Measurement of BПBs → DsXч with Bs semileptonic tagging

Measurement of B ð B

_s

→ D

_s

X Þ with B

_s

semileptonic tagging

B. Wang,^7,45K. Kinoshita ,⁷H. Aihara,⁷⁷D. M. Asner,³T. Aushev,⁴⁹R. Ayad,⁷²V. Babu,⁸I. Badhrees,^72,34A. M. Bakich,⁷¹ P. Behera,²⁴C. Beleño,¹¹J. Bennett,⁴⁷M. Bessner,¹⁵V. Bhardwaj,²⁰T. Bilka,⁵J. Biswal,³¹A. Bobrov,^4,59G. Bonvicini,⁸⁰ A. Bozek,⁵⁶ M. Bračko,^44,31T. E. Browder,¹⁵M. Campajola,^28,51 L. Cao,³²D. Červenkov,⁵ A. Chen,⁵³K. Chilikin,⁴⁰ H. E. Cho,¹⁴K. Cho,³⁵S.-K. Choi,¹³Y. Choi,⁷⁰D. Cinabro,⁸⁰S. Cunliffe,⁸ N. Dash,²¹F. Di Capua,^28,51 S. Di Carlo,³⁸

Z. Doležal,⁵ S. Eidelman,^4,59,40 D. Epifanov,^4,59 J. E. Fast,⁶¹T. Ferber,⁸ B. G. Fulsom,⁶¹R. Garg,⁶²V. Gaur,⁷⁹ A. Garmash,^4,59 A. Giri,²³P. Goldenzweig,³²Y. Guan,⁷K. Hayasaka,⁵⁸H. Hayashii,⁵²W.-S. Hou,⁵⁵ K. Inami,⁵⁰ A. Ishikawa,¹⁶M. Iwasaki,⁶⁰Y. Iwasaki,¹⁶S. Jia,²Y. Jin,⁷⁷D. Joffe,³³K. K. Joo,⁶A. B. Kaliyar,²⁴K. H. Kang,³⁷G. Karyan,⁸

C. Kiesling,⁴⁵D. Y. Kim,⁶⁹K. T. Kim,³⁶S. H. Kim,¹⁴P. Kodyš,⁵ S. Korpar,^44,31D. Kotchetkov,¹⁵P. Križan,^41,31 R. Kroeger,⁴⁷P. Krokovny,^4,59T. Kuhr,⁴²A. Kuzmin,^4,59Y.-J. Kwon,⁸²J. S. Lange,¹⁰I. S. Lee,¹⁴J. Y. Lee,⁶⁷S. C. Lee,³⁷ L. K. Li,²⁵Y. B. Li,⁶³L. Li Gioi,⁴⁵J. Libby,²⁴K. Lieret,⁴²D. Liventsev,^79,16T. Luo,⁹J. MacNaughton,⁴⁸C. MacQueen,⁴⁶ M. Masuda,⁷⁶T. Matsuda,⁴⁸D. Matvienko,^4,59,40M. Merola,^28,51 K. Miyabayashi,⁵²R. Mizuk,^40,49G. B. Mohanty,⁷³

R. Mussa,²⁹M. Nakao,^16,12K. J. Nath,²² M. Nayak,^80,16N. K. Nisar,⁶⁴S. Nishida,^16,12K. Nishimura,¹⁵S. Ogawa,⁷⁴ H. Ono,^57,58 Y. Onuki,⁷⁷G. Pakhlova,^40,49B. Pal,³ T. Pang,⁶⁴ S. Pardi,²⁸H. Park,³⁷S.-H. Park,⁸²T. K. Pedlar,⁴³ R. Pestotnik,³¹L. E. Piilonen,⁷⁹V. Popov,^40,49E. Prencipe,¹⁸M. Prim,³²M. Ritter,⁴²A. Rostomyan,⁸ G. Russo,⁵¹ S. Sandilya,⁷ L. Santelj,¹⁶T. Sanuki,⁷⁵V. Savinov,⁶⁴O. Schneider,³⁹ G. Schnell,^1,19C. Schwanda,²⁶A. J. Schwartz,⁷ Y. Seino,⁵⁸K. Senyo,⁸¹M. E. Sevior,⁴⁶V. Shebalin,¹⁵J.-G. Shiu,⁵⁵A. Sokolov,²⁷E. Solovieva,⁴⁰M. Starič,³¹J. F. Strube,⁶¹

T. Sumiyoshi,⁷⁸M. Takizawa,^68,17,65K. Tanida,³⁰F. Tenchini,⁸ T. Uglov,^40,49S. Uno,^16,12 Y. Usov,^4,59R. Van Tonder,³² G. Varner,¹⁵A. Vinokurova,^4,59E. Waheed,⁴⁶C. H. Wang,⁵⁴M.-Z. Wang,⁵⁵P. Wang,²⁵O. Werbycka,⁵⁶E. Won,³⁶

S. B. Yang,³⁶H. Ye,⁸ Y. Yusa,⁵⁸ Z. P. Zhang,⁶⁶V. Zhilich,^4,59V. Zhukova,⁴⁰and V. Zhulanov^4,59

(Belle Collaboration)

