energyresolutionin the EMCat 1GeV, is 2.5% inthe barrel regionand5.0%intheend-capregion.Particleidentification(PID) combinestheionizationenergyloss(dE
/
dx) intheMDC with in-formation from the TOF to identify particle types. More details about the design and performance of the detector are given in Ref. [5].GEANT4-based [6] Monte Carlo (MC) simulation software is
used to understand the backgrounds and to determine the
de-tectionefficiencies. Thegenerator KKMC[7,8] isusedto simulate the
e
+e−collisionincorporatingtheeffectsofbeam-energyspread and initial-state radiation (ISR). An inclusive MC sample includ-ing D0D¯
0, D+D− andnon-DD events,¯
ISR productionofψ(3686)
and J/ψ,
andcontinuumprocessese
+e−→
qq (q¯
=
u,
d,
s) isused to study the potential backgrounds. The known decay modesas specified in the Particle Data Group (PDG) [9] are generated by EVTGEN [10,11],whiletheremainingunknowndecaysof charmo-niumaremodeledbyLundCharm [12].3. Analysisstrategy
Atthe
ψ(3770)
resonance, D0D¯
0 pairs are produced in a co-herent1−−statewithoutadditionalparticles.ADTmethod,which wasfirstdevelopedbytheMARK-IIICollaboration [13,14],isused tomeasuretheabsoluteBFs.WefirstselectSTeventsinwhicha¯
D0mesonisreconstructedinaspecifichadronicdecaymode.Then wesearchfor
D
0decaysintheremainingtracks,andDTeventsare thosewhere D0D¯
0 pairsare fullyreconstructed.The absoluteBFs forD0decaysarecalculatedbyB
sig=
N sig DTB
int α NαSTDTsig,α
/
α ST
,
(1)wherethe superscript ‘sig’ representsa specific D0 signal decay,
NαST,
α
ST and
sig,α
DT are the yield of ST events, the ST detection efficiency and DT detection efficiency for a specific ST mode
α
, respectively,whileN
sigDT isthetotalyieldforDTsignalevents,andB
intistheproductofthedecayBFsfortheintermediate statesin theD
0 signaldecay.4. Dataanalysis
ChargedtracksarereconstructedfromhitsintheMDCandare requiredtohaveapolarangle
θ
satisfying|
cosθ
|
<
0.93.Thepoint of the closest approach of any charged track to the interaction point(IP) is required tobe within 1 cm inthe plane perpendic-ulartothe beamand±
10 cm alongthebeam. Informationfrom theTOF systemandthe dE/
dx information inthe MDCare com-binedtoformPIDC.L.sfortheπ
and K hypotheses. Eachtrackis assignedtotheparticletypewiththehighestPIDC.L.Photon candidates are reconstructed using clusters of energy depositedintheEMCcrystals.Theenergyisrequiredtobelarger than 25 MeV in the barrel region (
|
cosθ
|
<
0.8) or 50 MeV inTable 1
Requirementson E (in GeV),ST yieldsindata (NSTα),ST (STα (in%)) and DT (DTπ0π0π0,α,
π0π0η,α DT ,
π0ηη,α DT and
ηηη,α
DT (in%))efficiencies.Theuncertaintiesare statisticalonly.BFsof
π
0 andη
decaystotwophotonsarenotincludedinthe efficiencies. ST mode K+π− K+π−π0 K+π−π−π+ E (−0.027,0.025) (−0.071,0.041) (−0.025,0.022) NαST 530634±739 1030144±1129 707080±925 STα 64.83±0.04 33.75±0.02 38.01±0.02 DTπ0π0π0,α 10.56±0.02 4.46±0.01 4.78±0.02 DTπ0π0η,α 9.74±0.02 4.09±0.01 4.38±0.01 DTπ0ηη,α 8.23±0.02 3.47±0.01 3.58±0.01 DTηηη,α 10.02±0.02 4.14±0.01 4.57±0.01the end-capregion (0.86
<
|
cosθ
|
<
