Measurement of $e^+e^-\to D_s^{(*)+} D_s^{(*)-}$ cross sections near threshold using initial-state radiation

0.36 MB·English

by  G. Pakhlova et al.

Measurement of e+e− → Ds(∗)+Ds(∗)− cross sections near threshold using initial-state
radiation
G. Pakhlova,17 I. Adachi,10 H. Aihara,50 K. Arinstein,1,38 T. Aushev,24,17 T. Aziz,45 A. M. Bakich,44
V. Balagura,17 E. Barberio,28 A. Bay,24 K. Belous,16 V. Bhardwaj,40 B. Bhuyan,13 A. Bondar,1,38
A. Bozek,34 M. Braˇcko,26,18 T. E. Browder,9 A. Chen,31 P. Chen,33 B. G. Cheon,8 R. Chistov,17 I.-S. Cho,55
K. Cho,21 K.-S. Choi,55 S.-K. Choi,7 Y. Choi,43 J. Dalseno,27,46 M. Danilov,17 Z. Doleˇzal,2 A. Drutskoy,4
S. Eidelman,1,38 D. Epifanov,1,38 N. Gabyshev,1,38 A. Garmash,1,38 B. Golob,25,18 H. Ha,22 J. Haba,10
K. Hayasaka,29 H. Hayashii,30 Y. Horii,49 Y. Hoshi,48 W.-S. Hou,33 H. J. Hyun,23 T. Iijima,29 K. Inami,29
R. Itoh,10 M. Iwabuchi,55 Y. Iwasaki,10 N. J. Joshi,45 T. Julius,28 J. H. Kang,55 P. Kapusta,34 H. Kawai,3
1
1 T. Kawasaki,36 C. Kiesling,27 H. J. Kim,23 H. O. Kim,23 M. J. Kim,23 S. K. Kim,42 Y. J. Kim,6 K. Kinoshita,4
0 B. R. Ko,22 S. Korpar,26,18 P. Kriˇzan,25,18 T. Kumita,51 A. Kuzmin,1,38 Y.-J. Kwon,55 S.-H. Kyeong,55
2 J. S. Lange,5 M. J. Lee,42 S.-H. Lee,22 C. Liu,41 Y. Liu,33 D. Liventsev,17 R. Louvot,24 A. Matyja,34 S. McOnie,44

n K. Miyabayashi,30 H. Miyata,36 Y. Miyazaki,29 R. Mizuk,17 G. B. Mohanty,45 T. Mori,29 Y. Nagasaka,11
a E. Nakano,39 M. Nakao,10 H. Nakazawa,31 S. Nishida,10 K. Nishimura,9 O. Nitoh,52 T. Nozaki,10 S. Ogawa,47
J
T. Ohshima,29 S. Okuno,19 S. L. Olsen,42,9 P. Pakhlov,17 H. Palka,34 C. W. Park,43 H. Park,23 H. K. Park,23
7
R. Pestotnik,18 M. Petriˇc,18 L. E. Piilonen,53 A. Poluektov,1,38 M. Ro¨hrken,20 S. Ryu,42 H. Sahoo,9 K. Sakai,10
1
Y. Sakai,10 O. Schneider,24 C. Schwanda,15 K. Senyo,29 M. E. Sevior,28 M. Shapkin,16 V. Shebalin,1,38 C. P. Shen,9

] J.-G. Shiu,33 B. Shwartz,1,38 F. Simon,27,46 P. Smerkol,18 Y.-S. Sohn,55 A. Sokolov,16 E. Solovieva,17 S. Staniˇc,37
x
M. Stariˇc,18 T. Sumiyoshi,51 Y. Teramoto,39 I. Tikhomirov,17 K. Trabelsi,10 S. Uehara,10 T. Uglov,17 Y. Unno,8
e
- S. Uno,10 G. Varner,9 K. E. Varvell,44 A. Vinokurova,1,38 A. Vossen,12 C. H. Wang,32 M.-Z. Wang,33
p
P. Wang,14 M. Watanabe,36 Y. Watanabe,19 R. Wedd,28 E. Won,22 Y. Yamashita,35 C. Z. Yuan,14
e
h Z. P. Zhang,41 V. Zhilich,1,38 P. Zhou,54 V. Zhulanov,1,38 T. Zivko,18 A. Zupanc,20 and O. Zyukova1,38
[
(The Belle Collaboration)

2 1Budker Institute of Nuclear Physics, Novosibirsk
v 2Faculty of Mathematics and Physics, Charles University, Prague
7 3Chiba University, Chiba
9 4University of Cincinnati, Cincinnati, Ohio 45221
3 5Justus-Liebig-Universit¨at Gießen, Gießen
4
6The Graduate University for Advanced Studies, Hayama
.
1 7Gyeongsang National University, Chinju
1 8Hanyang University, Seoul
0 9University of Hawaii, Honolulu, Hawaii 96822
1 10High Energy Accelerator Research Organization (KEK), Tsukuba
v: 11Hiroshima Institute of Technology, Hiroshima
i 12University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
X 13Indian Institute of Technology Guwahati, Guwahati
r 14Institute of High Energy Physics, Chinese Academy of Sciences, Beijing
a 15Institute of High Energy Physics, Vienna
16Institute of High Energy Physics, Protvino
17Institute for Theoretical and Experimental Physics, Moscow
18J. Stefan Institute, Ljubljana
19Kanagawa University, Yokohama
20Institut fu¨r Experimentelle Kernphysik, Karlsruher Institut fu¨r Technologie, Karlsruhe
21Korea Institute of Science and Technology Information, Daejeon
22Korea University, Seoul
23Kyungpook National University, Taegu
24E´cole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne
25Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana
26University of Maribor, Maribor
27Max-Planck-Institut fu¨r Physik, Mu¨nchen
28University of Melbourne, School of Physics, Victoria 3010
29Nagoya University, Nagoya
30Nara Women’s University, Nara
31National Central University, Chung-li
32National United University, Miao Li
2
33Department of Physics, National Taiwan University, Taipei
34H. Niewodniczanski Institute of Nuclear Physics, Krakow
35Nippon Dental University, Niigata
36Niigata University, Niigata
37University of Nova Gorica, Nova Gorica
38Novosibirsk State University, Novosibirsk
39Osaka City University, Osaka
40Panjab University, Chandigarh
41University of Science and Technology of China, Hefei
42Seoul National University, Seoul
43Sungkyunkwan University, Suwon
44School of Physics, University of Sydney, NSW 2006
45Tata Institute of Fundamental Research, Mumbai
46Excellence Cluster Universe, Technische Universita¨t Mu¨nchen, Garching
47Toho University, Funabashi
48Tohoku Gakuin University, Tagajo
49Tohoku University, Sendai
50Department of Physics, University of Tokyo, Tokyo
51Tokyo Metropolitan University, Tokyo
52Tokyo University of Agriculture and Technology, Tokyo
53CNP, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
54Wayne State University, Detroit, Michigan 48202
55Yonsei University, Seoul
Wereportameasurementofexclusivee+e− →Ds(∗)+Ds(∗)− crosssectionsasafunctionofcenter-
of-mass energy near Ds(∗)+Ds(∗)− threshold with initial-state radiation. The analysis is based on a
data sample collected with theBelle detector with an integrated luminosity of 967fb−1.