1University of the Basque Country UPV/EHU, 48080 Bilbao

2Beihang University, Beijing 100191

3Brookhaven National Laboratory, Upton, New York 11973

4Budker Institute of Nuclear Physics SB RAS, Novosibirsk 630090

5Faculty of Mathematics and Physics, Charles University, 121 16 Prague

6Chonnam National University, Kwangju 660-701

7University of Cincinnati, Cincinnati, Ohio 45221

8Deutsches Elektronen–Synchrotron, 22607 Hamburg

9Key Laboratory of Nuclear Physics and Ion-beam Application (MOE) and Institute of Modern Physics, Fudan University, Shanghai 200443

10Justus-Liebig-Universität Gießen, 35392 Gießen

11II. Physikalisches Institut, Georg-August-Universität Göttingen, 37073 Göttingen

12SOKENDAI (The Graduate University for Advanced Studies), Hayama 240-0193

13Gyeongsang National University, Chinju 660-701

14Hanyang University, Seoul 133-791

15University of Hawaii, Honolulu, Hawaii 96822

16High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

17J-PARC Branch, KEK Theory Center, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801

18Forschungszentrum Jülich, 52425 Jülich

19IKERBASQUE, Basque Foundation for Science, 48013 Bilbao

20Indian Institute of Science Education and Research Mohali, SAS Nagar, 140306

21Indian Institute of Technology Bhubaneswar, Satya Nagar 751007

22Indian Institute of Technology Guwahati, Assam 781039

23Indian Institute of Technology Hyderabad, Telangana 502285

24Indian Institute of Technology Madras, Chennai 600036

25Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049

26Institute of High Energy Physics, Vienna 1050

27Institute for High Energy Physics, Protvino 142281

28INFN—Sezione di Napoli, 80126 Napoli

29INFN—Sezione di Torino, 10125 Torino

30Advanced Science Research Center, Japan Atomic Energy Agency, Naka 319-1195

31J. Stefan Institute, 1000 Ljubljana

32Institut für Experimentelle Teilchenphysik, Karlsruher Institut für Technologie, 76131 Karlsruhe

33Kennesaw State University, Kennesaw, Georgia 30144

34King Abdulaziz City for Science and Technology, Riyadh 11442

35Korea Institute of Science and Technology Information, Daejeon 305-806

36Korea University, Seoul 136-713

37Kyungpook National University, Daegu 702-701

38LAL, Univ. Paris-Sud, CNRS/IN2P3, Universit´e Paris-Saclay, Orsay

39École Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne 1015

40P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991

41Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana

42Ludwig Maximilians University, 80539 Munich

43Luther College, Decorah, Iowa 52101

44University of Maribor, 2000 Maribor

45Max-Planck-Institut für Physik, 80805 München

46School of Physics, University of Melbourne, Victoria 3010

47University of Mississippi, University, Mississippi 38677

48University of Miyazaki, Miyazaki 889-2192

49Moscow Institute of Physics and Technology, Moscow Region 141700

50Graduate School of Science, Nagoya University, Nagoya 464-8602

51Universit `a di Napoli Federico II, 80055 Napoli

52Nara Women’s University, Nara 630-8506

53National Central University, Chung-li 32054

54National United University, Miao Li 36003

55Department of Physics, National Taiwan University, Taipei 10617

56H. Niewodniczanski Institute of Nuclear Physics, Krakow 31-342

57Nippon Dental University, Niigata 951-8580

58Niigata University, Niigata 950-2181

59Novosibirsk State University, Novosibirsk 630090

60Osaka City University, Osaka 558-8585

61Pacific Northwest National Laboratory, Richland, Washington 99352

62Panjab University, Chandigarh 160014

63Peking University, Beijing 100871

64University of Pittsburgh, Pittsburgh, Pennsylvania 15260

65Theoretical Research Division, Nishina Center, RIKEN, Saitama 351-0198

66University of Science and Technology of China, Hefei 230026

67Seoul National University, Seoul 151-742

68Showa Pharmaceutical University, Tokyo 194-8543

69Soongsil University, Seoul 156-743

70Sungkyunkwan University, Suwon 440-746

71School of Physics, University of Sydney, New South Wales 2006

72Department of Physics, Faculty of Science, University of Tabuk, Tabuk 71451

73Tata Institute of Fundamental Research, Mumbai 400005

74Toho University, Funabashi 274-8510

75Department of Physics, Tohoku University, Sendai 980-8578

76Earthquake Research Institute, University of Tokyo, Tokyo 113-0032

77Department of Physics, University of Tokyo, Tokyo 113-0033

78Tokyo Metropolitan University, Tokyo 192-0397

79Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

80Wayne State University, Detroit, Michigan 48202

81Yamagata University, Yamagata 990-8560

82Yonsei University, Seoul 120-749

(Received 21 June 2021; revised 3 December 2021; accepted 17 December 2021; published 11 January 2022)

Published by the American Physical Society under the terms of theCreative Commons Attribution 4.0 Internationallicense. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

We report the first direct measurement of the inclusive branching fractionBðBs→DsXÞviaBstagging ine^þe⁻→ϒð5SÞevents. Tagging is accomplished through a partial reconstruction of semileptonic decays Bs→DsXlν, where X denotes unreconstructed additional hadrons or photons andl is an electron or muon. With 121.4fb⁻¹ of data collected at the ϒð5SÞ resonance by the Belle detector at the KEKB asymmetric-energy e^þe⁻ collider, we obtain BðBs→DsXÞ ¼ ð60.25.82.3Þ%, where the first uncertainty is statistical and the second is systematic.

