cross sections near threshold using initial-state radiation

Measurement of e

^þ

e

! D

^ðÞþs

D

^ðÞs

cross sections near threshold using initial-state radiation

G. Pakhlova,¹⁷I. Adachi,¹⁰H. Aihara,⁵⁰K. Arinstein,^1,38T. Aushev,^24,17T. Aziz,⁴⁵A. M. Bakich,⁴⁴V. Balagura,¹⁷ E. Barberio,²⁸A. Bay,²⁴K. Belous,¹⁶V. Bhardwaj,⁴⁰B. Bhuyan,¹³A. Bondar,^1,38A. Bozek,³⁴M. Bracˇko,^26,18 T. E. Browder,⁹A. Chen,³¹P. Chen,³³B. G. Cheon,⁸R. Chistov,¹⁷I.-S. Cho,⁵⁵K. Cho,²¹K.-S. Choi,⁵⁵S.-K. Choi,⁷ Y. Choi,⁴³J. Dalseno,^27,46M. Danilov,¹⁷Z. Dolezˇal,²A. Drutskoy,⁴S. Eidelman,^1,38D. Epifanov,^1,38N. Gabyshev,^1,38 A. Garmash,^1,38B. Golob,^25,18H. Ha,²²J. Haba,¹⁰K. Hayasaka,²⁹H. Hayashii,³⁰Y. Horii,⁴⁹Y. Hoshi,⁴⁸W.-S. Hou,³³ H. J. Hyun,²³T. Iijima,²⁹K. Inami,²⁹R. Itoh,¹⁰M. Iwabuchi,⁵⁵Y. Iwasaki,¹⁰N. J. Joshi,⁴⁵T. Julius,²⁸J. H. Kang,⁵⁵ P. Kapusta,³⁴H. Kawai,³T. Kawasaki,³⁶C. Kiesling,²⁷H. J. Kim,²³H. O. Kim,²³M. J. Kim,²³S. K. Kim,⁴²Y. J. Kim,⁶

K. Kinoshita,⁴B. R. Ko,²²S. Korpar,^26,18P. Krizˇan,^25,18T. Kumita,⁵¹A. Kuzmin,^1,38Y.-J. Kwon,⁵⁵S.-H. Kyeong,⁵⁵ J. S. Lange,⁵M. J. Lee,⁴²S.-H. Lee,²²C. Liu,⁴¹Y. Liu,³³D. Liventsev,¹⁷R. Louvot,²⁴A. Matyja,³⁴S. McOnie,⁴⁴ K. Miyabayashi,³⁰H. Miyata,³⁶Y. Miyazaki,²⁹R. Mizuk,¹⁷G. B. Mohanty,⁴⁵T. Mori,²⁹Y. Nagasaka,¹¹E. Nakano,³⁹ M. Nakao,¹⁰H. Nakazawa,³¹S. Nishida,¹⁰K. Nishimura,⁹O. Nitoh,⁵²T. Nozaki,¹⁰S. Ogawa,⁴⁷T. Ohshima,²⁹S. Okuno,¹⁹ S. L. Olsen,^42,9P. Pakhlov,¹⁷H. Palka,³⁴C. W. Park,⁴³H. Park,²³H. K. Park,²³R. Pestotnik,¹⁸M. Petricˇ,¹⁸L. E. Piilonen,⁵³ A. Poluektov,^1,38M. Ro¨hrken,²⁰S. Ryu,⁴²H. Sahoo,⁹K. Sakai,¹⁰Y. Sakai,¹⁰O. Schneider,²⁴C. Schwanda,¹⁵K. Senyo,²⁹

M. E. Sevior,²⁸M. Shapkin,¹⁶V. Shebalin,^1,38C. P. Shen,⁹J.-G. Shiu,³³B. Shwartz,^1,38F. Simon,^27,46P. Smerkol,¹⁸ Y.-S. Sohn,⁵⁵A. Sokolov,¹⁶E. Solovieva,¹⁷S. Stanicˇ,³⁷M. Staricˇ,¹⁸T. Sumiyoshi,⁵¹Y. Teramoto,³⁹I. Tikhomirov,¹⁷ K. Trabelsi,¹⁰S. Uehara,¹⁰T. Uglov,¹⁷Y. Unno,⁸S. Uno,¹⁰G. Varner,⁹K. E. Varvell,⁴⁴A. Vinokurova,^1,38A. Vossen,¹²