0.92). The energy deposited innearbyTOF countersisincludedtoimprovethereconstruction efficiency andenergyresolution. The difference ofthe EMC time fromthe eventstart time isrequired to be within[
0,700]
ns to suppresselectronicnoiseandshowersunrelatedtotheevent.The
π
0 andη
candidatesare reconstructedfromphotonpairs by requiring the invariant masses Mγ γ to satisfy 115<
Mγ γ<
150 MeV/c2or515<
Mγ γ<
570 MeV/c2,respectively.Toimprove theresolution,thephotonpairsarefittedkinematically constrain-ing their masses to the nominalπ
0 orη
masses [9], and the resultingenergies andmomenta ofthetwo photonsareused for subsequentanalysis.TheSTcandidates areselectedby reconstructing D
¯
0 decaystoK+
π
−,
K+π
−π
0 andK
+π
−π
−π
+.Twovariables,theenergydif-ference
E
≡
ED−
Ebeam andthebeam-energy-constrainedmassMBC
≡
E2beam
/
c4−
p2D/
c2,areusedtoidentifytheD¯
0 candidates.Here, Ebeam isthebeamenergy,andED
(
pD)
isthe reconstructedenergy (momentum) ofthe D
¯
0 candidate in thee
+e− center-of-masssystem.ThoseD¯
0candidatesareacceptedforfurtheranalysis thatsatisfy MBC>
1.83 GeV/c2 andmode-dependentE require-ments,whichareapproximatelythreetimesthevalueofthe reso-lutionaroundtheD
¯
0 nominalmass [9],assummarizedinTable1. ForeachSTmode,ifthereismorethanonecandidateintheevent, theonewiththeminimum|
E|
isselected.The
M
BCdistributionsoftheacceptedD¯
0candidatesareshown inFig.1,where D¯
0 signalsareobservedwithrelativelylow back-grounds.BinnedmaximumlikelihoodfitstotheM
BCdistributions areperformedtoobtaintheSTyields.Inthefits,thesignalshape ismodeledbytheMCsimulatedshapeconvolvedwithaGaussian functionrepresentingthedifferencebetweendataandMC simula-tion comingfromthebeam-energy spread,ISR, theψ(3770)
line shape, and resolution. The combinatorial background is modeled by an ARGUS function [15]. The STyields are calculated by sub-tracting the integrated ARGUS background yields from the total eventscountedin thesignal region1.859<
MBC<
1.871 GeV/c2. The STefficiencyis studiedusingthe sameprocedure onthe in-clusiveMCsample. TheresultingSTyields andthecorresponding STefficienciesaresummarizedinTable1.Candidatesfor theSCS decays, D0
→
π
0π
0π
0,π
0π
0η
,π
0ηη
andηηη
, are selected inthe systemrecoiling against the tagged¯
D0.Onlyeventswithoutanyadditionalchargedtrackarechosen. The D0 signal decays are reconstructed withanycombination of theselected
π
0 andη
candidatesthathavenot beenusedinthe ST side and do not sharethe same photon candidate. To distin-guishthesignaldecayfromcombinatorialbackgrounds,theenergy differenceE and thebeam-constrainedmass
M
BC arealso calcu-latedforeachacceptedcombination.AD0 candidateisacceptedif itsatisfiesamode-dependentE requirement, whichcorresponds to three times the value of the resolution around the
E peak
Fig. 1. (Coloronline.) Fitstothe MBC distributionsofthe candidatesfor theST modes:(a)D¯0→K+π−,(b)D¯0→K+π−π0and(c)D¯0→K+π−π−π+.Points
withanerrorbar aredata,the bluesolidlinesarethetotalfit curves,thered dashedlinesarethesignalshapes,andthegreenlong-dashedlinesarethe back-groundshapes.