DOI:10.1103/PhysRevD.105.012004

The study of Bs-meson properties at the ϒð5SÞ reso- nance may provide important insights into the CKM matrix and hadronic structure, as well as sensitivity to new physics phenomena[1–3]. The branching fraction for the inclusive decay B_s→DsX plays an important role in the determi- nation of theBsproduction rate in ϒð5SÞevents[4]. This rate, usually expressed as the fractionfsofbb¯ events at the ϒð5SÞ, is necessary for measuring absolute rates and branching fractions. Two experiments at LEP, ALEPH [5], and OPAL [6], measured the product branching fraction Bðb¯ →B⁰sÞ·BðB⁰s→DsXÞ. The branching frac- tionBðB⁰s →DsXÞwas evaluated using a model-dependent value of Bðb¯ →B⁰sÞ and was subject to large statistical and theory uncertainties. Belle measured the branching fractions of ϒð5SÞ→DsX and ϒð5SÞ→D⁰X [7] with 1.86fb⁻¹of data collected at theϒð5SÞenergy. These are related to the inclusive B_s branching fractions toD_s and D⁰=D¯⁰ by the following relations,

Bðϒð5SÞ→D_xXÞ=2¼f_s·BðB_s→D_xXÞ

þfq·BðB→DxXÞ; ð1Þ whereDxisDsorD⁰=D¯⁰,fsis the fraction ofϒð5SÞevents containingBs-meson pairs, andfqis the fraction contain- ing charged or neutralBpairs. Using the measured value of Bðϒð5SÞ→D⁰XÞ [7], and assuming fq¼1−fs and BðB_s→D⁰Xþc:c:Þ ¼ ð87Þ% [8], which was esti- mated based on phenomenological arguments, Belle found fs¼ ð18.13.67.5Þ% [7]. This input, with the mea- suredBðϒð5SÞ→DsXÞ[7], was used to evaluateBðBs→ DsXÞ ¼ ð911841Þ%[7]. The current world average, ð9325Þ%[9], is based on measurements made with the methods described above, which rely on model-dependent assumptions.

In this paper, we present the first direct measurement of BðB_s→D_sXÞ using a B_s semileptonic tagging method with ϒð5SÞ events. Throughout this paper, the inclusive branching fraction BðBs→DsXÞ is defined as the mean number of Ds-mesons per Bs decay.

We use a data sample of121.4fb⁻¹, collected with the Belle detector[10]at the KEKB asymmetric-energye^þe⁻ collider[11]operating near theϒð5SÞresonance. The Belle detector is a general-purpose large-solid-angle spectrom- eter consisting of a silicon vertex detector (SVD), a central

drift chamber (CDC), an array of aerogel threshold Cherenkov counters (ACC), a barrel-like arrangement of time-of-flight scintillation counters (TOF), and an electromagnetic calorimeter (ECL) located inside a super- conducting solenoid coil that provides a 1.5 T magnetic field. Outside the coil, an iron flux-return yoke is instru- mented to detectK⁰_L-mesons and to identify muons (KLM).

A detailed description of the detector can be found in Ref.[10].

All charged tracks, except those from K⁰_S decay, are required to be consistent with originating from the inter- action point (IP), with the point of closest approach to the IP within 2.0 cm along the beam axis and within 0.5 cm in the plane transverse to the beam. Additionally, all tracks must have, within the SVD, at least one associated hit in the plane transverse to the beam and two hits along the beam axis. To suppress the continuum background frome^þe⁻ → q¯qwithq¼u,d,s, orc, we require that the variable R2, the ratio of second- to zeroth-order Fox-Wolfram moments [12], be less than 0.4. Kaon and pion hypotheses are assigned to the tracks based on likelihood, which is calculated using information from the Cherenkov light yield in the ACC, the time-of-flight information of the TOF, and the specific ionization (dE=dx) in the CDC. Charged kaon (pion) candidates are required to have a kaon/pion likelihood ratio LK=ðLKþLπÞ>0.6ð<0.6Þ. The angle between each lepton and the positron beam is required to be between 18° and 150° for electrons and between 25° and 145° for muons. Selected electrons and muons must have a minimum momentum of1.0GeV=cin thee^þe⁻center-of- mass (CM) frame. An electron/pion likelihood ratio (Le) is calculated based on information from the CDC, ACC, and ECL. A muon/hadron likelihood ratio is calculated based on information from the KLM. Tracks with L_e>0.8 (L_μ>0.8) are included as electrons (muons) in the analysis. The efficiency for electron (muon) tracks to pass this criterion isð94.70.2Þ%ðð96.70.2Þ%Þ.

