Measurement of the near-threshold $e^+e^- \to D \bar D$ cross section using initial-state radiation

0.18 MB·English

by  Belle Collaboration

.
Measurement of the near-threshold e+e− DD cross section using initial-state
→
radiation
G. Pakhlova,14 I. Adachi,9 H. Aihara,42 K. Arinstein,1 V. Aulchenko,1 T. Aushev,18,14 A. M. Bakich,39
V. Balagura,14 A. Bay,18 I. Bedny,1 U. Bitenc,15 A. Bondar,1 A. Bozek,27 M. Braˇcko,20,15 J. Brodzicka,9
T. E. Browder,8 P. Chang,26 A. Chen,24 W. T. Chen,24 B. G. Cheon,7 R. Chistov,14 S.-K. Choi,6 Y. Choi,38
J. Dalseno,21 M. Danilov,14 A. Drutskoy,3 S. Eidelman,1 D. Epifanov,1 N. Gabyshev,1 B. Golob,19,15 K.Hayasaka,22
H. Hayashii,23 D. Heffernan,32 Y. Hoshi,41 W.-S. Hou,26 H. J. Hyun,17 T. Iijima,22 K. Inami,22 A. Ishikawa,35
8 H. Ishino,43 R. Itoh,9 Y. Iwasaki,9 D. H. Kah,17 J. H. Kang,47 N. Katayama,9 H. Kawai,2 T. Kawasaki,29
0
A. Kibayashi,9 H. Kichimi,9 H. O. Kim,17 S. K. Kim,37 Y. J. Kim,5 K. Kinoshita,3 S. Korpar,20,15 P. Krokovny,9
0
2 R. Kumar,33 C. C. Kuo,24 A. Kuzmin,1 Y.-J. Kwon,47 J. S. Lange,4 J. S. Lee,38 M. J. Lee,37 T. Lesiak,27
A. Limosani,21 S.-W. Lin,26 Y. Liu,5 D. Liventsev,14 F. Mandl,12 A. Matyja,27 S. McOnie,39 T. Medvedeva,14
n
a W. Mitaroff,12 K. Miyabayashi,23 H. Miyata,29 Y. Miyazaki,22 R. Mizuk,14 G. R. Moloney,21 S. Nishida,9
J O. Nitoh,45 T. Nozaki,9 S. Ogawa,40 T. Ohshima,22 S. Okuno,16 S. L. Olsen,8,11 H. Ozaki,9 P. Pakhlov,14

4 C. W. Park,38 L. S. Peak,39 R. Pestotnik,15 L. E. Piilonen,46 A. Poluektov,1 H. Sahoo,8 Y. Sakai,9 O. Schneider,18
1 A. J. Schwartz,3 R. Seidl,10,34 K. Senyo,22 M. Shapkin,13 V. Shebalin,1 H. Shibuya,40 J.-G. Shiu,26 B. Shwartz,1

J. B. Singh,33 A. Sokolov,13 A. Somov,3 S. Staniˇc,30 M. Stariˇc,15 T. Sumiyoshi,44 S. Y. Suzuki,9 F. Takasaki,9
]
x K. Tamai,9 Y. Teramoto,31 I. Tikhomirov,14 S. Uehara,9 K. Ueno,26 T. Uglov,14 Y. Unno,7 S. Uno,9 Y. Usov,1
e
G. Varner,8 K. Vervink,18 S. Villa,18 A. Vinokurova,1 C. H. Wang,25 P. Wang,11 X. L. Wang,11 Y. Watanabe,16
-
p B. D. Yabsley,39 C. Z. Yuan,11 Y. Yusa,46 Z. P. Zhang,36 V. Zhilich,1 V. Zhulanov,1 A. Zupanc,15 and O. Zyukova1
e
(The Belle Collaboration)
h
[ 1Budker Institute of Nuclear Physics, Novosibirsk

2Chiba University, Chiba
3
3University of Cincinnati, Cincinnati, Ohio 45221
v
4Justus-Liebig-Universit¨at Gießen, Gießen
2
5The Graduate University for Advanced Studies, Hayama
8
6Gyeongsang National University, Chinju
0
0 7Hanyang University, Seoul
. 8University of Hawaii, Honolulu, Hawaii 96822
8 9High Energy Accelerator Research Organization (KEK), Tsukuba
0 10University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
7 11Institute of High Energy Physics, Chinese Academy of Sciences, Beijing
0
12Institute of High Energy Physics, Vienna
:
v 13Institute of High Energy Physics, Protvino
i 14Institute for Theoretical and Experimental Physics, Moscow
X
15J. Stefan Institute, Ljubljana
r 16Kanagawa University, Yokohama
a
17Kyungpook National University, Taegu
18E´cole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne
19University of Ljubljana, Ljubljana
20University of Maribor, Maribor
21University of Melbourne, School of Physics, Victoria 3010
22Nagoya University, Nagoya
23Nara Women’s University, Nara
24National Central University, Chung-li