C. H. Wang,³²M.-Z. Wang,³³P. Wang,¹⁴M. Watanabe,³⁶Y. Watanabe,¹⁹R. Wedd,²⁸E. Won,²²Y. Yamashita,³⁵ C. Z. Yuan,¹⁴Z. P. Zhang,⁴¹V. Zhilich,^1,38P. Zhou,⁵⁴V. Zhulanov,^1,38T. Zivko,¹⁸A. Zupanc,²⁰and O. Zyukova^1,38

(The Belle Collaboration)

1Budker Institute of Nuclear Physics, Novosibirsk

2Faculty of Mathematics and Physics, Charles University, Prague

3Chiba University, Chiba

4University of Cincinnati, Cincinnati, Ohio 45221

5Justus-Liebig-Universita¨t Gießen, Gießen

6The Graduate University for Advanced Studies, Hayama

7Gyeongsang National University, Chinju

8Hanyang University, Seoul

9University of Hawaii, Honolulu, Hawaii 96822

10High Energy Accelerator Research Organization (KEK), Tsukuba

11Hiroshima Institute of Technology, Hiroshima

12University of Illinois at Urbana-Champaign, Urbana, Illinois 61801

13Indian Institute of Technology Guwahati, Guwahati

14Institute of High Energy Physics, Chinese Academy of Sciences, Beijing

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 Fe´de´rale 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

33Department of Physics, National Taiwan University, Taipei PHYSICAL REVIEW D83,011101(R) (2011)

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

(Received 19 November 2010; published 6 January 2011)

We report a measurement of exclusivee^þe!D^ðÞþs D^ðÞs cross sections as a function of center-of- mass energy near theD^ðÞþs D^ðÞs threshold with initial-state radiation. The analysis is based on a data sample collected with the Belle detector with an integrated luminosity of967 fb¹.

DOI:10.1103/PhysRevD.83.011101 PACS numbers: 13.66.Bc, 13.87.Fh, 14.40.Lb

Recently a number of measurements of exclusive cross sections fore^þe annihilation into charmed hadron pairs above open-charm threshold were performed by the B-factory experiments using initial-state radiation (ISR).

These include Belle measurements [1] ofe^þe cross sec- tions for the DD (D¼D⁰ or D^þ), D^þD, D^þD, D⁰D^þ, D⁰D^þ, and ^þ_cc final states [2–6] and BABARmeasurements of theDD,DD,DD final states [7,8], which are, in general, consistent with those of Belle.

In addition, CLEO scanned thee^þecenter-of-mass energy range from 3.97 to 4.26 GeV and obtained exclusive cross sections for theDD,DD,DD,DD , andDD final states [9]. The first measurements of the exclusive cross sections fore^þeannihilation intocharmed strangemeson pairsD^ðÞþs D^ðÞs were performed by CLEO with high ac- curacy but with limited maximum energy (4.26 GeV) [9].

RecentlyBABARpresentede^þe!D^ðÞþs D^ðÞs cross sec- tions averaged over 100 MeV wide bins [10]. The observed cross sections were found to be an order of magnitude smaller than those for nonstrange charmed meson production.

Although the recent BES fit to the total cross section for hadron production ine^þeprovided new parameter values for the c resonances [11], the available exclusivee^þe cross sections have not yet been qualitatively explained.

One of the main problems is the numerous open-charm thresholds in the region that influence the cross section behavior and, thus, complicate theoretical descriptions.

TheYstates [12] (with masses above open charm thresh- old and quantum numbers J^PC ¼1), which do not ex- hibit strong decays to any of the measured open-charm final states and have remain unexplained since their dis- covery more than five years ago, provide additional moti- vation to pursue all possible experimental information about the decomposition of charmed particle production in the charm-threshold region.