The neutral intermediate particlesϕ,K⁰_SandK⁰[13]are reconstructed from charged tracks. For ϕ→K^þK⁻ reconstruction, any pair of oppositely charged kaons with invariant mass within15MeV=c²of the ϕnominal mass [9]is considered to be aϕcandidate. TheK⁰_Scandidates are reconstructed via the decay K⁰_S→π^þπ⁻, following stan- dard criteria [14], and are further required to have an invariant mass within20MeV=c²(≈4.4σin resolution) of

the nominal mass. ForK⁰→K^þπ⁻, the candidate tracks are oppositely charged K and π, with invariant mass within50MeV=c².

Candidates for D^þ_s are reconstructed in the final states ϕπ^þ, K⁰_SK^þ, and K¯⁰K^þ. The CM momentum of the candidate is required to be in the range 0.5GeV=c–3.0GeV=c. Candidates with invariant mass in the range 1.92–2.02GeV=c² are considered. For ϕπ^þ andK¯⁰K^þ modes, a vertex fit is performed for the three tracks used to reconstruct the candidate, and theχ²of the fit output is required to be less than 100. Nearly all correctly reconstructed Ds, ð98.10.1Þ%, are found to pass this requirement. The decays D^þs →ϕðK^þK⁻Þπ^þ and D^þs → K¯⁰ðK⁻π^þÞK^þare transitions of a pseudoscalar particle to a vector and a pseudoscalar, with the vector decaying to two pseudoscalars. To suppress combinatorial background, we require jcosθhelj>0.5, where the helicity angle θhel is defined as the angle between the momentum of theD^þs and K^þ (π^þ) in the rest frame of theϕ(K¯⁰) resonance.

We tag B_s events through a “partial reconstruction” of the semileptonic decayB⁰_s →D⁻_sXl^þν, with theD⁻_s modes ϕπ⁻andK⁰_SK⁻, using a procedure similar to one applied at the ϒð4SÞ resonance [15], where a lepton (electron or muon) is paired with a charm meson to form aBcandidate.

In contrast to theϒð4SÞ, where the exclusive production of BB¯ ensures that each B-meson’s total energy is half the CM energy, ffiffiffi

ps

=2, the B_s’s in ϒð5SÞ events occur predominantly in B_sB¯_s events. In this case the energy of eachBsis well approximated as ffiffiffi

ps

=2−δE, whereδE=c² is the Bs−Bs mass difference. We useδE¼47.3 MeV.

We thus define the“missing mass squared”of the selected D⁻sl^þ candidate as

M²_miss¼ ð ffiffiffi ps

=2−δE−E_DlÞ²−ðp_DlÞ²; ð2Þ whereE_Dl andp_Dl are the energy and momentum of the Dslsystem in the CM frame. The distribution inM²missfor tagged B_s represents the undetected neutrino plus addi- tional low-momentum daughters of excited D_s, photons and pions, and is expected to peak broadly at M²_miss¼0. The thrust angle,θthrustis defined as the angle between the thrust axis[16]of the selectedD_slsystem and that of the remaining tracks in the event. To suppress continuum background, we require jcosθthrustj<0.8. In events with more than one tag candidate, we perform a combined fit on each candidate’s three-trackDsvertex, and on the vertex of the extrapolatedDstrajectory with the lepton, and select the candidate having the smallest χ².

The number of B_s tags for each D_s decay channel is found by a binned 2D maximum-likelihood fit of the distribution in M²_miss and the invariant mass of the D_s candidate,MD_s tag, to a sum of three components, according to candidate origin:

(1) Correctly tagged candidates.

(2) Incorrect tag, where a lepton from aBssemileptonic decay is paired with a realDsfrom the otherBs. This can happen ifBs mixing has occurred.

(3) Other incorrect tags: all other sources of candidates.

In addition to B^ðÞs B¯^ðÞs events, sources include u¯u, dd¯,s¯s,c¯c, andB^ðÞB¯^ðÞX events.

For each component, theM²_missdistribution is taken to be a histogram obtained via Monte Carlo (MC) simulation. For correctly reconstructed D_s, the distribution in M_{Ds tag} is represented by a sum of two Gaussians with a common mean. The widths of the Gaussians and their relative areas are obtained from MC simulation. For combinatorial Ds

background, each distribution is well-represented by a linear function. Tag decays, Bs→DsXlν, are modeled as a sum ofBs→Dslν andBs→Dslν; all semileptonic Bs decays to higher excited Ds states observed to date involve DK rather than D_s in the final state, and decays including the statesD_s0ð2317ÞandD_s1ð2460Þ, which are known to decay toD_s, have not been observed [9]. The presence of higher mass excitedD_s inD_sXlνfinal states would be manifested as a knee or bump to the right side of theM²_miss peak. The data are found to be consistent with contributions fromDs andDs only (Fig.1, top). We find N^ϕπtag ¼6473119 and N^Ktag^0SK¼4435126. The fit results forDs→ϕπ are shown in Fig.1.

After selecting aBscandidate as the tag, we reconstruct the“signal-side”Dsfrom the remaining tracks in the event.