25National United University, Miao Li
26Department of Physics, National Taiwan University, Taipei
27H. Niewodniczanski Institute of Nuclear Physics, Krakow
28Nippon Dental University, Niigata
29Niigata University, Niigata
30University of Nova Gorica, Nova Gorica
31Osaka City University, Osaka
32Osaka University, Osaka
33Panjab University, Chandigarh
34RIKEN BNL Research Center, Upton, New York 11973
2
35Saga University, Saga
36University of Science and Technology of China, Hefei
37Seoul National University, Seoul
38Sungkyunkwan University, Suwon
39University of Sydney, Sydney, New South Wales
40Toho University, Funabashi
41Tohoku Gakuin University, Tagajo
42Department of Physics, University of Tokyo, Tokyo
43Tokyo Institute of Technology, Tokyo
44Tokyo Metropolitan University, Tokyo
45Tokyo University of Agriculture and Technology, Tokyo
46Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061
47Yonsei University, Seoul
Wereportmeasurementsoftheexclusivecrosssectionfore+e− →DD,whereD=D0 orD+,in
thecenter-of-mass energy range from theDD threshold to5 GeV with initial-state radiation. The
analysis is based on a data sample collected with the Belle detector with an integrated luminosity
of 673 fb−1.
PACSnumbers: 13.66.Bc,13.87.Fh,14.40.Gx
The total cross section for hadron production in e+e− tected;itspresenceintheeventisinferredfromapeakat
annihilation in the √s region above the open-charm zero in the spectrum of the recoil mass against the DD
threshold was measured precisely by the Crystal Ball [1] system. The square of the recoil mass is defined as:
and BES [2] collaborations. However, the parameters of
the JPC = 1−− charmonium states obtained from fits Mr2ec(DD)=(Ec.m.−EDD)2−p2DD, (1)
to the inclusive cross section [3, 4] are poorly under-
stood theoretically [5]. Since interference between dif- where E is the initial e+e− center-of-mass (c.m.) en-
c.m.
ferent resonant structures depends upon the specific fi- ergy, E and p are the c.m. energy and momen-
DD DD
nalstates,studies ofexclusive crosssections forcharmed tum of the DD combination, respectively. To suppress
mesonpairsinthisenergyrangeareneededtoclarifythe backgrounds we consider two cases: (1) the γ is
ISR
situation. Recently, CLEO-c performed a scan over the out of detector acceptance in which case the polar an-
energy range from 3.970 to 4.260GeV and measured ex- gle for the DD combination in the c.m. frame is re-
clusivecrosssectionsforDD,DD∗andD∗D∗finalstates quired to be cos(θ ) > 0.9; (2) the fast γ is
at twelve points with high accuracy [6]. Belle has used a withinthedete|ctoraDccDep|tance(cos(θ ) <0.9),IiSnRthis
partialreconstructiontechniquetoperformfirstmeasure- case the γ is required to be| deteDctDed|and the mass
ISR
mentsoftheexclusivecrosssectionsσ(e+e− D±D∗∓) of the DDγ combination is required to be greater
and σ(e+e− D∗+D∗−) for √s near the D→+D∗− and than E I0S.R58GeV/c2. To suppress backgroundfrom
D∗+D∗− thre→sholdswithinitial-stateradiation(ISR)[7]. e+e− c.mD.−D(n)πγ processes we exclude events that
ISR
Recently Belle[8]hasreportedameasurementofthe ex- contai→n additional charged tracks that are not used in
clusive cross section for the process e+e− D0D−π+ the D or D reconstruction.