basedonMCsimulation,assummarizedinTable2.Theshiftand asymmetry ofthe
E distributions are mainlyduetothe energy lossintheEMCformulti-photonfinalstates.Iftherearemultiple combinations fora given signal decay inan event, the one with theminimum
|
E|
isselected.Except for the decay D0
→
ηηη
, MC studies indicate thatthe selected candidates have large backgrounds from D0
→
π
0π
0π
0π
0 decay, which has a relatively large decay BF, and contain some background events from cross feeds betweensig-nal channels. Both backgrounds peak around the nominal D0
mass [9] intheMBC distributions.Toreduce thebackgroundfrom
D0
→
π
0π
0π
0π
0 in D0→
π
0π
0π
0 andπ
0π
0η
decays,thejoint chi-squareχ
24π
=
4i=1
χ
π2i isrequiredtobelarger than20ifthe candidateeventhasatleastfourindependentπ
0 candidates(not includingπ
0 candidates fromthe STside).Here,χπ
i
=
Miγ γ−mπ0
σi
γ γ
for the ith
π
0 candidate is calculated with theγ γ
invariant mass Mγ γ (beforei the kinematic fit) and its resolutionσ
iγ γ , as
well as the
π
0 nominal massmπ0 [9]. To reduce the cross feed between the signal decays, we define the analogical joint chi-square variables,
χ
2 A BC= (
M1 γ γ−mA σ1 γ γ)
2+ (
M2γ γ−mB σ2 γ γ)
2+ (
M3γ γ−mC σ3 γ γ)
2, where mA(B,C) is the nominal mass ofπ
0 orη
[9], andre-quire
χ
2π0π0η
>
20 for D0→
π
0π
0π
0 decay,χ
π20π0π0>
20 forD0
→
π
0π
0η
decayaswellasχ
2π0π0π0
>
20 andχ
π20π0η>
20 forD0
→
π
0ηη
decay.However, MC studies indicate that backgrounds remain from
photon mis-combinationsin
π
0 andη
candidates.These aredue to the matches ofa good photon with noise in the EMC, which usuallycorrespondstoafakelowenergyphoton.Furthermore,the MCindicatesthatthisbackgroundcanbereducedbyrequiringno othercombinationwiththesamefinalstateandwithχ
2<
20.For instanceforD0→
π
0π
0π
0,thisrequirementlosesonly5%of sig-naleventswhileitrejects30%ofmis-combinationbackground.For D0
→
π
0π
0π
0 andπ
0π
0η
decays, the events with anyπ
0π
0 invariant mass satisfying 445<
Mπ0π0
<
535 MeV/c2 are vetoed to reject the backgrounds from the Cabibbo-favored (CF) decays D0→
K0S
π
0 and K0Sη
with K0S→
π
0π
0, which haveex-actlythesamefinalstatesasthesignalchannels.
Withthe aboveselection criteria, the MBC distributions ofthe accepted D0 candidate events in data are shown in Fig. 2. The
D0
→
π
0π
0π
0,π
0π
0η
andπ
0ηη
signalsare clear,butno obvi-ous D0→
ηηη
signal is observed. The peaking backgrounds are dominated by the decay D0→
π
0π
0π
0π
0, and the CF decaysD0
→
K0Sπ
0/
η
for D0→
π
0π
0π
0/
η
. The contributionsfrom the cross feeds are smalland will be considered in determining the signalyields.Themis-combinationbackgroundisnegligible.To determine the signal yields of the decays D0
→
π
0π
0π
0,π
0π
0η
, andπ
0ηη
