Observation of B_s0->D_s*- pi+, B_s0->D_s(*)- rho+ Decays and Measurement of B_s0->D_s*- rho+ Polarization
KKEK Preprint 2010-5BELLE Preprint 2010-7
Observation of B s → D ∗− s π + , B s → D ( ∗ ) − s ρ + Decaysand Measurement of B s → D ∗− s ρ + Polarization
R. Louvot, O. Schneider, T. Aushev,
19, 12
K. Arinstein,
1, 33
A. M. Bakich, V. Balagura, E. Barberio, A. Bay, K. Belous, M. Bischofberger, A. Bondar,
1, 33
A. Bozek, M. Braˇcko,
21, 13
T. E. Browder, P. Chang, Y. Chao, A. Chen, K.-F. Chen, P. Chen, B. G. Cheon, C.-C. Chiang, I.-S. Cho, Y. Choi, M. Danilov, M. Dash, A. Drutskoy, S. Eidelman,
1, 33
P. Goldenzweig, H. Ha, J. Haba, T. Hara, Y. Horii, Y. Hoshi, W.-S. Hou, Y. B. Hsiung, H. J. Hyun, T. Iijima, K. Inami, R. Itoh, M. Iwabuchi, M. Iwasaki, Y. Iwasaki, N. J. Joshi, D. H. Kah, J. H. Kang, P. Kapusta, N. Katayama, T. Kawasaki, C. Kiesling, H. J. Kim, H. O. Kim, J. H. Kim, M. J. Kim, Y. J. Kim, K. Kinoshita, B. R. Ko, P. Kodyˇs, S. Korpar,
21, 13
P. Kriˇzan,
20, 13
P. Krokovny, T. Kumita, Y.-J. Kwon, S.-H. Kyeong, J. S. Lange, M. J. Lee, S.-H. Lee, J. Li, C. Liu, A. Matyja, S. McOnie, K. Miyabayashi, H. Miyata, Y. Miyazaki, G. B. Mohanty, M. Nakao, H. Nakazawa, S. Nishida, K. Nishimura, O. Nitoh, T. Ohshima, S. Okuno, S. L. Olsen,
37, 7
P. Pakhlov, G. Pakhlova, H. Palka, H. Park, H. K. Park, R. Pestotnik, M. Petriˇc, L. E. Piilonen, A. Poluektov,
1, 33
M. Prim, M. R¨ohrken, S. Ryu, H. Sahoo, Y. Sakai, C. Schwanda, A. J. Schwartz, K. Senyo, M. E. Sevior, M. Shapkin, V. Shebalin,
1, 33
C. P. Shen, J.-G. Shiu, J. B. Singh, P. Smerkol, A. Sokolov, S. Staniˇc, M. Stariˇc, T. Sumiyoshi, G. N. Taylor, Y. Teramoto, K. Trabelsi, S. Uehara, Y. Unno, S. Uno, G. Varner, K. E. Varvell, K. Vervink, C. H. Wang, M.-Z. Wang, P. Wang, J. Wicht, E. Won, B. D. Yabsley, Y. Yamashita, Z. P. Zhang, T. Zivko, and O. Zyukova
1, 33 (Belle Collaboration) Budker Institute of Nuclear Physics, Novosibirsk Faculty of Mathematics and Physics, Charles University, Prague University of Cincinnati, Cincinnati, Ohio 45221 Justus-Liebig-Universit¨at Gießen, Gießen The Graduate University for Advanced Studies, Hayama Hanyang University, Seoul University of Hawaii, Honolulu, Hawaii 96822 High Energy Accelerator Research Organization (KEK), Tsukuba Institute of High Energy Physics, Chinese Academy of Sciences, Beijing Institute of High Energy Physics, Vienna Institute of High Energy Physics, Protvino Institute for Theoretical and Experimental Physics, Moscow J. Stefan Institute, Ljubljana Kanagawa University, Yokohama Institut f¨ur Experimentelle Kernphysik, Karlsruher Institut f¨ur Technologie, Karlsruhe Korea Institute of Science and Technology Information, Daejeon Korea University, Seoul Kyungpook National University, Taegu ´Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana University of Maribor, Maribor Max-Planck-Institut f¨ur Physik, M¨unchen University of Melbourne, School of Physics, Victoria 3010 Nagoya University, Nagoya Nara Women’s University, Nara National Central University, Chung-li National United University, Miao Li Department of Physics, National Taiwan University, Taipei H. Niewodniczanski Institute of Nuclear Physics, Krakow Nippon Dental University, Niigata Niigata University, Niigata University of Nova Gorica, Nova Gorica Novosibirsk State University, Novosibirsk Osaka City University, Osaka Panjab University, Chandigarh University of Science and Technology of China, Hefei Seoul National University, Seoul Sungkyunkwan University, Suwon School of Physics, University of Sydney, NSW 2006 a r X i v : . [ h e p - e x ] M a r Tata Institute of Fundamental