PACSnumbers: 13.66.Bc,13.87.Fh,14.40.Lb
Recently a number of measurements of exclusive cross not exhibit strong decays to any of the measured open
sectionsfore+e− annihilationintocharmedhadronpairs charm final states and have remain unexplained since
above open-charm threshold were performed by the B- their discovery more than five years, provide additional
factory experiments using initial-state radiation (ISR). motivation to pursue all possible experimental informa-
These include Belle measurements [1] of e+e− cross sec- tion about the decomposition of charmed particle pro-
tions for the DD (D = D0 or D+), D+D∗−, D∗+D∗−, duction in the charm-threshold region.
D0D−π+, D0D∗−π+ and Λ+Λ− final states [2–6] and Here we report a measurement of exclusive e+e− →
c c
BaBar measurements of the DD, DD∗, D∗D∗ final D(∗)+D(∗)− crosssectionsasafunctionofcenter-of-mass
s s
states [7, 8], which are, in general, consistent with those energy from the D(∗)+D(∗)− thresholds to 5.0GeV, con-
of Belle. In addition, CLEO scanned the e+e− center of s s
tinuing our studies of the exclusive open charm produc-
mass energy range from 3.97 to 4.26GeV and obtained
tioninthis massrange. Theanalysisisbasedonastudy
∗ ∗ ∗
exclusive cross sections for the DD, DD , D D , DDπ
of events with ISR photons in a data sample collected
∗
and DD π final states [9]. The first measurements of
with the Belle detector at the Υ(nS) (n = 1,...,5) res-
the exclusive cross sections for e+e− annihilation into
onances and nearby continuum with an integrated lumi-
charmedstrangemesonpairsDs(∗)+Ds(∗)−wereperformed nosityof967fb−1 attheKEKBasymmetric-energye+e−
byCLEOwithhighaccuracybutwithlimitedmaximum
collider.
energy(4.26GeV)[9]andby BaBar[10]witha 100MeV
Wefollowthefullreconstructionmethodthatwaspre-
bin size. The observed cross sections were found to be viouslyusedforthe measurementsofthee+e− crosssec-
anorderofmagnitudesmallerthanthosefornon-strange tions to DD, D0D−π+ and D0D∗−π+ final states [2,
charmed meson production. 4, 5]. We select e+e− → D(∗)+D(∗)−γ signal events
s s ISR
Although the recent BES fit to the total cross section in which the D(∗)+ and D(∗)− mesons are fully recon-
for hadron production in e+e− provided new parame- s s
structed. In general, the γ is not required to be
ter values for the ψ resonances [11], the available exclu- ISR
detected and its presence in the event is inferred from
sive e+e− cross sections have not yet been qualitatively
a peak at zero in the spectrum of recoil mass squared
explained. One of the main problems is the numerous againsttheD(∗)+D(∗)− system. Therecoilmasssquared
open charm thresholds in the region that influence the s s
is defined as:
cross section behavior and, thus, complicate theoretical
descriptions.
The Y states [12] (with masses above open charm Mr2ecoil(Ds(∗)+Ds(∗)−)=(Ec.m.−EDs(∗)+Ds(∗)−)2−
threshold and quantum numbers JPC =1−−), which do p2Ds(∗)+Ds(∗)−, (1)
3
where E is the initial e+e− center-of-mass (c.m.) didates, the tracks from the D+ candidate are fitted to
c.m. s
ethnreereg-ym, oEmDens(∗t)u+mDs(∗o)f−thaenDd(∗p)+DDs(∗)(+∗)D−s(∗c)−ombarineateinoenr,gryespaencd- acacnodmidmatoensvaerretreexcownitshtruacmteadssusDins+gmthaessDcs+oγnsdtercaainytm. Dods∗e+.
s s A ±15MeV/c2 mass window is used (∼ 2.5σ). A mass-
tively. To suppress backgrounds two cases are consid-
constrained fit is also applied to D∗+ candidates.
ered: (1) the γ is outside of the detector acceptance s
and the polarISaRngle for the D(∗)+D(∗)− combination TheDs+ andDs∗+ sidebandsusedforbackgroundstud-
s s iesarefourtimesaslargeasthe signalregionandaredi-
in the c.m. frame is in the range |cos(θDs(∗)+Ds(∗)−)| > vided into windows of the same width as that of the sig-
0.9; (2) the γISR is within the detector acceptance nal. To avoid signal over-subtraction, the selected side-
γ(|cos(iθsDrs(∗e)q+uDis(r∗e)d−)|to<be0d.9e)t.ecteIdn atnhde tlhatetemracsasseo,f tthhee bTahnedDs a(rDe∗s)hcifatneddidbayte3s0fMroemV/thc2esferosimdetbhaendsisganraelrreefigtitoend.
ISR s s
D(∗)+D(∗)−γ combination should to be greater than to the central mass value of each window.
s s ISR
(Ec.m. − 0.5GeV). To suppress backgrounds from The Mr2ecoil(Ds+Ds−) distribution for MDs+Ds− <
e+e− → D(∗)+D(∗)−(n)(π+π−)γ ,(n > 0) processes, 5.0GeV/c2 after all the requirements described above
s s ISR
we excludeevents thatcontainadditionalchargedtracks is shown in Fig. 1a). A clear peak corresponding to
that were not used in the Ds(∗)+ and the Ds(∗)− recon- the e+e− → Ds+Ds−γISR process is evident near zero
recoil mass. The shoulder at positive values is mainly
struction.
due to e+e− → D+D∗−γ background. We de-
All charged tracks are required to originate from the s s ISR
fine the signal region with an asymmetric requirement
vicinity of the interaction point (IP); we impose the re-
−0.7(GeV/c2)2 < M2 (D+D−) < 0.4(GeV/c2)2 to
quirements |dr| < 1cm and |dz| < 4cm, where dr and recoil s s
suppress event this background. The polar angle distri-
dz aretheimpactparametersperpendiculartoandalong
bution of the D+D− combinations and the mass spec-
the beam direction with respect to the IP, respectively. s s
trum of the D+D−γ combinations (after subtraction
Charged kaons are required to have a ratio of particle s s ISR
of E ) in case (2), after M2 (D+D−) requirement,
identificationlikelihood,PK =LK/(LK+Lπ)>0.6[13]. c.m. recoil s s
are shown in Figs. 1b,c). These distributions are in
No identification requirements are applied for pion can-
agreement with a MC simulation and are typical of ISR
didates.