, unbinned maximum likelihood fits are per-formed tothe MBC distributions.The probability densityfunction (PDF) for signal is modeled with the MC simulated shape con-volved with a Gaussian function representing the resolution dif-ference anda potential massshift betweendataandMC simula-tion. The peakingbackgroundsfrom theCF decay D0→
K0Sπ
0/
η
(BKG I) and the decay D0→
π
0π
0π
0π
0 (BKG II) aswell as the cross feeds (BKG III)are alsoincluded inthe fit.The combinato-rial background (BKG IV)is modeled by an ARGUS function [15]. The shapesofthevariouspeakingbackgroundsaremodeledwith those of MC simulations, andthe corresponding magnitudes are fixed to thevaluesestimatedwitha datadrivenmethod.We se-lecta controlsample of D0→
π
0π
0π
0π
0 fromdatawithan ap-proach similar to the signal selection, andobtain the yield N4π0 froma fitto theresulting MBC distribution. AmixedMC sample, which includes the possible resonant decays D0→ ¯
K∗(892)
0π
0,ηπ
0, K0Sf0, f0(980)
π
0π
0, KL0π
0, K0SKS0 andη
π
0, is generatedwithknownBFs [9] andissubjecttotheselectioncriteriaof
D
0→
π
0π
0π
0 and D0→
π
0π
0π
0π
0 to evaluatethemis-identification rate3π0 andthedetectionefficiency
4π0,respectively.The mag-nitude of the background D0
→
π
0π
0π
0π
0 in the selection ofD0
→
π
0π
0π
0 is givenby N4π0
·
3π0
/
4π0. Similar data driven approaches areapplied to determine themagnitudeof the peak-ingbackground D0
→
π
0π
0π
0π
0,thecrossfeedandthenumber ofCFdecaysD
0→
K0S
π
0/
η
ineachsignaldecay.Theresultingfitsfor
D
0→
π
0π
0π
0,π
0π
0η
andπ
0ηη
areshowninFigs.2(a),(b) and(c),respectively.Thesignalyields andstatisticalsignificances, which are estimated from the likelihood difference between the fits with and without the signal included after considering theTable 2
Summaryof E requirements,signalyields(NsigDT),statisticalsignificances,BFsbythismeasurement andinthePDG [9].Thefirstandseconduncertaintiesarestatisticalandsystematic,respectively.The upperlimitissetatthe90%C.L.
Mode E(GeV) NsigDT Significance B(×10−4) BPDG(×10−4)
π0π0π0 (−0.115,0.059) 60±13 4.8σ 2.0±0.4±0.3 <3.5 π0π0η (−0.088,0.053) 42±12 3.8σ 3.8±1.1±0.7 – π0ηη (−0.061,0.045) 27±6 5.5σ 7.3±1.6±1.5 – ηηη (−0.030,0.028) – – <1.3 –
Fig. 2. (Coloronline.) FitstotheMBCdistributionsoftheacceptedcandidateevents for(a)D0→π0π0π0,(b)D0→π0π0η,(c)D0→π0ηηand(d)D0→ηηη.Dots witherrorbarsaredata,thebluesolidlinesarethetotalfitcurves,andthered dot-tedlinesarethesignalshapes.Thegreendashed,magentadash-dotted,orangedash two-dottedandbluelong-dashedlinesdenoteBKGI,BKGII,BKGIIIandBKG IV(see text),respectively.Thevioletlongdash-dottedlinesaretheremainingD0D¯0 back-ground.Theinsetinplot(d)showsthenormalizedlikelihooddistributionincluding thesystematicuncertainty,asafunctionoftheexpectedBF.Thebluearrow indi-catestheupperlimitontheBFatthe90%C.L.
changeinthe numberofdegreesof freedom,are summarizedin Table2.