Here we report a measurement of exclusive e^þe! D^ðÞþs D^ðÞs cross sections as a function of center-of-mass energy from theD^ðÞþs D^ðÞs thresholds to 5.0 GeV, continu- ing our studies of the exclusive open-charm production in this mass range. The analysis is based on a study of events with ISR photons in a data sample collected with the Belle detector [13] at the ðnSÞ (n¼1;. . .;5) resonances and nearby continuum with an integrated luminosity of967 fb¹ at the KEKB [14] asymmetric-energye^þecollider.

We follow the full reconstruction method that was pre- viously used for the measurements of the e^þe cross sections to DD, D⁰D^þ, and D⁰D^þ final states [2,4,5]. We select e^þe !D^ðÞþs D^ðÞs ISR signal events in which the D^ðÞþs and D^ðÞs mesons are fully recon- structed. ISR photon candidates are indicated by ISR. In general, an _ISR is not required to be detected and its presence in the event is inferred from a peak at zero in the spectrum of recoil mass squared against theD^ðÞþs D^ðÞs

system. The recoil mass squared is defined as

G. PAKHLOVAet al. PHYSICAL REVIEW D83,011101(R) (2011)

M²_recoilðD^ðÞþs D^ðÞs Þ ¼ ðE_c:m:E_D^ðÞþ

s D^ðÞ_s Þ²p²_DðÞþ

s D^ðÞs ; (1) where Ec:m: is the initial e^þe center-of-mass (c.m.) en- ergy, and E_D^ðÞþ

s D^ðÞs andp_D^ðÞþ

s D^ðÞs are energy and three- momentum of the D^ðÞþs D^ðÞs combination, respectively.

To suppress backgrounds two cases are considered: (1) the ISR is outside of the detector acceptance and the polar angle for theD^ðÞþs D^ðÞs combination in the c.m. frame is in the rangejcosð_D^ðÞþ

s D^ðÞs Þj>0:9; (2) the_ISR is within the detector acceptance [jcosð_D^ðÞþ

s D^ðÞs Þj<0:9]. In the latter case, the _ISR is required to be detected and the mass of the D^ðÞþs D^ðÞs ISR combination should to be greater than (Ec:m:0:5 GeV). To suppress backgrounds frome^þe!D^ðÞþs D^ðÞs ðmÞð^þÞISR, ðm¼1;2;. . .Þ processes, we exclude events that contain additional charged tracks that were not used in the D^ðÞþs and the D^ðÞs reconstruction.

All charged tracks are required to originate from the vicinity of the interaction point; we impose the require- mentsjdrj<1 cmandjdzj<4 cm, wheredranddzare the impact parameters perpendicular to and along the beam direction with respect to the interaction point, respectively.

Charged kaons are required to have a ratio of particle identification likelihood, P_K¼L_K=ðL_KþLÞ>0:6 [15]. No identification requirements are applied for pion candidates.

K⁰_Scandidates are reconstructed from^þ pairs with an invariant mass within10 MeV=c² of theK⁰_Smass. The distance between the two pion tracks at theK_S⁰vertex must be less than 1 cm, the transverse flight distance from the interaction point is required to be greater than 0.1 cm, and the angle between the K⁰_S momentum direction and the flight direction in the x-y plane should be smaller than 0.1 rad.

Photons are reconstructed in the electromagnetic calo- rimeter as showers with energies greater than 50 MeV that are not associated with charged tracks. Pairs of photons are combined to form⁰ candidates. If the mass of apair lies within 15 MeV=c² of the ⁰ mass, the pair is fitted with a ⁰ mass constraint and considered as a⁰ candi- date. ISR photon candidates are required to have energies greater than 2.5 GeV. Photon candidates used in,⁰, and D^þ_s reconstruction are required to have energies greater than 100 MeV.

candidates are reconstructed using ^þ0 ( 10 MeV=c² mass window) and (20 MeV=c² mass window) decay modes (2:5 in each case). ⁰ candi- dates are reconstructed using ^þ (10 MeV=c² mass window) and^þ(15 MeV=c²mass window) decay modes (2:0in each case). A mass- and vertex- constrained fit is applied toand⁰candidates.