Candidates are reconstructed in all three modes discussed earlier, and we allow none of the tracks from the selected tag candidate to be used. The rate of signalDs in tagged events is determined through a binned 3D maximum- likelihood fit in the tag-side variables,M²_miss andMD_s tag, and the invariant mass of the signal-side D_s candidate, M_{Ds sig}. Each tagþsignal candidate corresponds on the tag side to one of the three components comprising the 2D fit and on the signal side with a real or combinatorial Ds. Events containing B_s→D_sXlν and inclusive B_s→D_sX may have a correctly reconstructed tag (component 1) with a signalDsor an incorrect tag (component 2) with aDsthat is actually from the tag side. We define the first type of event as“signal”and the second as“cross-feed.”Both types are included in our fit and used to determine the rate ofBs→DsX.

For signal events, where the tag-side (signal-side) Ds

decays to channeli(j), the raw branching fraction (Braw) is found by dividing the number observed (Nsig;ij) by the total number of reconstructed tags in channel i (Ntag;i), the branching fraction for the channel j (B_j), and the reconstruction efficiency (E_ij;tag) forDs in channel j:

Braw¼ N_sig;ij

Ntag;iBjEij;tag: ð3Þ

We evaluate E_ij;tag via MC for each pair of channels (Table I).

For cross-feed events, the raw branching fraction is obtained through the relationship of their rate to that of signal events. For both signal and cross-feed, the number of events found in a data set depends on many of the same factors: number ofB_s events, branching fractions of the reconstructed D_s modes, branching fractions of Bs→DsXlν, andBs→DsX. The reason for this is clear:

the two types have a common origin, differing only in the assigning ofD_sto tag-vssignal-side. The differences stem from the selection processes and the fact that cross-feed is sourced only from the 50% of events where Bs↔B¯s

mixing has occurred. Thus, the expected ratio, Rij of observed cross-feed to signal events for each pair of D_s decay channels is the ratio of selection efficiencies times 0.5. These ratios are obtained via MC simulation. From the number of observed cross-feed (Ncf;ij) we then have

Braw ¼ Ncf;ij

Ntag;iBjEij;tagRij

: ð4Þ

A fit for Braw is performed simultaneously for the sixDstag-signal channel combinations, using the efficien- cies and efficiency ratios determined as described above.

Intermediate branching fractions are fixed to PDG values.

Our fit yieldsBraw ¼ ð58.25.8Þ%, which corresponds to a fitted total of10110signal and 364cross-feed events. Projections of the fit are shown in Fig.2. To obtain BðBs→DsXÞ, we must make a correction toBraw, due to the fact that the signal mode,Bs→DsX, is inclusive of the tagging mode,Bs→DsXlν. We defineBðBs→DsXeνÞ þ BðB_s→D_sXμνÞ≡B_Dsl, BðB_s→D_sXÞ≡B_Ds, and the respective reconstruction efficiencies ϵD_sl and ϵD_s. We take N_BsBs to be the number of B^ðÞs B¯^ðÞs events. The numbers of tags and signal are then

Ntag ¼NB_sB_sð2ϵD_slBD_sl−ðϵD_slBD_slÞ²Þ

¼N_BsBsϵ_DslB_Dslð2−ϵ_DslB_DslÞ; ð5Þ Nsig¼NBsBsð2ϵDslBDslϵDsBDs −ðϵDslBDslÞ²Þ

¼N_BsBsϵ_DslB_Dslð2ϵ_DsB_Ds −ϵ_DslB_DslÞ: ð6Þ Their ratio, corrected for efficiencies, isBraw:

Braw ¼Nsig=ϵD_s

Ntag

¼2ϵ_DsB_Ds−ϵ_DslB_Dsl ϵDsð2−ϵDslBDslÞ

¼ B_Ds −_2ϵ^ϵDsl

DsB_Dsl

1−ϵ_DslB_Dsl=2: ð7Þ Thus,

BD_s ¼Braw

1−ϵ_DslB_Dsl 2

þϵ_Dsl

2ϵD_s

BD_sl: ð8Þ To estimate ϵD_sl, we use BD_sl ¼ ð16.22.6ðsysÞÞ%[9], 2N_BsBs ¼ ð1.660.27ðsysÞÞ×10⁷ [17], Ntag ¼10908 173ðstatÞ (our measurement), where errors are indicated

)2

(GeV/c2 2

Mmiss

−10 −8 −6 −4 −2 0 2 4

)2 )2 Events / (0.15 (GeV/c

0 100 200 300 400 500 600 700

2) (GeV/c

Ds_tag

M

1.92 1.94 1.96 1.98 2

)2Events / (0.001 GeV/c

0 200 400 600 800 1000

FIG. 1. Distributions in M²miss (top) and Ds candidate mass (bottom) for tag candidates withDs→ϕπ in data (points with error bars), overlaid with fit results (cumulative): correct tags (red, solid), incorrect tags with realDs (blue, dashed), and other incorrect tags (green, dotted). In each plot, a signal band requirement is made on the quantity that is not displayed (m^PDGDs 0.015GeV=c²,jM²missj<2ðGeV=c²Þ²)).

TABLE I. Signal-side Ds reconstruction efficiencies, by tag- side and signal-sideDs decay channel.