and the first observation of ψ(4415) → DD→∗2(2460) de- We ensure that all charged tracks originate from the
cay. interaction point (IP) with the requirements dr < 2cm
In this paper we report measurements of the exclu- and dz < 4cm, where dr and dz are the impact
sive cross sections for the processes e+e− D+D− and param| et|ers perpendicular to and |alo|ng the beam di-
e+e− D0D0 using ISR that are a conti→nuation of our rection with respect to the IP. Charged kaons are re-
→
studies of the near-threshold exclusive open charm pro- quired to have a ratio of particle identification likeli-
duction. Recently several new charmonium-like states hoods, = /( + ) [15], larger than 0.6. No
K K K π
P L L L
were observed in this mass range (Y(4260) [9, 10], identification requirements are applied for pion candi-
Y(4360), Y(4660) [11], X(4160) [12]) decaying to either dates. K0 candidatesarereconstructedfromπ+π− pairs
S
open- or closed-charm final states. Our study provides with aninvariantmass within 10MeV/c2 of the nominal
further information on the dynamics of charm quarks K0 mass. The distance between the two pion tracks at
S
at these center of mass energies. The data sample cor- the K0 vertex must be less than 1cm, the transverse
S
responds to an integrated luminosity of 673fb−1 col- flight distance from the interaction point is required to
lectedwiththeBelledetector[13]attheΥ(4S)resonance be greater than 0.1cm, and the angle between the K0
S
and nearby continuum at the KEKB asymmetric-energy momentumdirectionandthe flightdirectioninthex y
e+e− collider [14]. plane should be smaller than 0.1rad. The pion pair c−an-
We select e+e− DDγ signal events by recon- didates are refitted to the K0 mass. Photons are recon-
structingboththeD→andDImSResons,whereDD =D0D0 structed in the electromagnSetic calorimeter as showers
or D+D−. In general,the γ is not requiredto be de- with energies greater than 50MeV that are not asso-
ISR
3
ciated with charged tracks. Pairs of photons are com- 2c
binedtoformπ0 candidates. Ifthemassofaγγ pairlies V/ 100 30
e (a) (a)
within 15MeV/c2 of the nominal π0 mass, the pair is fit M
with a π0 mass constraint and considered as a π0 candi- 20 75 20
N/
date. D0 candidates [16] are reconstructedusing five de-
50
cay modes: K−π+, K−K+, K−π−π+π+, KS0π+π− and 10
K−π+π0. D+ candidates are reconstructed using the 25
decay modes K0π+ and K−π+π+. A 15MeV/c2 mass
window is usedSfor all modes except±for K−π−π+π+, 0 0
where a 10MeV/c2 requirement is applied ( 2.5σ in
each case±). To improve the momentum resolu∼tion of D 30 (b) (b)
10
meson candidates, final tracks are fitted to a common
vertex and a D0 or D+ mass constraint is applied. The 20
D candidates from a sideband region are refitted to the
5
mass,correspondingto the center ofthe sideband region 10
with the same width as the signal window.
The distribution of M2 (DD) after all the require- 0 0
rec 3.7 3.8 3.9 4 3.8 4 4.2 4.4 4.6 4.8 5
ments is shown in Fig. 1(a). A clear peak correspond- M(D D–), GeV/c2
ing to the e+e− DDγ process is evident around
ISR
zero. The shoulde→r at positive values is due to e+e−
D(∗)D(∗)(n)π0γ events. To suppress the tail of su→ch FIG. 2: The mass spectra of DD combinations (points with
ISR error bars): (a) D0D0; (b) D+D−. The total contribution
events we define a signal region by the requirement:
fromcombinatorialbackground(1–2)isshownasthehatched
M2 (DD) < 0.7(GeV/c2)2. The polar angle distri-
| rec | histogram, thecontribution from background(4) isshown as
bution for DD after the requirements on M2 (DD) is
rec the(barely visible) solid histogram.
showninFig.1(c). Thesharppeakingat 1ischaracter-
±
istic of ISR production andagreeswith the Monte Carlo
(MC) simulation. The mass distribution of the DDγISR The following sources of backgroundare considered:
combinations where the γ is detected is shown in
ISR
Fig.1(b)afteralltheselectionrequirements. Itpeaksat (1) combinatorial D(D) mesons combined with a real
theE . TheasymmetricshapeoftheM distri- D(D) coming from the signal or other processes;
c.m. DDγISR
butionisdue to higher-orderISRprocesses. TheM
D0D0 (2) both D and D are combinatorial;
222(GeV/c) 230000 (a) 20.1 GeV/c 110500 (b) (3) awrenifltdheceat+inoen−exf→rtormaDπtDm0hei∗sγspIriSnoRcte,hsfesoelfislonewa+leeds−tba→yteD;D∗D→πm0Dissπγm0IiSsRs,
N/0. N/ (4) reflection from the process e+e− DD∗γISR, fol-
100 50 lowed by D∗0 D0γ, with an ex→tra soft γ in the
→
final state;
0 0
-2 -1 0 1 2 8 9 10 11
M2 (D D–), (GeV/c2)2 M(D D–g ), GeV/c2 (5) a contribution from e+e− →DDπ0 when an ener-
rec getic π0 is misidentified as a single γISR.