D^þs candidates are reconstructed using six decay modes:

K_S⁰K^þ,KK^þþ,KK^þþ0,K_S⁰K^þþ,^þ, and

^0þ. Before calculation of the D^þ_s candidate mass, a vertex fit to a common vertex is performed for tracks that form theD^þ_s candidate. A15 MeV=c² mass signal win- dow is used for all modes (3in each case). To improve the momentum resolution of D^þ_s meson candidates, the tracks from the D^þs candidate are fitted to a common ver tex with aD^þs mass constraint.D^þs candidates are recon- structed using theD^þ_sdecay mode. A15 MeV=c²mass window is used (2:5). A mass-constrained fit is also applied toD^þs candidates.

TheD^þ_s andD^þ_s sidebands used for background studies are 4 times as large as the signal region and are divided into windows of the same width as that of the signal. To avoid signal oversubtraction, the selected sidebands are shifted by30 MeV=c² from the signal region. TheDsðD_sÞcandi- dates from these sidebands are refitted to the central mass value of each window.

The M²_recoilðD^þ_sDsÞ distribution for MD^þsDs <

5:0 GeV=c² after all the requirements described above is shown in Fig. 1(a). A clear peak corresponding to the e^þe!D^þ_sD_sISR process is evident near zero recoil mass. The shoulder at positive values is mainly due to e^þe!D^þ_sD_{s ISR} background. We define the signal region with an asymmetric requirement0:7 ðGeV=c²Þ²<

M_recoil² ðD^þ_sDsÞ<0:4ðGeV=c²Þ² to suppress this back- ground. The polar angle distribution of theD^þ_sD_s combi- nations and the mass spectrum of the D^þ_sD_sISR combinations (after subtraction of E_c:m:) in case (2), after the M²_recoilðD^þ_sD_sÞ requirement, are shown in Figs. 1(b) and1(c). These distributions are in agreement with a Monte Carlo (MC) simulation and are typical of ISR

0 10 20 30

-2 -1 0 1 2 0

10 20 30 40

-1 -0.5 0 0.5 1

0 5 10 15 20

-1.5 -1 -0.5 0 0.5 N/0.2 (GeV/c2 )2

M²_recoil(D_s⁺D_s^–), (GeV/c²)² a)

N/0.05

cosθ b)

N/0.1 GeV/c2

M(D_s⁺D_s^–γISR) – E_c.m., GeV c)

N/40 MeV/c2

M(D_s⁺D_s^–), GeV/c² d)

0 5 10 15

3.8 4 4.2 4.4 4.6 4.8 5

FIG. 1. (a) The distribution of M_recoil² ðD^þsDsÞfor MD^þsDs <

5:0 GeV=c²after all the requirements are applied. (b) The polar angle distribution of the D^þsDs combinations. (c) The mass spectrum of the D^þsDsISR combinations after subtraction of Ec:m: energy in case (2). (d) TheMD^þsDs spectrum after all the requirements applied. Crosshatched histograms show the nor- malizedMD^þs andMDs sideband contributions. Feed down from the D^þsDs final state is shown by the open histograms. The signal windows are shown by vertical dashed lines.

e e D D

production. TheM_D^þ_sDs spectrum with all the requirements applied is shown in Fig.1(d). A clear peak is seen at the threshold near thecð4040Þmass.

The M²_recoilðD^þsDs Þ distribution for MD^þ_sD_s <

5:0 GeV=c²after all the requirements are applied is shown in Fig. 2(a). A clear peak corresponding to e^þe ! D^þ_sD_{s ISR} signal process is again evident around zero.