KS0 candidatesarereconstructedfromπ+π−pairswith production. The MDs+Ds− spectrum with all the require-
aninvariantmasswithin10MeV/c2oftheK0 mass. The ments applied is shown in Fig. 1d). A clear peak is seen
S
distance between the two pion tracks at the K0 vertex at threshold near the ψ(4040) mass.
S
must be less than 1cm, the transverse flight distance
f0r.o1mcmt,heanindttehraecatinognlepboeintwteisenretqhueirKedS0tmoobmeegnrteuamterdtihreacn- 22V/c)30 a) N/0.053400 b)
e
stimonallaenrdththane fl0i.g1hrtadd.irectionin the x−y plane should be 2 (G20 20
0.10 10
Photons are reconstructed in the electromagnetic N/
0 0
calorimeterasshowerswithenergiesgreaterthan50MeV -2 -1 0 1 2 -1 -0.5 0 0.5 1
thatarenotassociatedwithchargedtracks. Pairsofpho- M2 (D+D–), (GeV/c2)2 cosq
recoil s s
tons are combined to form π0 candidates. If the mass of 2c 2c
a γγ pair lies within 15MeV/c2 of the π0 mass, the pair V/20 c) V/15 d)
e e
isfittedwithaπ0 massconstraintandconsideredasaπ0 G15 M
candidate. ISR photon candidates are required to have 0.1 10 40 10
energies greater than 2.5GeV. Photon candidates used N/ 5 N/ 5
in η, η′ and D∗+ reconstructionare required to have en- 0 0
s -1.5 -1 -0.5 0 0.5 3.8 4 4.2 4.4 4.6 4.8 5
ergies greater than 100MeV. M(D+D– g ) – E , GeV M(D+D–), GeV/c2
η candidates are reconstructed using π+π−π0 s s ISR c.m. s s
(m±a1s0sMweinVd/ocw2) mdeacsasy mwionddeosw()∼ a2n.5dσγinγ ea(c±h20caMsee)V./cη2′ F5.I0GG.e1V:/ac)2TahfetedrisatlrlibtuhteiorneqoufiMremr2eceonilt(sDas+reDs−ap)pfoliredM. Dbs+)Ds−Th<e
cmaansdsidwaitnedsoawre) raencdonγsπtr+uπc−ted(±u1si5nMg ηeVπ+/cπ2−m(±as1s0wMinedVo/wc2) pmoalsasrsapnegclterudmistorfibtuhteioDns+oDfs−thγeISDRs+coDms−bicnoamtiboinnsataifotners.sucb)tTrahce-
decay modes (∼ 2.0σ in each case). A′ mass- and tion of Ec.m. energy in case (2). d) The MDs+Ds− spectrum
vertex-constrainedfit is applied to η and η candidates. after all the requirements applied. Cross-hached histograms
moDds+es:cKanS0dKid+at,eKs −aKre+πre+c,onKst−rKuc+teπd+πu0s,inKgS0Ksix−πd+eπca+y, FsheoewddthowennofrrmomalitzheedDMs+DDs+s∗−anfidnMalDsts−atseidiesbsahnodwncobnytrtibhuetoiopnesn.
ηπ+ and η′π+. Before calculation of the D+ candidate histograms. Thesignalwindowsareshownbyverticaldashed
s
mass, a vertex fit to a common vertex is performed for lines.
tracksthatformtheD+ candidate. A±15MeV/c2 mass
signal window is used fsor all modes (∼3σ in each case). The Mr2ecoil(Ds+Ds∗−) distribution for MDs+Ds∗− <
To improvethe momentum resolutionofD+ mesoncan- 5.0GeV/c2afteralltherequirementsareappliedisshown
s
4
qdWDinuiss+eitFrDrdeiimgebs∗fi.−uentγn2ieItoaSnt±R)h.0oes.fi7gsAit(nghGancellaeepVDlarrr/s+oeccgDp2ei)eoss∗2asn−kaifsrcoocoaroumgrMnarbdeirin2senzpcaeeoovtrilnio(ioddD.neiTnss+ngthDaenats∗rdop−oo)utelhnab+erdyea−mzaneagrr→soeles-. 22N/0.2 (GeV/c)11505 a) N/0.051125050 b)
spectrumofD+D∗−γ combinations(aftersubtraction 0 0
s s ISR -2 -1 0 1 2 -1 -0.5 0 0.5 1
Mof2the E(Dc.+mD. e∗n−e)rgisya)pinpliceadsear(e2)shaoftwenr itnheFirgesq.u2irbe,mc)e.ntTohne M2 recoil(Ds*+Ds*–), (GeV/c2)2 cosq
recoil s s 2c 2c
MDs+Ds∗− spectrumafterallthe requirementsareapplied eV/ 8 c) eV/ 8 d)
is shown in Fig. 2d). Two clear peaks are seen at the G 6 M 6
ψ(4160) and the ψ(4415) masses. 0.1 4 40 4
N/ N/
2 2
0 0
22V/c)6800 a) N/0.056800 b) -1M.5(Ds*-+1Ds*– g-I0S.R5) – E0c.m., Ge0V.5 4 4M.2(Ds4*+.4Ds*–4),. 6GeV4./8c2 5
e
G
N/0.2 (2400 2400 MFIDGs∗.+3D:s∗−a)<T5h.0eGdeiVst/ricb2uatifotenrsaolfl tthhee rMeqr2ueciorielm(Desn∗+tsDas∗p−p)liefodr.
0-2 -1 0 1 2 0-1 -0.5 0 0.5 1 b)ThepolarangledistributionoftheDs∗+Ds∗− combinations.