Tag channel Signal channel Efficiency (%)

ϕπ

ϕfK^þK⁻gπ 26.10.5 K⁰_Sfπ^þπ⁻gK 38.50.6 K⁰fKπ^∓gK 24.60.5 K⁰_SK

ϕfK^þK⁻gπ 27.60.5 K⁰_Sfπ^þπ⁻gK 37.80.6 K⁰fKπ^∓gK 24.60.4

as being statistical or systematic in origin. We calculate ϵ_Ds from Table I and branching fractions from [9]. We find

ϵ_Dsl≈ Ntag

2N_BsBsB_Dsl

¼ ð4.10.1ðstatÞ 0.7ðsysÞÞ×10⁻³; ð9Þ ϵ_Ds ¼X

i

ϵ_iB_i

¼ ð1.620.03ðsysÞÞ×10⁻²: ð10Þ The first correction term is found to be negligible (less than 10⁻³), and the second is

B_Ds−Braw¼ϵ_Dsl 2ϵD_s

B_Dsl

¼ ð2.030.03ðstatÞ 0.33ðsysÞÞ×10⁻²: ð11Þ We thus find

B_Ds ¼ ð60.25.80.3Þ%: ð12Þ As a cross-check of our method, we fit for signal while floating the cross-feed component and find Braw¼ ð64.88.1Þ%, which is consistent with our result.

To confirm the 3D fitting procedure and correction to Braw, we generated ensembles of simulated data distribu- tions with varied signal content. Signal and crossfeed distributions were generated by randomly selecting from our large sample of MC-generated signal events. For background we generated distributions according to those used in the fit, with parameters fixed to the results of the fit to data. Ensembles of 200 experiments were generated for each of ten branching fractions in the range 10%–100%, in 10% increments. Each distribution was fitted according to our procedure. The resulting ensemble mean branching fractions, corrected and plotted against input branching fractions, were fitted to a line. This test was repeated for each of the six Ds mode combinations, as well as the combined set. All showed consistency with a unit slope and no systematic shifts.

Our estimates of systematic uncertainties are summa- rized in Table II. We evaluate the effects from the considered sources by varying each and taking the resulting shift observed inBrawas the uncertainty. In cases affecting the Ds mode combinations separately, the maximum excursion is taken as a conservative estimate of the uncertainty on the combined result. Because this measure- ment involves tagging, many of the systematic uncertainties associated with tagging cancel approximately in taking the ratio of tags, with and without signal. The effect from the uncertainty due to the composition and model of Bs→ D_sXlν on efficiency and on the M²_miss fitting shape is estimated by varying the relative rates ofBs→Dslνand Bs→Dslνwithin the uncertainties[9]and by varying the HQET2 parameters in the MC generator by10%. For the

“other incorrect tag”(type 3, above), theM²_missdistribution

/ GeV/c2 Ds_sig

M

1.92 1.94 1.96 1.98 2

)2 Events / (0.005 GeV/c

0 10 20 30 40 50 60

/ GeV/c2 Ds_tag

M

1.92 1.94 1.96 1.98 2

)2 Events / (0.005 GeV/c

0 10 20 30 40 50 60 70

)2

/ (GeV/c2 2

Mmiss

−10 −8 −6 −4 −2 0 2 4

)2 )2 Events / (1 (GeV/c

0 10 20 30 40 50 60 70

FIG. 2. 1D Projections of results from 3D fits, allDs modes combined, for M^sigDs (top), M^tagDs (center) and M²miss (bottom):

data (points with error bars), signal (red, dashed), cross-feed (blue, dash-dotted), background (green, dotted), and total (black, solid). For each projected variable, signal band requirements are made in the other two: M^sig_Ds; M^tag_Ds∈m^PDG_Ds 0.02GeV=c², M²miss∈½−2;2ðGeV=c²Þ².

in data from tags with “sideband” D_s candidates, jM_cand−m_Ds 40j<10MeV, is substituted in the fit.

Uncertainties due to fitting of theDsmass distributions are determined by changing the signal shape from two Gaussians to three and the background from a first-order to a second-order polynomial. We vary each ratio of signal to cross-feed efficiency in the fit by1σ. The uncertainties due to branching fractions of the reconstructedD_sdecays are estimated by varying each by1σ[9]of its value in the fitting procedure. The reconstruction efficiencies are varied by the amount of their statistical error from the MC sample.

The uncertainty due to the limited statistical power of our linearity test is estimated by varying the parameters from the linear fit by1σ. To estimate effects from our selection of a single tag candidate per event, we reanalyze the data using random selection and take the shift in the result to be the uncertainty.

The uncertainty on the tracking efficiency affects only the three signal-side tracks comprising the Ds candidate and is estimated to be 0.35% per track, thus, we take 1.1%

as the uncertainty from this source. The systematic uncer- tainty fromK−πidentification efficiencies is estimated to be 1.3%.