We define the signal region for M²_recoilðD^þ_sD_s Þ by a re- quirement0:7ðGeV=c²Þ² around zero. The polar angle distribution of the D^þsDs combinations and the mass spectrum of D^þsDs ISR combinations (after subtraction of the E_c:m: energy) in case (2) after the requirement on M²_recoilðD^þ_sD_s Þis applied are shown in Figs.2(b)and2(c).

The MD^þ_sD_s spectrum after all the requirements are ap- plied is shown in Fig.2(d). Two clear peaks are seen at the cð4160Þand the cð4415Þmasses.

The M_recoil² ðD^þ_s D_s Þ distribution for M_D^þ_{s Ds} <

5:0 GeV=c² after all the requirements are applied is shown in Fig. 3(a). A peak corresponding to e^þe ! D^þs Ds ISR is again evident around zero recoil mass.

We define the signal region for M²_recoilðD^þ_s Ds Þ by a requirement 0:7ðGeV=c²Þ² around zero recoil mass.

The polar angle distribution of theD^þs Ds combinations and the mass spectrum of theD^þs Ds ISR combinations (after subtraction ofEc:m:) that survive theM_recoil² ðD^þs Ds Þ requirement in case (2) are shown in Figs.3(b)and3(c).

The fullM_D^þ_{s Ds} spectrum after all the requirements are applied is shown in Fig.3(d). With such limited statistics no structures are evident.

The contribution of multiple entries after all the require- ments is found to be6%,22%,23%, for theD^þsDs, D^þsDs , and D^þs Ds final states, respectively. In such cases, only one D^ðÞþs D^ðÞs combination per event, that with the minimum value of ²_tot¼²_MðDþ

sÞþ²_MðD

sÞþ

ð²_MðDþ

s ÞÞ þ ð²_MðD

s ÞÞ, is used, where ²_MðDþ

sÞ, ²_MðD

sÞ, ²_MðDþ

s Þ, and ²_MðD

s Þ correspond to the mass fits for the D^þ_s,D_s,D^þ_s , and theD_s candidates.

The following sources of background are considered:

(1) combinatorial background under theD^ðÞþs [D^ðÞs ] peak combined with a correctly reconstructedD^ðÞs [D^ðÞþs ] from the signal or other processes; (2) both the D^ðÞþs and the D^ðÞs are combinatorial; (3) for the D^þsDs final state, reflections from the e^þe!D^þsDs ISR and e^þe! D^þs Ds ISR processes followed by Ds !Ds, where the low momentum is not reconstructed; for the D^þsDs final state, reflection from the e^þe! D^þs Ds ISR process followed by Ds !Ds, where the low momentumis not reconstructed; (4) reflection from the e^þe!D^ðÞþs D^ðÞs ⁰_missISR processes, where the ⁰_missis not reconstructed; (5) the contribution ofe^þe! D^ðÞþs D^ðÞs ⁰, when an energetic ⁰ is misidentified as a single_ISR.

The contribution from background (1) is extracted using the D^ðÞs andD^ðÞþs sidebands. Background (2) is present in both the M_D^ðÞþ

s and M_D^ðÞ

s sidebands and is, thus, subtracted twice. To account for this oversubtraction we use a double sideband region, when events are selected from both the M_D^ðÞþ

s and the M_D^ðÞ

s sidebands. The

0 20 40 60 80

-2 -1 0 1 2 0

20 40 60 80

-1 -0.5 0 0.5 1

0 10 20 30

-1.5 -1 -0.5 0 0.5 N/0.2 (GeV/c2 )2

M²_recoil(D_s⁺D_s^*–), (GeV/c²)² a)

N/0.05

cosθ b)

N/0.1 GeV/c2

M(D_s⁺D_s^*–γ_ISR) – E_c.m., GeV c)

N/40 MeV/c2

M(D_s⁺D_s^*–), GeV/c² d)

0 10 20

4 4.2 4.4 4.6 4.8 5

FIG. 2. (a) The distribution of the M²_recoilðD^þsDs Þ for MD^þsDs <5:0 GeV=c² after all the requirements are applied.

(b) The polar angle distribution of the D^þsDs combinations.