Research, Mumbai Tohoku Gakuin University, Tagajo Tohoku University, Sendai Department of Physics, University of Tokyo, Tokyo Tokyo Metropolitan University, Tokyo Tokyo University of Agriculture and Technology, Tokyo IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 Yonsei University, Seoul (Dated: October 27, 2018)First observations of the B s → D ∗− s π + , B s → D − s ρ + and B s → D ∗− s ρ + decays are reportedtogether with measurements of their branching fractions: B ( B s → D ∗− s π + ) = (2 . +0 . − . (stat . ) ± . . ) ± . f s )) × − , B ( B s → D − s ρ + ) = (8 . +1 . − . (stat . ) ± . . ) ± . f s )) × − and B ( B s → D ∗− s ρ + ) = (11 . +2 . − . (stat . ) ± . . ) ± . f s )) × − ( f s = N B ( ∗ ) s ¯ B ( ∗ ) s /N b ¯ b ). Fromhelicity-angle distributions, we measured the longitudinal polarization fraction in B s → D ∗− s ρ + de-cays to be f L ( B s → D ∗− s ρ + ) = 1 . +0 . − . (stat . ) +0 . − . (syst . ). These results are based on a 23.6 fb − data sample collected at the Υ(5 S ) resonance with the Belle detector at the KEKB e + e − collider. PACS numbers: 12.39.Hg, 12.39.St, 13.25.Gv, 13.25.Hw, 13.88.+e, 14.40.Nd
The measurement of exclusive B s → D ( ∗ ) − s h + [1]( h + = π + or ρ + ) decays is an important milestone in thestudy of the poorly understood decay processes of the B s meson. In Refs. [2–5] Belle confirmed the large po-tential of B factories for B s investigations due to the lowmultiplicities of charged and neutral particles and highreconstruction efficiencies. We have now observed threenew exclusive B s modes with relatively large branchingfractions and neutral particles such as photons or π ’sin their final states. The leading amplitude for the four B s → D ( ∗ ) − s π + and B s → D ( ∗ ) − s ρ + modes is a b → c tree diagram of order λ (in the Wolfenstein parameter-ization [6] of the CKM quark-mixing matrix [7]) with aspectator s quark. The study of B s decays provides use-ful tests of the heavy-quark theories that predict, basedon an SU (3) symmetry, similarities between B s -mesondecay modes and their corresponding B -meson counter-parts. These include the unitarized quark model [8], theheavy quark effective theory (HQET) [9–12], and a morerecent approach based on chiral symmetry [13]. Our B s branching fraction results can be used to normalize mea-surements of B s decays made at hadron collider experi-ments, where the number of B s mesons produced has asubstantial systematic uncertainty.The decay B s → D ∗− s h + is mediated by the same treediagram as B → D ∗− h + , but with a spectator s quark.The contribution of the strongly suppressed W -exchangediagram is expected to be negligibly small. Moreover,the helicity amplitudes in B → V V decays can be usedto test the factorization hypothesis [12, 14]. The relativestrengths of the longitudinal and transverse states canbe measured with an angular analysis of the decay prod-ucts. In the helicity basis, the expected B s → D ∗− s ρ + differential decay width isd Γ( B s → D ∗− s ρ + )d cos θ D ∗− s d cos θ ρ + ∝ f L sin θ D ∗− s cos θ ρ + + (1)(1 − f L )(1 + cos θ D ∗− s ) sin θ ρ + , where f L = | H | / (cid:80) λ | H λ | is the longitudinal polariza-tion fraction, H λ ( λ = ± ,
0) are the helicity amplitudes,and θ D ∗− s ( θ ρ + ) is the helicity angle of the D ∗− s ( ρ + ) de-fined as the supplement of the angle between the B s andthe D − s ( π + ) momenta in the D ∗− s ( ρ + ) frame.Here we report measurements performed withfully reconstructed B s → D ∗− s π + , B s → D − s ρ + and B s → D ∗− s ρ + decays in a data set corresponding to anintegrated luminosity of L int = (23 . ± .