The fitted shape of the M²_miss distribution depends on theB_s−B_smass difference,δE=c², and its uncertainty may affect the fit in two ways: in the value used to generate the MC signal events (vs the actual value) and in the value used to calculate M²miss. For this analysis, the values are 45.9MeV=c² for MC generation and 47.3MeV=c² forM²_miss. The PDG presents two numbers,

ð46.11.5ÞMeV=c²as a world average and a PDG fit of ð48.6^þ1.8_−1.5ÞMeV=c² [9]. As M²_miss is fitted in both the numerator and denominator to obtain Braw, effects from such differences are expected to cancel, at least in part. To estimate possible systematic shifts due to these differences, we vary separately the calculation usingδE=c² and the value used in MC generation in the range 45.9–49.0MeV=c². Changing the calculation of M²_miss results in a maximum excursion in Braw of less than 0.1%. Changing the value in the MC generator results in a maximum excursion of 1.2%. We assign an uncertainty of 1.2%.

We consider possible contributions to the tag-side sample from the nonstrangeBdecayBðB→D^ðÞs KlνÞ, which is not included in our generic MC generator. We use BðB^þ → D^ðÞ−s K^þl^þνÞ ¼ ð6.11.0Þ×10⁻⁴ [9], assume that BðB⁰→D^ðÞ−s K⁰l^þνÞis the same, and multiply by a factor of two to account for both electrons and muons. Taking Bðϒð5SÞ→BBXÞ¼76%¯ , Bðϒð5SÞ→BsB¯sXÞ¼20%, and BðB_s→XlνÞ ¼9.6%[9], we estimate

Bðϒð5SÞ→BBXÞ¯ ·BðB→D^ðÞs KlνÞ

Bðϒð5SÞ→B^ðÞs B¯^ðÞs Þ·BðBs→DsXlνÞ≈0.048: ð13Þ As the shape inM²miss includes a kaon in addition to the neutrino, it is expected to peak more broadly and at a higher value than does theB_schannel. This is confirmed in studies of MC-generatedBBX¯ events containingB→D^ðÞs Klνin TABLE II. Systematic uncertainties onBraw, in %. The total is the sum in quadrature from all sources.

Channel

ϕπTag K⁰_SK Tag

Source ϕπ K⁰_SK K⁰K ϕπ K⁰_SK K⁰K Combined

Model, tag 1.5 1.1 1.5

Model, signal 0.1 0.1 0.3 0.1 0.1 0.1 0.3

Model, cross-feed 0.4 0.3 0.3 0.2 0.1 0.1 0.4

M²miss shape,MBs−MBs 1.2 1.2 1.2

M²miss background 0.1 0.2 0.1 0.5 0.2 0.3 0.5

MðDsÞsignal shape 0.2 0.2 1.2 0.1 0.1 1.0 1.2

MðDsÞbackground shape 1.0 0.6 <0.1 <0.1 0.1 0.1 1.0

Cross-feed efficiency 0.5 0.3 0.6 0.3 0.1 0.3 0.6

Reconstruction efficiency 0.4 0.2 0.4 0.2 0.1 0.2 0.4

Statistics, linearity test 0.2 0.3 0.3 0.3 0.4 0.4 0.4

B→D^ðÞs Klν <0.02 0.5 0.5

BðD_s→ϕπÞ … 1.2

BðDs→K⁰_SKÞ … 0.5

BðDs→K⁰KÞ … 1.2

Single tag selection … 1.0

Tracking … 1.1

K-π identification … 1.3

Total … 3.8

the D_s tag modes. Figure 3 illustrates the difference. We measure the effect on our MC tag fit of including such events, and estimate a contribution toBðBs→DsXlνÞ of

<0.02%(0.5%) to theDs→ϕπ(Ds→K⁰_SK) channel. We assign an overall systematic uncertainty of 0.5%. The uncertainties from the above sources are summed in quad- rature to arrive at the total fractional systematic uncertainty in Braw of 3.8%. Adding the systematic uncertainties in quadrature, we find

BðB_s→D_sXÞ ¼ ð60.25.82.3Þ%: ð14Þ The central value is lower than the theoretical expectation ð86^þ8₋₁₃Þ%[18], and≈1.3σbelow the world average,ð93 25Þ%[9]. Given the history of uncertainty on the rates and composition of charm states at higher mass inB decay, a lower value may be explained by a rate ofc¯stoDvsDsthat is higher than anticipated. The implications of a lower central value are notable. Experimentally, the value affects the derived fractionf_sofB_sevents amongϒð5SÞdecays, which impacts the absolute normalization of allBsbranch- ing fractions measured via ϒð5SÞ decays. In the earlier Belle measurements of fs [7,17], Eq. (1) was used with f_q¼1−f_s. More recently, it has been found that there is a nonzero rate to bottomonia, includingϒð1SÞ, ϒð2SÞ, ϒð3SÞ, h_bð1PÞ and h_bð2PÞ. We take the rate of events with “no open bottom” to be fnob¼ 4.9^þ5.0_−0.6%[19]. Charm is highly suppressed in these decays, so we takef_q¼1−f_s−fnob. UsingBðϒð5SÞ→D_sXÞ ¼ ð45.43.0Þ%[20]andBðB→DsXÞ ¼ ð8.30.8Þ%[9], we solve Eq.(1)forf_sand find