(c) The mass spectrum of the D^þsDs ISR combinations after subtraction of Ec:m: in case (2). (d) The obtained MD^þsDs

spectrum. Crosshatched histograms show the normalized MD^þs

andMDs sideband contributions. The small contamination from the D^þs Ds final state is shown by the open histograms. The signal windows are shown by vertical dashed lines.

0 5 10 15

-2 -1 0 1 2 0

5 10 15 20

-1 -0.5 0 0.5 1

0 2 4 6 8

-1.5 -1 -0.5 0 0.5 N/0.2 (GeV/c2 )2

M²_recoil(D_s^*+D_s^*–), (GeV/c²)² a)

N/0.05

cosθ b)

N/0.1 GeV/c2

M(D_s^*+D_s^*–γISR) – E_c.m., GeV c)

N/40 MeV/c2

M(D_s^*+D_s^*–), GeV/c² d)

0 2 4 6 8

4 4.2 4.4 4.6 4.8 5

FIG. 3. (a) The distributions of the M_recoil² ðD^þs Ds Þ for MD^þs Ds <5:0 GeV=c² after all the requirements are applied.

(b) The polar angle distribution of the D^þs Ds combinations.

(c) The mass spectrum of the D^þs Ds ISR combinations after subtraction ofEc:m: in case (2). (d) TheMD^þs Ds spectrum after all the requirements are applied. Crosshatched histograms show the normalized MD^þs and MDs sideband contributions. The signal windows are shown by vertical dashed lines.

G. PAKHLOVAet al. PHYSICAL REVIEW D83,011101(R) (2011)

contributions from the combinatorial backgrounds (1–2) are shown in Figs. 1(d) and 2(d) as crosshatched histograms.

Backgrounds (3–4) are suppressed by the tight require- ment onM_recoil² ðD^ðÞþs D^ðÞs Þ. The remaining background (3) for theD^þsDs final state is estimated using a MC simu- lation of thee^þe !D^þs Ds ISRprocess. To reproduce the shape of theD^þsDs mass spectrum we use the initial measurement of theD^þs Ds mass spectrum. The remain- der of background (3) for theD^þsDs final state is estimated using a MC simulation of the e^þe!D^þsDs ISR and e^þe!D^þs Ds ISR processes. To reproduce the shape of theD^þsDs mass spectrum we use the initial measure- ment of theD^þs Ds mass spectrum and the first iteration of the D^þsDs mass spectrum. The contributions from background (3) for theD^þsDs and theD^þsDs final states are shown in Figs.1(a),1(d),2(a), and2(d)as open histo- grams. Uncertainties in these estimates are included in the systematic errors.

To estimate the contribution from background (4), we study thee^þe!D^ðÞþs D^ðÞs ⁰ISRprocesses using fully reconstructed final states. From a MC study we estimate the fraction of reconstructed events for the cases where the ⁰is not detected. After the application of the requirement onM²_recoilðD^ðÞþs D^ðÞs Þthis contribution is found to be less than 0.5% and negligibly small; uncertainties in this esti- mate are included in the systematic errors.

The contribution from background (5), in which an energetic ⁰ is misidentified as the ISR candidate, is determined from the data using fully reconstructed e^þe!D^ðÞþs D^ðÞs ⁰ events. Only three events with MD^þ_sD_s <5:0 GeV=c² and M_D^þ_sDs⁰Ec:m:>0:5 GeV are found in the data. Assuming a uniform⁰ polar angle distribution, this background contribution in the jcosðD^þ_sD_sÞj>0:9signal subsample (case 1) is3 events= 9⁰0:6events in the wholeM_D^þ_sDs mass range, where ⁰is the⁰reconstruction efficiency. For theD^þsDs and the D^þs Ds final states the expected backgrounds are 0:6 events and 0 events in the whole MD^þ_sD_s and MD^þs Ds mass ranges. The probability of⁰ !misiden- tification due to asymmetric⁰ !decays is also esti- mated to be small. Thus the contribution from

background (5) is found to be negligibly small; uncertain- ties in these estimates are included in the systematic error.