M2 (D+D*–), (GeV/c2)2 cosq c)ThemassspectrumoftheDs∗+Ds∗−γISRcombinationsafter
recoil s s
2V/c30 c) 2V/c20 d) sauftbetrraaclltitohneorfeEquc.imre.minenctasseap(p2l)i.edd.)CTrhoessM-hDas∗c+hDeds∗−hissptoegctrraumms
0.1 Ge20 40 Me10 sthioonws.tThehensoirgmnaalliwzeidndMowDss∗a+reasnhdowMnDbs∗y−vseirdteicbaalnddasshcoedntlriinbeus-.
N/10 N/
0 0
-1.5 -1 -0.5 0 0.5 4 4.2 4.4 4.6 4.8 5 used,whereχ2 ,χ2 ,χ2 andχ2 cor-
M(D+D*– g ) – E , GeV M(D+D*–), GeV/c2 M(Ds+) M(Ds−) M(Ds∗+) M(Ds∗−)
s s ISR c.m. s s respond to the mass fits for the D+, D−, D∗+ and the
s s s
∗−
FIG. 2: a) The distribution of the Mr2ecoil(Ds+Ds∗−) for Ds candidates.
MDs+Ds∗− < 5.0GeV/c2 after all the requirements applied. The following sources of background are con-
b)The polarangle distribution of theDs+Ds∗− combinations. sidered: (1) combinatorial background under the
c) Themassspectrum of theDs+Ds∗−γISR combinationsafter Ds(∗)+(Ds(∗)−) peak combined with a correctly recon-
subtraction of Ec.m. in case (2). d) The obtained MDs+Ds∗− structedDs(∗)−(Ds(∗)+)fromthesignalorotherprocesses;
spectrum. Cross-hached histograms show the normalized (2) both the D(∗)+ and the D(∗)− are combinatorial;(3)
MtamDs+inaatniodnMfroDms∗−thseidDebs∗+anDds∗s−cfionnatrlisbtuattieonisss.hoTwhnebsymtahlelocpoenn- Dfor+Dth∗e−Dγs+Ds−ansfidnael+set−ate→: reDfls∗e+ctDio∗n−sγfromptrhoecees+sees−fo→l-
histograms. Thesignalwindowsareshownbyverticaldashed s s ISR s s ISR
∗
lowed by D →D γ, where the low momentum γ is not
lines. s s
reconstructed;fortheD+D∗− finalstate: reflectionfrom
s s
The Mr2ecoil(Ds∗+Ds∗−) distribution for MDs∗+Ds∗− < Dtheγ,e+weh−ere→thDes∗l+owDs∗m−oγmISeRntpurmoceγssisfonlolotwreedcobnystrDucs∗te→d;
F5.i0g.G3eaV)/.cA2 apfetaekraclolrtrheesproenqduiinregmtoenet+sea−pp→lieDd∗is+sDh∗o−wγnin (4s) reflection from the e+e− → Ds(∗)+Ds(∗)−πm0issγISR
s s ISR processes, where the π0 is not reconstructed. (5) the
is again evident around zero recoil mass. We define miss
the signal region for M2 (D∗+D∗−) by a requirement contribution of e+e− → Ds(∗)+Ds(∗)−π0, when an ener-
±0.7(GeV/c2)2 aroundrezceorilo rescoilsmass. The polar an- getic π0 is misidentified as a single γISR.
gle distribution of the D∗+D∗− combinations and the The contributionfrombackground(1)isextractedus-
s s
mass spectrum of the Ds∗+Ds∗−γISR combinations (after ing the Ds(∗)− and Ds(∗)+ sidebands. Background (2) is
subtraction of Ec.m.) that survive the Mr2ecoil(Ds∗+Ds∗−) present in both the MDs(∗)+ and MDs(∗)− sidebands and
requirement in case (2) are shown in Figs. 3b,c). The is, thus, subtracted twice. To account for this over-
fullMDs∗+Ds∗− spectrumafteralltherequirementsareap- subtractionweuseadoublesidebandregion,whenevents
pnloiesdtriuscsthuorewanreinevFiidge.n3t.d). With such limited statistics baraendsesl.ecTtehdefcroonmtrbiboutthiotnhsefMroDms(∗t)+heancodmtbhienaMtoDrs(i∗a)−l bsaidcke--
The contribution of multiple entries after all the re- grounds (1–2) are shown in Figs. 1d) and 2d) as cross-
quirements is found to be ∼ 6%, ∼ 22%, ∼ 23%, for hatched histograms.
the Ds+Ds−, Ds+Ds∗− and the Ds∗+Ds∗− final states, re- Backgrounds (3–4) are suppressed by the tight re-
spectively. In such cases, only one Ds(∗)+Ds(∗)− com- quirementon Mr2ecoil(Ds(∗)+Ds(∗)−). The remaining back-
bination per event, that with the minimum value of ground (3) for the D+D∗− final state is estimated us-
s s
χ2tot = χ2M(Ds+) +χ2M(Ds−) +(χ2M(Ds∗+))+(χ2M(Ds∗−)), is ing a MC simulation of the e+e− → Ds∗+Ds∗−γISR pro-
5
cess. To reproduce the shape of the D+D∗− mass spec- theπ0 reconstructionefficiency. FortheD+D∗− andthe
s s s s
trum we use the initial measurement of the D∗+D∗− D∗+D∗− finalstatestheexpectedbackgroundsare∼0.6
s s s s
mthaesDs s+spDesc−trfiunmal.stTatheeisreemstiaminadteerdoufsinbgacakgMroCusnidmu(3la)tifoonr emvaesnstsraanngdes0.eTvhenetpsrionbtahbeiliwtyhoolfeπM0D→s+Dγs∗m−iasinddenMtiDfics∗+atDios∗−n
of the e+e− → Ds+Ds∗−γISR and e+e− → Ds∗+Ds∗−γISR due to asymmetric π0 → γγ decays is also estimated to
processes. To reproduce the shape of the Ds+Ds− mass be small. Thus the contribution from background (5) is
spectrumweusetheinitialmeasurementoftheDs∗+Ds∗− found to be negligibly small; uncertainties in these esti-
massspectrumandthefirstiterationoftheDs+Ds∗−mass mates are included in the systematic error.