fs¼0.2850.032ðstatÞ 0.037ðsysÞ: ð15Þ This value is larger than the world average,fs¼0.201 0.031[9], which is evaluated assuming the model-based

estimates BðBs→DsXÞ ¼ ð9211Þ% and BðBs→ D⁰XÞ ¼ ð87Þ%[7]; the impact of introducing fnob to the calculation is minor. Our result uses the same value of Bðϒð5SÞ→DsXÞfrom whichfsis derived in[17]and thus supersedes the value presented there. It is consistent with a recent Belle measurement offsby an independent method [19]. An older Belle measurement off_sfrom semileptonic decays[21]assumed that onlyD_s1andD_s2contribute to non-strange charm,Bs→DKXlν. Given recently reported evidence of substantial contributions from nonresonant DKðXÞ[22], this value is likely an underestimate, so we do not compare it with the result reported here.

Applying Eq. (1) with BðB→D⁰=D¯⁰XÞ ¼ ð61.5 2.9Þ% [9], Bðϒð5SÞ→D⁰XÞ ¼ ð1088Þ% [9], and our result for fs, we find BðBs→D⁰XÞ ¼ ð462ðstatÞ 20ðsysÞÞ%, where the systematic uncertainties on Bðϒð5SÞ→D⁰XÞ and fnob dominate. This value is con- sistent with our finding of a lower rate ofDsfromBsdecay, as the total charm content would need to be accounted for by an increased rate of nonstrange charm. No experimental results forB_s→D⁰X are currently included in the PDG tables[9].

To summarize, we have made the first direct measure- ment of theBs→DsXinclusive branching fraction, using a Bs semileptonic tagging method at the ϒð5SÞ resonance.

We find

BðBs→DsXÞ ¼ ð60.25.8ðstatÞ 2.3ðsysÞÞ%; ð16Þ which is substantially lower than the world average but consistent within its large uncertainties. This result is used to recalculate the fractionf_sofϒð5SÞevents containingB_s,

fs¼0.2850.032ðstatÞ 0.037ðsysÞ: ð17Þ This value supersedes that reported in[17].

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 Pacific Northwest National Laboratory (PNNL) Environmental Molecular Sciences Laboratory (EMSL) computing group for strong computing support; and the National Institute of Informatics, and Science Information NETwork 5 (SINET5) for valuable 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 including grants No. DP180102629, No. DP170102389, No. DP170102204, No. DP150103061, No. FT130100303;

Austrian Federal Ministry of Education, Science and Research (FWF) and FWF Austrian Science Fund No. P 31361-N36; the National Natural Science Foundation of

)2

/ (GeV/c2 miss

M2

−10 −8 −6 −4 −2 0 2 4

)2 )2 Events / (0.3 (GeV/c

0 100 200 300 400 500 600 700

FIG. 3. The distributions inM²miss forBs→DsXlν(red) and B→DsKXlν(black), withDs→ϕπ.

China under Contracts No. 11435013, No. 11475187, No. 11521505, No. 11575017, No. 11675166, No. 11705209; Key Research Program of Frontier Sciences, Chinese Academy of Sciences (CAS), Grant No. QYZDJ-SSW-SLH011; the CAS Center for Excellence in Particle Physics (CCEPP); the Shanghai Pujiang Program under Grant No. 18PJ1401000; the Shanghai Science and Technology Committee (STCSM) under Grant No. 19ZR1403000; the Ministry of Education, Youth and Sports of the Czech Republic under Contract No. LTT17020; Horizon 2020 ERC Advanced Grant No. 884719 and ERC Starting Grant No. 947006

“InterLeptons” (European Union); the Carl Zeiss Foundation, the Deutsche Forschungsgemeinschaft, the Excellence Cluster Universe, and the VolkswagenStiftung; the Department of Atomic Energy (Project Identification No. RTI 4002) and the Department of Science and Technology of India; the Istituto Nazionale di Fisica Nucleare of Italy; National Research Foundation (NRF) of Korea Grants No. 2016R1D1A1B01010135, No. 2016R1D1A1B02012900, No. 2018R1A2B3003643,

No. 2018R1A6A1A06024970, No. 2019K1A3A7A09033840, No. 2019R1I1A3A01058933, No. 2021R1A6A1A03043957, No. 2021R1F1A1060423, No. 2021R1F1A1064008;

Radiation Science Research Institute, Foreign Large-size Research Facility Application Supporting project, the Global Science Experimental Data Hub Center of the Korea Institute of Science and Technology Information and KREONET/GLORIAD; the Polish Ministry of Science and Higher Education and the National Science Center; the Ministry of Science and Higher Education of the Russian Federation, Agreement No. 14.W03.31.0026, and the HSE University Basic Research Program, Moscow; University of Tabuk research grants No. S-1440-0321, No. S-0256- 1438, and No. S-0280-1439 (Saudi Arabia); the Slovenian Research Agency Grants No. J1-9124 and No. P1-0135;

Ikerbasque, Basque Foundation for Science, Spain; the Swiss National Science Foundation; the Ministry of Education and the Ministry of Science and Technology of Taiwan; and the United States Department of Energy and the National Science Foundation.

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