5
0
0. The contribution from background (1) is extracted us-
N/ (c)
102 ing MD and MD sidebands that are four times as large
as the signal region. These sidebands are shifted by
30MeV/c2(20MeV/c2fortheD0 K−π−π+π+ mode)
→
10 from the signal region to avoid signal over-subtraction.
Background(2)is presentin boththe M andM side-
D D
-1 -0.5 0 0.5 1 bands andis,thus, subtractedtwice. To accountfor this
cosq over-subtractionweusea2-dimensionalsidebandregion,
whereeventsareselectedfromboththeM andtheM
D D
FIG. 1: a) The observed distributions of (a) M2 (DD); (b) sidebands. The total contribution of the combinatorial
rec
M(DDγISR) and (c)DD polar angles. Histograms show the backgrounds (1–2) is shown in Fig. 2 as a hatched his-
normalized contributions from MD and MD sidebands. The togram. Backgrounds (3–4) are suppressed by the tight
selected signal windows are illustrated by vertical lines. requirement on M2 (DD). The remaining contribu-
rec
tion from background (3) is estimated directly from the
and MD+D− spectra obtained after all the requirements data by applying a similar full reconstructionmethod to
are shown in Fig. 2. the isospin-conjugate process e+e− D0D−π+ γ .
→ miss ISR
4
Here the requirement on absence of additional charged b)
tracks in the event is relaxed. Since there is a charge (n 5 (a) (a)
imbalance in the D0D− final state, only events with an s
extra missing π+ can contribute to the M2 (DD) sig- 0.5
miss rec
nal window. To extract the level of background (3), the
D0D− mass spectrum is rescaled according to the ratio
of D0 and D− reconstruction efficiencies and an isospin
0 0
factor of 1/2. When this is done, the contribution from
background (3) is found to be negligibly small. Uncer- 5 (b) (b)
tainties in this estimate are included in the systematic
error. Background (4) contributes only to the D0D0 0.5
final state. It is estimated using a MC simulation of
e+e− D0D∗0γ , followed by D∗0 D0γ. To re-
ISR
produc→e the shape of the D0D∗0 mass→distribution we 0 0
use the D±D∗∓ cross section measured in our previous
10
(c) (c)
study[7]. Thecontributionfrombackground(4)isfound
tobesmall(showninFig.2(a)asasolidhistogram)and
1
issubtractedfromthe D0D0 massspectrum. Uncertain-
ties in this estimate areincluded in the systematic error.
The contribution from background(5), determined from
reconstructede+e− DDπ0 eventsinthedata,isfound 0 0
3.7 3.8 3.9 4 3.8 4 4.2 4.4 4.6 4.8 5
to be negligibly sma→ll and taken into account in the sys- M(D D–), GeV/c2
tematic error.
Thee+e− DD crosssectionsareextractedfromthe FIG. 3: The exclusive cross sections for: (a) e+e− →D0D0;
D0D0 and D→+D− mass distributions [17] (b)e+e− → D+D−; (c) e+e− → DD. The dotted lines
correspond to the ψ(3770), ψ(4040), ψ(4160) and ψ(4415)
dN/dm masses [20].
σ(e+e− DD)= , (2)
→ η dL/dm
tot
where m M , dN/dm is the obtained mass spectra, Thesystematicerrorsfortheσ(e+e− DD)measure-
≡ DD →
whileη isthetotalefficiency. ThefactordL/dmisthe mentsaresummarizedinTable I. Thesystematicerrors
tot
differential ISR luminosity
α 1+C 2m TABLE I: Contributions to the systematic error in the cross
dL/dm= πx(cid:16)(2−2x+x2)ln1 C −x2C(cid:17)E2L ,(3) sections, [%].
− c.m.
where x = 1 m2/E2 , is the total integrated
luminosity and−C = coc.smθ. , Lwhere θ defines the po- Source D0D0 D+D− DD
0 0
lar angle range for the γ in the e+e− c.m. frame: Background subtraction ±4 ±3 ±3
ISR
θ < θ < 180◦ θ . The total efficiency determined Reconstruction ±7 ±6 ±7
b0yMCγIsSimRulationg−row0slinearlywithM from0.095% Cross section calculation ±5 ±5 ±5
DD
near threshold to 0.46% at 5GeV/c2 for the D0D0 and B(D) ±4 ±6 ±5
from 0.038% to 0.17% for the D+D− mode. The result- Kaon identification ±2 ±2 ±2
ing e+e− D0D0, e+e− D+D− and e+e− DD Total ±10 ±10 ±10
→ → →
exclusive cross sections, averaged over the bin width,
are shown in Fig. 3 with statistical uncertainties only.
Since the bin width in the cross section distributions is associatedwiththe background(1–2)subtractionarees-
much larger than the resolution (which is 3MeV/c2 timated to be 2% due to the uncertainty in the scaling
at threshold and 5MeV/c2 at M 5G∼eV/c2), no factors for the sideband subtractions. This systematic
∼ DD ∼
correction for resolution is applied. error is estimated using fits to the M and M distri-
D D
We calculate the cross section ratio butions with differentsignalandbackgroundparameter-
σ(e+e− D+D−)/σ(e+e− D0D0) for the M bin izations. Uncertainties in backgrounds (3–5) are conser-
(3.76 3→.78)GeV/c2 corresp→onding to M MDD vatively estimatedto be smallerthan 2%ofthe signalin
− DD ≈ ψ(3770)
to be (0.72 0.16 0.06). This value is in agreement thecaseofD0D0;thesetwosourcesareaddedlinearlyto
within error±s with ±CLEO-c [18] and BES [19] measure- give 4% in total. In the D+D− case, backgrounds (3–5)
ments. The ratio σ(e+e− D+D−)/σ(e+e− D0D0) are estimated using the data and only the uncertainty
integrated over the M →range from 3.8 to 5.→0GeV/c2 in the scaling factor for the subtracted distributions is
DD
is found to be (1.15 0.13 0.10)and is consistent with taken into account. A second source of systematic error
± ±
unity. comes from the uncertainties in track and photon recon-
5
struction efficiencies, which are 1% per track, 1.5% per putergroupandtheNationalInstitute ofInformaticsfor
photon and 5% per K0, respectively. The systematic er- valuable computing and Super-SINET network support.
S
ror ascribed to the cross section calculation is estimated WeacknowledgesupportfromtheMinistryofEducation,
to be 5% and includes the error on the differential ISR Culture, Sports, Science, and Technology of Japan and
luminosity and the error from the efficiency fit. Other theJapanSocietyforthePromotionofScience;theAus-
contributions come from the uncertainty in the identifi- tralianResearchCouncilandtheAustralianDepartment
cation efficiency and the absolute D0 and D+ branching ofEducation,ScienceandTraining;theNationalScience
fractions[20]. Thetotalsystematicuncertaintiesare10% FoundationofChinaandtheKnowledgeInnovationPro-
and comparable to the statistical errors in the differen- gramoftheChineseAcademyofSciencesundercontract
tial cross section around the ψ(3770) peak; for the other No. 10575109 and IHEP-U-503; the Department of Sci-
M ranges statistical errors dominate. ence and Technology of India; the BK21 program of the
DD
In summary, we report measurements of e+e− MinistryofEducationofKorea,theCHEPSRCprogram
D0D0 and e+e− D+D− exclusive cross sections f→or and Basic Research program (grant No. R01-2005-000-
√s near the D0D→0 and D+D− thresholds with initial- 10089-0) of the Korea Science and Engineering Founda-
state radiation. The observed e+e− DD exclusive tion,andthe PureBasicResearchGroupprogramofthe
→
crosssectionsareconsistentwith recentBaBarmeasure- KoreaResearchFoundation;thePolishStateCommittee
ments [21] and are in qualitative agreement with the for Scientific Research; the Ministry of Education and
coupled-channel model predictions of Ref. [22]. This in- Science of the Russian Federation and the Russian Fed-
cludes the peak at 3.9GeV/c2 that is seen both in Belle eral Agency for Atomic Energy; the Slovenian Research
and BaBar cross section spectra. Agency; the Swiss National Science Foundation; the Na-
tional Science Council and the Ministry of Education of
We thank the KEKB group for the excellent opera-
Taiwan; and the U.S. Department of Energy.
tionoftheaccelerator,theKEKcryogenicsgroupforthe
efficient operation of the solenoid, and the KEK com-
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