spectrum. The contributions from background (3) for The e+e− → D(∗)+D(∗)− cross sections are extracted
the Ds+Ds− and the Ds+Ds∗− final states are shown in fromthebackgrousndsubstractedD(∗)+D(∗)− massdistri-
Figs. 1a), 1d) and Figs. 2a), 2d) as open histograms. s s
butions
Uncertainties in these estimates are included in the sys-
tematic errors. dN/dm
To estimate the contribution from background(4), we σ(e+e− →Ds(∗)+Ds(∗)−)= η dL/dm, (2)
study the e+e− → D(∗)+D(∗)−π0γ processes using tot
s s ISR
ftuimllyatreectohnesftrrauccttieodnfionfarlesctoantsetsr.uFctreodmeaveMntCs fsotrudthyewceaseess- swpheecrterumm,≡ηMDs(i∗s)+tDhs(e∗)−t,otdaNl /edffimcieisnctyheaonbdtatihneedfamcatosrs
tot
wheretheπ0 isnotdetected. Aftertheapplicationofthe dL/dm is the differential ISR luminosity [15]. The to-
requirement on Mr2ecoil(Ds(∗)+Ds(∗)−) this contribution is tal efficiencies determined by the MC simulation grow
found to be less than 0.5% and negligibly small; uncer- quadratically with energy from 0.015%, 0.010%, 0.005%
tainties in this estimate are included in the systematic nearthresholdto 0.045%,0.025%,0.011%at5.0GeV/c2
errors. for the D+D−, D+D∗− and the D∗+D∗− final states,
s s s s s s
The contribution from background (5), in which an respectively. The resulting e+e− → D(∗)+D(∗)− exclu-
s s
energetic π0 is misidentified as the γ candidate,is de-
ISR sivecrosssectionsaveragedoverthebinwidthareshown
terminedfromthedatausingfullyreconstructede+e− →
in Fig. 4. Since the bin width is much larger than the
Ds(∗)+Ds(∗)−π0 events. OnlythreeeventswithMDs+Ds− < MDs(∗)+Ds(∗)− resolution, which varies from ∼ 2MeV/c2
5.0GeV/c2 and MDs+Ds−π0 −Ec.m. > 0.5GeV are found around threshold to ∼ 6MeV/c2 at MDs(∗)+Ds(∗)− =
inthedata. Assumingauniformπ0 polarangledistribu- 5.0GeV/c2, no correction for resolution is applied. The
tion,thisbackgroundcontributioninthe|cos(θDs+Ds−)|> next-to-leadingorderradiativecorrectionsaretakeninto
0.9 signal sub-sample (case 1) is 3events/9ǫ ∼ 0.6 account by the dL/dm formula. The next-to-next-to-
π0
events in the whole MDs+Ds− mass range, where ǫπ0 is leadingordercorrectionsareincludedinthesystematics.
b)0.6 b) b)0.8
n a) n 1 b) n c)
( ( (0.6
s 0.4 s s
0.4
0.5
0.2 0.2
0
0 0
3.8 4 4.2 4.4 4.6 4.8 5 4 4.2 4.4 4.6 4.8 5 4.2 4.4 4.6 4.8 5
2 2 2
M(D +D –), GeV/c M(D +D *–), GeV/c M(D *+D *–), GeV/c
s s s s s s
FIG.4: Thecrosssectionaveragedoverthebinwidthfora)thee+e− →Ds+Ds−process;b)thee+e− →Ds+Ds∗−+c.c. process;
c) the e+e− → Ds∗+Ds∗− process. Error bars show statistical uncertainties only. There is a common systematic uncertainty
for all measurements, 11% for Ds+Ds−, 17% for Ds+Ds∗− and 31% for Ds∗+Ds∗−. This uncertainty is described in the text The
dotted lines show masses of the ψ(4040), ψ(4160) and ψ(4415) states [14].
The R ratio, defined as R = σ(e+e− → torsforthesidebandsubtractions. Thisisdoneusingfits
4hπaαdr2o/n3ss),/σf(oer+et−he→sµu+mµ−o)f, wthheereeσx(celu+sei−ve→eµ++e−µ−)→= tdoifftehreenMtDsis(g∗)n+alanadndMbDas(∗c)k−grdoiustnrdibuptairoanmseintetrhizeadtiaotnaswainthd
D(∗)+D(∗)− cross sections is shown in Fig. 5. arefoundtobe3%,7%and24%fortheD+D−,D+D∗−
s s s s s s
andthe D∗+D∗− finalstates, respectively. Uncertainties
s s
The systematic errors for the σ(e+e− → D(∗)+D(∗)−) in the contribution from background (3) are estimated
s s
measurements are summarized in Table I. The system- to be 2% for the D+D− final state and smaller than 1%
s s
aticerrorsassociatedwiththebackground(1–2)subtrac- for the D+D∗− final state. Uncertainties in the back-
s s
tionareestimatedfromtheuncertaintyinthescalingfac- grounds(4–5)areestimatedconservativelyto be smaller
6
R The limited statistics do notrevealany structures in the
0.3 e+e− →D∗+D∗− crosssection. TheobtainedRratiofor
s s
the sum of e+e− →D(∗)+D(∗)− cross sections has a rich
0.2 s s
structure including peaks around the ψ(4040), ψ(4160)
andtheψ(4415)masses. Boththee+e− →D+D∗− cross
0.1 s s
section and the R ratio exhibit an obvious dip near the
Y(4260) mass, similar to what is seen in e+e− →D∗D∗
0
andin the totalcross sectionfor charmproduction. The
3.8 4 4.2 4.4 4.6 4.8 5
obtained cross sections are consistent within errors with
M(Ds(*)+Ds(*)–) GeV/c2 those from BaBar [10]. The CLEO exclusive cross sec-
tions [9] are not directly comparable to those from Belle
FIG. 5: The R ratio for the sum of the Ds+Ds−, Ds+Ds∗− and as they are not radiativelycorrected, but generallyseem
the Ds∗+Ds∗− final states. The vertical dotted lines show the to reflect consistency.
massesoftheψ(4040),ψ(4160)andψ(4415)states[14]. Error
In this study we do not perform a fit to the obtained
bars show statistical uncertainties only.
e+e− →D(∗)+D(∗)− cross sections. The numerous open
s s
charmthresholds in this regioncomplicate the cross sec-
TABLE I:Contributions tothesystematic error on thecross tions behavior and coupled-channel modifications to the
sections. description of any particular final state require one to
take into account all other final states contributing to
Source Ds+Ds− Ds+Ds∗− Ds∗+Ds∗− the total cross section for charm production.
Background subtraction ±4% ±7% ±24%
We thank the KEKB group for the excellent opera-
Cross section calculation ±7% ±11% ±12%
tionoftheaccelerator,theKEKcryogenicsgroupforthe
B(Ds(∗)) ±5% ±5% ±5% efficient operation of the solenoid, and the KEK com-
Reconstruction ±6% ±10% ±16% puter group and the National Institute of Informatics
Kaon identification ±2% ±2% ±2% for valuable computing and SINET3 network support.