Sincenoobvious D0
→
ηηη
signal isobserved,anupperlimit onitsdecayBF isdetermined.Wefit theM
BC distributionoftheD0
→
ηηη
candidateevents,wherethesignalisdescribed bythe MCsimulatedshapeconvolutedwithaGaussianfunction andthe backgroundby an ARGUS function. The parameters of the Gaus-sianfunctionarefixedtothoseobtainedinthefitofD0→
π
0ηη
decay. The resultant best fit is shown in Fig. 2 (d). The PDF for theexpectedsignal yieldistakentobethenormalizedlikelihoodL
versus the BF in the fit, incorporating the systematic uncer-tainties as described below, and is shown as the inset plot in Fig.2(d).TheupperlimitontheBFatthe90%C.L.,corresponding to0upL(
x)
dx/
0∞L(
x)
dx=
0.9,iscalculatedtobe<
1.3×
10−4.The detection efficiencies for various decays of interest must take intoaccount the effectofany intermediatestates. The exis-tenceofintermediatestatesinthe
D
0three-bodydecaysis inves-tigatedbyexaminingthecorrespondingDalitzplots.Exceptforthe decay D0→
π
0ηη
, no obvious intermediate states are observed. Therefore,thedetectionefficienciesforthedecaysD
0→
π
0π
0π
0,Fig. 3. (Coloronline.) FitstotheMπ0ηdistribution.Dotswitherrorbarsaredata, thebluesolidlineisthetotalfitcurve,andthereddottedlineisthesignalshape. Thebluelong-dashedlineisthebackgroundestimatedfromtheinclusiveMC.
π
0π
0η
andηηη
are obtained with MC samples of three-body phasespacedecaywithuniformangulardistributions.Forthedecay D0
→
π
0ηη
,thea
0(980)0 isevident intheπ
0η
invariant mass Mπ0η distribution. Fig. 3 shows the Mπ0η spec-trumof23eventswithtwoentriesper eventfromthedata sam-ple withadditional requirements−
0.023<
E
<
0.020 GeV and 1.859<
MBC<
1.871 GeV/c2.Anunbinnedmaximumlikelihoodfit isperformedontheMπ0η distributiontodetermine thea
0(980)0 signalyield.Inthefit,theshapeofthe
a
0(980)0isdescribedwiththeshape fromtheMCsample ofD0→
a0(980)0η
→
π
0ηη
,whichhastwo components:one withtheπ
0 combinedwiththecorrectη
com-ingfromthea
0(980)0 decay,andtheotherwiththeπ
0 combined with the wrongη
coming directly from the D0 decay. The first peaks aroundthe a0(980)0 mass,while the second contributesa broadshapeinthe Mπ0η distribution.TheMCshapeisconvolved witha Gaussian function to account for themass resolution dif-ference betweendata and MC simulation. In the MC simulation, the intermediate a0(980)0 state is parameterized withthe Flatté formula [16] with the central mass and the a0(980)0 coupling constants comingfromtheCrystalBarrelexperiment [17,18].The componentfromthedirectD
0 three-bodydecayisincludedinthe fit, andits shape isthe MC simulated shape,which is similar to that ofthewrongη
contributionin thea
0(980)0 shape.We also includethe backgroundin thefit, whereits shape isdetermined fromtheinclusiveMCsample.BothmagnitudesfortheD
0 three-bodydecaycomponentandbackgroundareleftfreeinthefit.The fitcurvesareshowninFig.3.Thefityields are21±
5 eventsfor thea
0(980)0 signaland0±
4 eventsforthe D0 directthree-body decay, which impliesthe predominant process in thethree-body decayofD
0→
π
0ηη
is D0→
a0(980)0η
.Wealsoperformafitwithoutthe
a
0(980)0signalincluded,and thestatisticalsignificanceofthea
0(980)0signaliscalculatedwith the change of likelihood value withrespect to that of the nom-inal fittaking into account the change ofnumber offreedom in the fit. The significance for the a0(980)0 signal is only 2.6σ
, al-thoughitisthepredominantcomponentinthethree-body decay. Therefore,inthedecayof D0→
π
0ηη
,thedetectionefficiencyis estimatedwiththeMCsampleofD0→
a0(980)0η
→
π
0ηη
as de-scribedabove.TheresultantDTefficienciesforvariousdecaysarelistedin Ta-ble 1. The BFs of these decays are calculated with Eq. (1), and summarizedinTable2.
5. Systematicuncertainties
WiththeDTtechnique,theBFmeasurementsareinsensitiveto systematicscomingfromtheSTsidesincetheymostly cancel.For