The e^þe!D^ðÞþs D^ðÞs cross sections are extracted from the background subtractedD^ðÞþs D^ðÞs mass distribu- tions

ðe^þe!D^ðÞþs D^ðÞs Þ ¼ dN=dm

totdL=dm; (2) wheremM_D^ðÞþ

s D^ðÞs ,dN=dmis the obtained mass spec- trum, and tot is the total efficiency [16]. The factor dL=dmis the differential ISR luminosity:

dL=dm¼ x

ð22xþx²Þln1þC 1Cx²C

2mL

Ec:m:2; (3) where x¼1m²=E²_c:m:, L is the total integrated lumi- nosity, and C¼cos₀, where₀ denotes the polar angle range for _ISR in the e^þe c:m: frame (₀< _ISR<

1800). The total efficiencies determined by the MC simulation grow quadratically with energy from 0.015%, 0.010%, 0.005% near threshold to 0.045%, 0.025%, 0.011% at 5:0 GeV=c² for the D^þsDs, D^þsDs , and the D^þ_s D_s final states, respectively. The resulting e^þe! D^ðÞþs D^ðÞs exclusive cross sections averaged over the bin width are shown in Fig. 4. Since the bin width is much larger than the M_D^ðÞþ

s D^ðÞs resolution, which varies from 2 MeV=c² around threshold to 6 MeV=c² at M_D^ðÞþ

s D^ðÞs ¼5:0 GeV=c², no correction for resolution is applied. The next-to-leading order radiative corrections are taken into account by the dL=dm formula. The next-to- next-to-leading order corrections are included in the sys- tematics. The contribution of final state radiation is strongly suppressed [17] and is neglected in this study.

The R ratio, defined as R¼ðe^þe!hadronsÞ=

ðe^þe! ^þ Þ, whereðe^þe! ^þ Þ ¼4²= 3s, for the sum of the exclusivee^þe!D^ðÞþs D^ðÞs cross sections is shown in Fig.5.

The systematic errors for the ðe^þe!D^ðÞþs D^ðÞs Þ measurements are summarized in TableI. The systematic errors associated with the background (1–2) subtraction are estimated from the uncertainty in the scaling factors

0 0.2 0.4 0.6

3.8 4 4.2 4.4 4.6 4.8 5 0 0.5 1

4 4.2 4.4 4.6 4.8 5

σ(nb)

M(D_s⁺D_s^–), GeV/c² a)

σ(nb)

M(D_s⁺D_s^*–), GeV/c² b)

σ(nb)

M(D_s^*+D_s^*–), GeV/c² c)

0 0.2 0.4 0.6 0.8

4.2 4.4 4.6 4.8 5

FIG. 4. The cross section averaged over the bin width for (a) thee^þe!D^þsDs process, (b) thee^þe!D^þsDs þc:c:process, and (c) thee^þe!D^þs Ds process. Error bars show statistical uncertainties only. There is a common systematic uncertainty for all measurements, 11% forD^þsDs, 17% forD^þsDs , and 31% forD^þs Ds . This uncertainty is described in the text. The dotted lines show masses of thecð4040Þ,cð4160Þ, andcð4415Þstates [18].

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for the sideband subtractions. This is done using fits to the M_D^ðÞþ

s and M_D^ðÞ

s distributions in the data with different signal and background parametrizations and are found to be 3%, 7%, and 24% for the D^þsDs, D^þsDs , and the D^þs Ds final states, respectively.

Uncertainties in the contribution from background (3) are estimated to be 2% for the D^þsDs final state and smaller than 1% for theD^þsDs final state. Uncertainties in the backgrounds (4–5) are estimated conservatively to be smaller than 1% of the signal for all final states. The systematic errors ascribed to the cross section calculation include an error on the differential ISR luminosity (2%) and statistical errors of the MC simulation for the total efficiency calculations. In the case of the D^þ_sD_s state there is an additional uncertainty due to the unknown helicity distribution, estimated following a procedure similar to that used in Ref. [3]. Another source of systematic error comes from the uncertainties in track and photon reconstruction efficiencies (1% per track, 1.5% per photon, and 7% per soft photon). Other con- tributions include the uncertainty in the identification efficiency and the absoluteD^þs and D^þs branching frac- tions [18]. The total systematic uncertainties are 11%, 17%, and 31% for theD^þsDs,D^þsDs , and theD^þs Ds

final states, respectively.