Total ±11% ±17% ±31% We acknowledge support from the Ministry of Educa-
tion, Culture, Sports, Science, and Technology (MEXT)
of Japan, the Japan Society for the Promotion of Sci-
ence(JSPS),andthe Tau-LeptonPhysicsResearchCen-
than 1% of the signal for all final states. The systematic
terofNagoyaUniversity;the AustralianResearchCoun-
errorsascribedtothecrosssectioncalculationincludean
cil and the Australian Department of Industry, Innova-
error on the differential ISR luminosity (2%) and statis-
tion, Science and Research; the National Natural Sci-
tical errors of the MC simulation for the total efficiency
ence Foundation of China under contract No. 10575109,
calculations. In the case of the D+D∗− state there is
s s 10775142, 10875115 and 10825524; the Ministry of Ed-
an additional uncertainty due to the unknown helicity
ucation, Youth and Sports of the Czech Republic un-
distribution, estimated following a procedure similar to
dercontractNo.LA10033andMSM0021620859;theDe-
that used in Ref [3]. Another source of systematic error
partment of Science and Technology of India; the BK21
comes from the uncertainties in track and photon recon-
and WCU program of the Ministry Education Science
structionefficiencies(1%pertrack,1.5%perphotonand
and Technology, National Research Foundation of Ko-
7%persoftphoton). Othercontributionsincludetheun-
rea, and NSDC of the Korea Institute of Science and
certainty in the identification efficiency and the absolute
Technology Information; the Polish Ministry of Science
D+ andD∗+ branchingfractions[14]. The totalsystem-
s s and Higher Education; the Ministry of Education and
atic uncertainties are11%,17%and31%forthe Ds+Ds−, Science of the Russian Federation and the Russian Fed-
D+D∗− and the D∗+D∗− final states, respectively.
s s s s eral Agency for Atomic Energy; the Slovenian Research
In summary, we report the measurement of the
Agency; the Swiss National Science Foundation; the Na-
e+e− → Ds(∗)+Ds(∗)− exclusive cross sections over the tional Science Council and the Ministry of Education of
center-of-massenergyrangefromtheD(∗)+D(∗)− thresh- Taiwan; and the U.S. Department of Energy. This work
s s
olds to 5.0GeV. A clear peak at threshold around the is supported by a Grant-in-Aid from MEXT for Science
ψ(4040) mass is seen in the e+e− → D+D− cross sec- Research in a Priority Area (“New Development of Fla-
s s
tion. In the e+e− → D+D∗− cross section two peaks vor Physics”),and from JSPS for Creative Scientific Re-
s s
are evidentaroundthe ψ(4160)and the ψ(4415)masses. search (“Evolution of Tau-lepton Physics”).
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Measurement of e+e− → Ds(∗)+Ds(∗)− cross sections near threshold using initial-state
radiation
G. Pakhlova,17 I. Adachi,10 H. Aihara,50 K. Arinstein,1,38 T. Aushev,24,17 T. Aziz,45 A. M. Bakich,44
V. Balagura,17 E. Barberio,28 A. Bay,24 K. Belous,16 V. Bhardwaj,40 B. Bhuyan,13 A. Bondar,1,38
A. Bozek,34 M. Braˇcko,26,18 T. E. Browder,9 A. Chen,31 P. Chen,33 B. G. Cheon,8 R. Chistov,17 I.-S. Cho,55
K. Cho,21 K.-S. Choi,55 S.-K. Choi,7 Y. Choi,43 J. Dalseno,27,46 M. Danilov,17 Z. Doleˇzal,2 A. Drutskoy,4
S. Eidelman,1,38 D. Epifanov,1,38 N. Gabyshev,1,38 A. Garmash,1,38 B. Golob,25,18 H. Ha,22 J. Haba,10
K. Hayasaka,29 H. Hayashii,30 Y. Horii,49 Y. Hoshi,48 W.-S. Hou,33 H. J. Hyun,23 T. Iijima,29 K. Inami,29
R. Itoh,10 M. Iwabuchi,55 Y. Iwasaki,10 N. J. Joshi,45 T. Julius,28 J. H. Kang,55 P. Kapusta,34 H. Kawai,3
1
1 T. Kawasaki,36 C. Kiesling,27 H. J. Kim,23 H. O. Kim,23 M. J. Kim,23 S. K. Kim,42 Y. J. Kim,6 K. Kinoshita,4
0 B. R. Ko,22 S. Korpar,26,18 P. Kriˇzan,25,18 T. Kumita,51 A. Kuzmin,1,38 Y.-J. Kwon,55 S.-H. Kyeong,55
2 J. S. Lange,5 M. J. Lee,42 S.-H. Lee,22 C. Liu,41 Y. Liu,33 D. Liventsev,17 R. Louvot,24 A. Matyja,34 S. McOnie,44

n K. Miyabayashi,30 H. Miyata,36 Y. Miyazaki,29 R. Mizuk,17 G. B. Mohanty,45 T. Mori,29 Y. Nagasaka,11
a E. Nakano,39 M. Nakao,10 H. Nakazawa,31 S. Nishida,10 K. Nishimura,9 O. Nitoh,52 T. Nozaki,10 S. Ogawa,47
J
T. Ohshima,29 S. Okuno,19 S. L. Olsen,42,9 P. Pakhlov,17 H. Palka,34 C. W. Park,43 H. Park,23 H. K. Park,23
7
R. Pestotnik,18 M. Petriˇc,18 L. E. Piilonen,53 A. Poluektov,1,38 M. Ro¨hrken,20 S. Ryu,42 H. Sahoo,9 K. Sakai,10
1
Y. Sakai,10 O. Schneider,24 C. Schwanda,15 K. Senyo,29 M. E. Sevior,28 M. Shapkin,16 V. Shebalin,1,38 C. P. Shen,9

] J.-G. Shiu,33 B. Shwartz,1,38 F. Simon,27,46 P. Smerkol,18 Y.-S. Sohn,55 A. Sokolov,16 E. Solovieva,17 S. Staniˇc,37
x
M. Stariˇc,18 T. Sumiyoshi,51 Y. Teramoto,39 I. Tikhomirov,17 K. Trabelsi,10 S. Uehara,10 T. Uglov,17 Y. Unno,8
e
- S. Uno,10 G. Varner,9 K. E. Varvell,44 A. Vinokurova,1,38 A. Vossen,12 C. H. Wang,32 M.-Z. Wang,33
p
P. Wang,14 M. Watanabe,36 Y. Watanabe,19 R. Wedd,28 E. Won,22 Y. Yamashita,35 C. Z. Yuan,14
e
h Z. P. Zhang,41 V. Zhilich,1,38 P. Zhou,54 V. Zhulanov,1,38 T. Zivko,18 A. Zupanc,20 and O. Zyukova1,38
[
(The Belle Collaboration)

2 1Budker Institute of Nuclear Physics, Novosibirsk
v 2Faculty of Mathematics and Physics, Charles University, Prague
7 3Chiba University, Chiba
9 4University of Cincinnati, Cincinnati, Ohio 45221
3 5Justus-Liebig-Universit¨at Gießen, Gießen
4
6The Graduate University for Advanced Studies, Hayama
.