3) fb − collectedwith the Belle detector at the KEKB asymmetric-energy(3.6 GeV on 8.2 GeV) e + e − collider [15] operated at theΥ(5 S ) resonance ( √ s = 10867 . ± . b ¯ b cross section at the Υ(5 S ) energy has been measuredto be σ Υ(5 S ) b ¯ b = (0 . ± . B s pro-duction modes are kinematically allowed at the Υ(5 S ): B ∗ s ¯ B ∗ s , B ∗ s ¯ B s + B s ¯ B ∗ s , and B s ¯ B s . The B ∗ s decays to B s , emitting a photon with energy E γ ∼
50 MeV. Thefraction of b ¯ b events containing a B ( ∗ ) s ¯ B ( ∗ ) s pair has beenmeasured to be f s = N B ( ∗ ) s ¯ B ( ∗ ) s /N b ¯ b = (19 . ± . B ( ∗ ) s ¯ B ( ∗ ) s events containing a B ∗ s ¯ B ∗ s pair ispredominant and has been measured with B s → D − s π + events to be f B ∗ s ¯ B ∗ s = (90 . +3 . − . ± . B s mesons produced in the dominant B ∗ s ¯ B ∗ s produc-tion mode is thus N B s = 2 × L int × σ Υ(5 S ) b ¯ b × f s × f B ∗ s ¯ B ∗ s =(2 . ± . × .The Belle detector is a large-solid-angle magnetic spec-trometer that consists of a silicon vertex detector, a cen-tral drift chamber (CDC), an array of aerogel thresholdCherenkov counters (ACC), a barrel-like arrangement oftime-of-flight scintillation counters (TOF), and an elec-tromagnetic calorimeter comprised of CsI(Tl) crystals(ECL) located inside a superconducting solenoid coil thatprovides a 1.5 T magnetic field. An iron flux-return lo-cated outside of the coil is instrumented to detect K L and to identify muons. The detector is described in de-tail elsewhere [18].Reconstructed charged tracks are required to have amaximum impact parameter with respect to the nom-inal interaction point of 0.5 cm in the radial directionand 3 cm in the beam-axis direction. A likelihood ra-tio R K/π = L K / ( L π + L K ) is constructed using ACC,TOF and CDC (ionization energy loss) measurements.A track is identified as a charged pion if R K/π < . ◦ to 150 ◦ that arenot associated with a charged track and that have anenergy deposit larger than 50 MeV. A photon candidateis retained only if the ratio of the energy deposited inthe array of the central 3 × × π → γγ decay with photon pairshaving an invariant mass within ±
13 MeV /c of the π mass. A mass-constrained fit is then applied to the π candidates.Neutral kaons are reconstructed via the decay K S → π + π − with no R K/π requirements for the two charged pi-ons. The K S candidates are required to have an invariantmass within ± . /c of the K S mass. Requirementsare applied on the K S vertex displacement from the inter-action point (IP) and on the difference between the K S flight directions obtained from the K S momentum andfrom the decay vertex and IP. The criteria are describedin detail elsewhere [19]. The K ∗ ( φ , ρ + ) candidates arereconstructed via the decay K ∗ → K + π − ( φ → K + K − , ρ + → π + π ) with an invariant mass within ±
50 MeV /c ( ±
12 MeV /c , ±
100 MeV /c ) of their nominal values.Candidates for D − s are reconstructed in the three modes D − s → φπ − , D − s → K ∗ K − , and D − s → K S K − andare required to have a mass within ±
10 MeV /c of the D − s mass. The D ∗− s candidates are reconstructed via thedecay D ∗− s → D − s γ by adding a photon candidate toa D − s candidate. The D − s γ pair is required to have amass difference m ( D − s γ ) − m ( D − s ) within ±