In summary, we report the measurement of thee^þe ! D^ðÞþs D^ðÞs exclusive cross sections over the center-of- mass energy range from the D^ðÞþs D^ðÞs thresholds to 5.0 GeV. A clear peak at threshold around the cð4040Þ mass is seen in thee^þe!D^þ_sD_s cross section. In the e^þe!D^þ_sD_s cross section two peaks are evident around thecð4160Þand the cð4415Þmasses. The limited statistics do not reveal any structures in the e^þe ! D^þs Ds cross section. The obtained R ratio for the sum ofe^þe !D^ðÞþs D^ðÞs cross sections has a rich structure including peaks around the cð4040Þ, cð4160Þ, and cð4415Þmasses. Both thee^þe!D^þsDs cross section and the R ratio exhibit an obvious dip near the Yð4260Þ mass, similar to what is seen ine^þe !DD and in the total cross section for charm production. The obtained

cross sections are consistent within errors with those from BABAR [10]. The CLEO exclusive cross sections [9] are not radiatively corrected and, therefore, cannot be directly compared to the results reported here.

In this study we do not perform a fit to the obtained e^þe!D^ðÞþs D^ðÞs cross sections. The numerous open- charm thresholds in this region complicate the cross sec- tions’ behavior and coupled-channel modifications to the description of any particular final state require one to take into account all other final states contributing to the total cross section for charm production.

We thank the KEKB group for the excellent operation of the accelerator, the KEK cryogenics group for the efficient operation of the solenoid, and the KEK computer group and the National Institute of Informatics for valuable computing and SINET3 network support. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology (MEXT) of Japan, the Japan Society for the Promotion of Science (JSPS), and the Tau-Lepton Physics Research Center of Nagoya University; the Australian Research Council and the Australian Department of Industry, Innovation, Science, and Research; the National Natural Science Foundation of China under Contracts No. 10575109, No. 10775142, No. 10875115, and No. 10825524; the Ministry of Education, Youth, and Sports of the Czech Republic under Contracts No. LA10033 and No. MSM0021620859; the Department of Science and Technology of India; the BK21 and WCU program of the Ministry of Education, Science, and Technology, National Research Foundation of Korea, and NSDC of the Korea Institute of Science and Technology Information; the Polish Ministry of Science and Higher Education; the Ministry of Education and Science of the Russian Federation and the Russian Federal Agency for Atomic Energy; the Slovenian Research Agency; the Swiss National Science Foundation; the National Science Council and the Ministry of Education of Taiwan; and the U.S. Department of Energy. This work is supported by a Grant-in-Aid from MEXT for Science Research in a Priority Area (‘‘New Development of Flavor Physics’’), and from JSPS for Creative Scientific Research (‘‘Evolution of Tau-lepton Physics’’).

GeV/c²

R

M(D_s^(*)+D_s^(*)–) 0

0.1 0.2 0.3

3.8 4 4.2 4.4 4.6 4.8 5

FIG. 5. The R ratio for the sum of the D^þsDs,D^þsDs , and D^þs Ds final states. The vertical dotted lines show the masses of thecð4040Þ,cð4160Þ, andcð4415Þstates [18]. Error bars show statistical uncertainties only.

TABLE I. Contributions to the systematic error on the cross sections.

Source D^þsDs D^þsDs D^þs Ds

Background subtraction 4% 7% 24%

Cross section calculation 7% 11% 12%

BðD^ðÞs Þ 5% 5% 5%

Reconstruction 6% 10% 16%

Kaon identification 2% 2% 2%

Total 11% 17% 31%

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