1 7Gyeongsang National University, Chinju
1 8Hanyang University, Seoul
0 9University of Hawaii, Honolulu, Hawaii 96822
1 10High Energy Accelerator Research Organization (KEK), Tsukuba
v: 11Hiroshima Institute of Technology, Hiroshima
i 12University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
X 13Indian Institute of Technology Guwahati, Guwahati
r 14Institute of High Energy Physics, Chinese Academy of Sciences, Beijing
a 15Institute of High Energy Physics, Vienna
16Institute of High Energy Physics, Protvino
17Institute for Theoretical and Experimental Physics, Moscow
18J. Stefan Institute, Ljubljana
19Kanagawa University, Yokohama
20Institut fu¨r Experimentelle Kernphysik, Karlsruher Institut fu¨r Technologie, Karlsruhe
21Korea Institute of Science and Technology Information, Daejeon
22Korea University, Seoul
23Kyungpook National University, Taegu
24E´cole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne
25Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana
26University of Maribor, Maribor
27Max-Planck-Institut fu¨r Physik, Mu¨nchen
28University of Melbourne, School of Physics, Victoria 3010
29Nagoya University, Nagoya
30Nara Women’s University, Nara
31National Central University, Chung-li
32National United University, Miao Li
2
33Department of Physics, National Taiwan University, Taipei
34H. Niewodniczanski Institute of Nuclear Physics, Krakow
35Nippon Dental University, Niigata
36Niigata University, Niigata
37University of Nova Gorica, Nova Gorica
38Novosibirsk State University, Novosibirsk
39Osaka City University, Osaka
40Panjab University, Chandigarh
41University of Science and Technology of China, Hefei
42Seoul National University, Seoul
43Sungkyunkwan University, Suwon
44School of Physics, University of Sydney, NSW 2006
45Tata Institute of Fundamental Research, Mumbai
46Excellence Cluster Universe, Technische Universita¨t Mu¨nchen, Garching
47Toho University, Funabashi
48Tohoku Gakuin University, Tagajo
49Tohoku University, Sendai
50Department of Physics, University of Tokyo, Tokyo
51Tokyo Metropolitan University, Tokyo
52Tokyo University of Agriculture and Technology, Tokyo
53CNP, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
54Wayne State University, Detroit, Michigan 48202
55Yonsei University, Seoul
Wereportameasurementofexclusivee+e− →Ds(∗)+Ds(∗)− crosssectionsasafunctionofcenter-
of-mass energy near Ds(∗)+Ds(∗)− threshold with initial-state radiation. The analysis is based on a
data sample collected with theBelle detector with an integrated luminosity of 967fb−1.
PACSnumbers: 13.66.Bc,13.87.Fh,14.40.Lb
Recently a number of measurements of exclusive cross threshold and quantum numbers JPC =1−−), which do
sectionsfore+e− annihilationintocharmedhadronpairs not exhibit strong decays to any of the measured open
above open-charm threshold were performed by the B- charm final states and have remain unexplained since
factory experiments using initial-state radiation (ISR). their discovery more than five years, provide additional
These include Belle measurements [1] of e+e− cross sec- motivation to pursue all possible experimental informa-
tions for the DD (D = D0 or D+), D+D∗−, D∗+D∗−, tion about the decomposition of charmed particle pro-
D0D−π+, D0D∗−π+ and Λ+Λ− final states [2–6] and duction in the charm-threshold region.
c c
∗ ∗ ∗
BaBar measurements of the DD, DD , D D final
states [7, 8], which are, in general, consistent with those
of Belle. In addition, CLEO scanned the e+e− center Here we report a measurement of exclusive e+e− →
of mass energy range from 3.97 to 4.26GeV and ob- D(∗)+D(∗)− crosssectionsasafunctionofcenter-of-mass
s s
tained exclusive cross sections for the DD, DD∗, D∗D∗, energy from the D(∗)+D(∗)− thresholds to 5.0GeV, con-
s s
∗
DDπ and DD π final states [9]. The first measure- tinuing our studies of the exclusive open charm produc-
ments of the exclusive cross sections for e+e− annihila- tioninthis massrange. Theanalysisisbasedonastudy
tion into charmed strange meson pairs Ds(∗)+Ds(∗)− were of events with ISR photons in a data sample collected
performedbyCLEOwithhighaccuracybutwithlimited with the Belle detector [13] at the Υ(nS) (n = 1,...,5)
maximum energy (4.26GeV) [9]. Recently BaBar pre- resonances and nearby continuum with an integrated
sented e+e− →D(∗)+D(∗)− cross sections averaged over luminosity of 967fb−1 at the KEKB [14] asymmetric-
s s
100MeVwidebins[10]. Theobservedcrosssectionswere energy e+e− collider.
foundtobeanorderofmagnitudesmallerthanthosefor
non-strange charmed meson production.
Wefollowthefullreconstructionmethodthatwaspre-
Although the recent BES fit to the total cross section
for hadron production in e+e− provided new parame- viouslyusedforthe measurementsofthee+e− crosssec-
tions to DD, D0D−π+ and D0D∗−π+ final states [2,
ter values for the ψ resonances [11], the available exclu-
sive e+e− cross sections have not yet been qualitatively 4, 5]. We select e+e− → Ds(∗)+Ds(∗)−γISR signal events
explained. One of the main problems is the numerous in which the D(∗)+ and D(∗)− mesons are fully recon-
s s
open charm thresholds in the region that influence the structed. ISR photon candidates are indicated by γ .
ISR
cross section behavior and, thus, complicate theoretical Ingeneral,anγ is not requiredto be detected andits
ISR
descriptions. presenceintheeventisinferredfromapeakatzerointhe
The Y states [12] (with masses above open charm spectrum of recoil mass squared against the D(∗)+D(∗)−
s s
3
system. The recoil mass squared is defined as: ηπ+ and η′π+. Before calculation of the D+ candidate
s
mass, a vertex fit to a common vertex is performed for
Mr2ecoil(Ds(∗)+Ds(∗)−)=(Ec.m.−EDs(∗)+Ds(∗)−)2− tracksthatformtheDs+ candidate. A±15MeV/c2 mass
p2 , (1) signal window is used for all modes (∼3σ in each case).
Ds(∗)+Ds(∗)− To improve the momentum resolutionof D+ meson can-
s
where E is the initial e+e− center-of-mass (c.m.) didates, the tracks from the D+ candidate are fitted to
c.m. s
ethnreereg-ym, oEmDens(∗t)u+mDs(∗o)f−thaenDd(∗p)+DDs(∗)(+∗)D−s(∗c)−ombarineateinoenr,gryespaencd- acacnodmidmatoensvaerretreexcownitshtruacmteadssusDins+gmthaessDcs+oγnsdtercaainytm. Dods∗e+.
s s A ±15MeV/c2 mass window is used (∼ 2.5σ). A mass-
tively. To suppress backgrounds two cases are consid- constrained fit is also applied to D∗+ candidates.
ered: (1) the γ is outside of the detector acceptance s
and the polarISaRngle for the D(∗)+D(∗)− combination TheDs+ andDs∗+ sidebandsusedforbackgroundstud-
s s iesarefourtimesaslargeasthe signalregionandaredi-
in the c.m. frame is in the range |cos(θDs(∗)+Ds(∗)−)| > vided into windows of the same width as that of the sig-
0.9; (2) the γ is within the detector acceptance
ISR nal. To avoid signal over-subtraction, the selected side-
(|cos(θDs(∗)+Ds(∗)−)| < 0.9). In the latter case, the bands are shifted by 30MeV/c2 from the signal region.
γIS(∗R)+is (r∗e)−quired to be detected and the mass of the TheDs(Ds∗)candidatesfromthesesidebandsarerefitted
Ds Ds γISR combination should to be greater than to the central mass value of each window.
(eE+ce.−m.→−D0s(.5∗)G+DeVs(∗)).−(mT)o(π+suπp−p)rγeIsSsR,b(mack=gr1o,u2n,d.s..)fprorom- 5.0TGheeV/Mc2r2ecaofitl(eDr s+aDlls−th)e driesqturiibreumtioenntsfodrescMribDes+dDs−abov<e
cesses,weexcludeeventsthatcontainadditionalcharged is shown in Fig. 1a). A clear peak corresponding to
tracksthatwerenotusedinthe Ds(∗)+ andthe Ds(∗)− re- the e+e− → Ds+Ds−γISR process is evident near zero
construction. recoil mass. The shoulder at positive values is mainly
All charged tracks are required to originate from the due to e+e− → D+D∗−γ background. We de-
s s ISR
vicinity of the interaction point (IP); we impose the re- fine the signal region with an asymmetric requirement
quirements |dr| < 1cm and |dz| < 4cm, where dr and −0.7(GeV/c2)2 < M2 (D+D−) < 0.4(GeV/c2)2 to
recoil s s
dz aretheimpactparametersperpendiculartoandalong suppress event this background. The polar angle distri-
the beam direction with respect to the IP, respectively. bution of the D+D− combinations and the mass spec-
s s
Charged kaons are required to have a ratio of particle trum of the D+D−γ combinations (after subtraction
s s ISR
identificationlikelihood,P =L /(L +L )>0.6[15]. of E ) in case (2), after M2 (D+D−) requirement,
K K K π c.m. recoil s s
No identification requirements are applied for pion can- are shown in Figs. 1b,c). These distributions are in
didates. agreement with a MC simulation and are typical of ISR
anKinS0vacrainadnitdmataesssawreitrheicno1n0stMruecVte/dc2froofmthπe+Kπ0−mpaaisrss.wTihthe pmreondtuscatpiopnl.ieTdhisesMhoDws+nDis−nsFpiegc.t1rudm). wAitchleaalrlptheaekreisquseireen-
S
distance between the two pion tracks at the K0 vertex at threshold near the ψ(4040) mass.
S
mfroumsttbhee ilnetsesrathctainon1pcomin,ttihseretqruainrsevdertsoebfleigghretadteisrttahnacne The Mr2ecoil(Ds+Ds∗−) distribution for MDs+Ds∗− <
5.0GeV/c2afteralltherequirementsareappliedisshown
0.1cm, and the angle between the KS0 momentum direc- in Fig. 2a). A clear peak corresponding to e+e− →
tion and the flight directionin the x−y plane should be D+D∗−γ signal process is again evident around zero.
smaller than 0.1rad. Wse desfineIStRhe signal region for M2 (D+D∗−) by a re-
Photons are reconstructed in the electromagnetic recoil s s
quirement ±0.7(GeV/c2)2 aroundzero. The polar angle
calorimeterasshowerswithenergiesgreaterthan50MeV distribution of the D+D∗− combinations and the mass
thatarenotassociatedwithchargedtracks. Pairsofpho- spectrumofD+D∗−γs scombinations(aftersubtraction
tons are combined to form π0 candidates. If the mass of s s ISR
of the E energy) in case (2) after the requirement on
a γγ pair lies within 15MeV/c2 of the π0 mass, the pair M2 (Dc.+mD. ∗−)isappliedareshowninFigs.2b,c). The
isfittedwithaπ0 massconstraintandconsideredasaπ0 recoil s s
candidate. ISR photon candidates are required to have MDs+Ds∗− spectrumafteralltherequirementsareapplied
is shown in Fig. 2d). Two clear peaks are seen at the
energies greater than 2.5GeV. Photon candidates used
in η, η′ and D∗+ reconstructionare required to have en- ψ(4160) and the ψ(4415) masses.
ergies greater tshan 100MeV. The Mr2ecoil(Ds∗+Ds∗−) distribution for MDs∗+Ds∗− <
η candidates are reconstructed using π+π−π0 5.0GeV/c2 afteralltherequirementsappliedisshownin
(±10MeV/c2 mass window) and γγ (±20MeV/c2 Fig.3a). Apeakcorrespondingtoe+e− →D∗+D∗−γ
s s ISR
′
mass window) decay modes (∼ 2.5σ in each case). η is again evident around zero recoil mass. We define
candidates arereconstructedusing ηπ+π− (±10MeV/c2 the signal region for M2 (D∗+D∗−) by a requirement
recoil s s
mass window) and γπ+π− (±15MeV/c2 mass window) ±0.7(GeV/c2)2 around zero recoil mass. The polar an-
decay modes (∼ 2.0σ in each case). A mass- and gle distribution of the D∗+D∗− combinations and the
s s
vertex-constrainedfit is applied to η and η′ candidates. mass spectrum of the D∗+D∗−γ combinations (after
s s ISR
D+ candidates are reconstructed using six decay subtraction of E ) that survive the M2 (D∗+D∗−)
s c.m. recoil s s
modes: K0K+, K−K+π+, K−K+π+π0, K0K−π+π+, requirement in case (2) are shown in Figs. 3b,c). The
S S