13 MeV /c of the D ∗− s − D − s mass difference. All mass values arethose reported in Ref. [17], and the applied mass win-dows correspond to ± (3 − σ around these values; themass resolution, σ , is obtained from MC signal simula-tions.The B s → D ∗− s π + and B s → D − s ρ + candidates arereconstructed using two variables: the beam-energy-constrained mass of the B s candidate M bc = (cid:113) E ∗ b2 − (cid:126)p ∗ B s , and the energy difference ∆ E = E ∗ B s − E ∗ b ,where ( E ∗ B s , (cid:126)p ∗ B s ) is the four-momentum of the B s can-didate and E ∗ b is the beam energy, both expressed in thecenter-of-mass frame. The two angles θ D ∗− s and θ ρ + areused as additional observables for the B s → D ∗− s ρ + can-didate. We select candidates with M bc > . /c and − . < ∆ E < . e + e − → q ¯ q ( q = u, d, s, c ). In addition, peakingbackgrounds can arise from specific B s decays. Usinga MC sample of e + e − → B ( ∗ ) s ¯ B ( ∗ ) s events correspond-ing to three times the integrated luminosity, we findthat B s → D − s π + and B s → D − s ρ + events make a signifi-cant contribution to the background in the B s → D ∗− s π + analysis. However, they are well separated from the sig-nal in the ∆ E distribution. If a B s → D − s π + decay iscombined with an extra photon, the energy is larger thanthe signal; the four charged tracks of a B s → D − s ρ + eventcan be selected with an additional photon giving a B s candidate with a smaller energy. Similarly, B s → D ∗− s ρ + decays give a significant contribution to the B s → D − s ρ + analysis at lower energies. For the B s → D ∗− s ρ + anal-ysis, there is no significant peaking background. MCstudies show that, for the three modes, all the other back-ground sources (mainly B and B + events) are smoothand small enough to be well described by the same shapethat is used for the continuum. The contribution of non-resonant B s → D ( ∗ ) − s π + π decays is studied by relaxingthe ( π + π ) mass ( M ππ ) requirement and doing a two-dimensional fit in M bc and ∆ E (see below). The signal M ππ distribution is then obtained using the s Plot method[22]. The resulting M ππ spectrum shows no indicationof B s → D ( ∗ ) − s π + π decays (consistent with results for B → D ( ∗ )+ π π − [23]), and we neglect this componentin our fit.To improve signal significance, criteria for eachof the three B s modes are chosen to maximize N sig / (cid:113) N sig + N q ¯ q bkg + N peak.bkg , evaluated in the ± . σB ∗ s ¯ B ∗ s signal region in the ( M bc , ∆ E ) plane. The ex-pected continuum background, N q ¯ q bkg , is estimated us-ing MC-generated continuum events corresponding tothree times the data. The expected signal, N sig ,and peaking background, N peakbkg , are obtained assuming B ( B s → D − s π + ) = B ( B s → D ∗− s π + ) = 3 . × − [17]and B ( B s → D − s ρ + ) = B ( B s → D ∗− s ρ + ) = 7 . × − [9].The efficiencies of exclusive B s decays are determinedusing MC simulations.To suppress the continuum background, we use theratio of the second and zeroth Fox-Wolfram moments[24], R . This variable has a broad distribution be-tween zero and one for jet-like continuum events andis concentrated in the range below 0 . ∼ B s → D ∗− s π + ( B s → D − s ρ + and B s → D ∗− s ρ + ) are required to have R < . < . B s → D ∗− s π + ( B s → D − s ρ + , B s → D ∗− s ρ + ) signal.After the event selection described above, about 15%,15%, and 28% of D ∗− s π + , D − s ρ + and D ∗− s ρ + candidateevents, respectively, have multiple candidates. We selectone candidate per event according to the following crite-ria. The D + s with the mass closest to the nominal valueis preferred. The D ∗ + s formed with the preferred D + s andwith the mass difference m ( D ∗ s ) − m ( D s ) closest to thenominal value is preferred. The B s → D ∗− s π + candidatewith the preferred D ∗− s and the π + with the best R K/π is retained. The preferred ρ + is the one with the π mass(before the mass-constrained fit) closest to the nominalvalue and the π + with the best R K/π . The B s → D − s ρ + ( B s → D ∗− s ρ + ) candidate with the preferred D − s ( D ∗− s )and the preferred ρ + is retained. After this selection,in MC signal simulations, 76%, 68% and 51% (64%) ofthe selected B s → D ∗− s π + , B s → D − s ρ + and longitudi-nally (transversally) polarized B s → D ∗− s ρ + candidatesare correctly reconstructed.The B s → D ∗− s π + and B s → D − s ρ + signals are ex-tracted from a two-dimensional unbinned extended maxi-mum likelihood fit [25] in M bc and ∆ E . The three decaysof the Υ(5 S ) ( B ∗ s ¯ B ∗ s , B ∗ s ¯ B s + B s ¯ B ∗ s and B s ¯ B s ) are con-sidered. Each signal probability density function (PDF)is described with sums of Gaussian or so-called “Novosi-birsk functions” [26]; the latter function is used to de-scribe the distribution if it is asymmetrical around itscentral value. Each signal PDF is composed of two com-ponents with their respective proportions fixed, repre-senting the correctly and the incorrectly reconstructedcandidates. In a simulated signal event, a candidate iscorrectly (incorrectly) reconstructed when the selecteddecay products do (do not) match the true combination.The fractions of correctly reconstructed candidates arefixed from MC samples and their uncertainties are in-cluded in the systematic error. The M bc and ∆ E resolu-tions for B s → D ∗− s π + ( B s → D − s ρ + and B s → D ∗− s ρ + )are calibrated by a multiplying factor measured with the B s → D − s π + [5] ( B → D ∗− ρ + ) signal. The mean val-ues of M bc and ∆ E for the three B s production modes (6parameters) are related to two floating parameters corre-sponding to the B s and B ∗ s meson masses [27]. The peak-ing background PDFs are analytically defined and fixedfrom specific MC samples. The continuum (together withpossible B + and B background) is modeled with an AR-GUS function [28] for M bc and a linear function for ∆ E .The endpoint of the ARGUS function is fixed to the beamenergy, while the two other parameters are left free. Allthe yields can float. TABLE I: Total efficiencies ( ε ), signal yields ( N S ) with sta-tistical errors, and significance ( S ) including systematic un-certainties, for the three measured modes.Mode Prod. mode ε (%) N S SB s → D ∗− s π + B ∗ s ¯ B ∗ s .
13 53 . +10 . − . . σB ∗ s ¯ B s + B s ¯ B ∗ s – − . +4 . − . – B s ¯ B s – 2 . +3 . − . – B s → D − s ρ + B ∗ s ¯ B ∗ s .
40 92 . +14 . − . . σB ∗ s ¯ B s + B s ¯ B ∗ s – − . +5 . − . – B s ¯ B s – − . +5 . − . – B s → D ∗− s ρ + B ∗ s ¯ B ∗ s – 77 . +14 . − . . σ Longitudinal component 2 .
66 81 . +16 . − . –Transverse component 2 . − . +8 . − . – For the B s → D ∗− s ρ + candidates, we perform a four-dimensional fit using the two observables cos θ D ∗− s andcos θ ρ + in addition to M bc and ∆ E . Only the main B s production mode is considered ( B ∗ s ¯ B ∗ s ), and three compo-nents are used in the likelihood: the transverse and longi-tudinal signals, and the background. We define the PDFfor M bc and ∆ E in the same way as described above,while the angular distributions are analytically describedwith polynomials of order up to five. The shape param-eters are floated for the background PDF but are fixedfor the two signal PDFs.The fitted signal yields are listed in Table I, whileFigs. 1 and 2 show the observed distributions in the B ∗ s ¯ B ∗ s signal region with the projections of the fit result. Thesignificance is defined by S = (cid:112) L max / L ), where L max ( L ) is the value at the maximum (with the cor-responding yield set to zero) of the likelihood functionconvolved with a Gaussian distribution that representsthe systematic errors of the yield. The linearity of thefloating parameters in the region near the results hasbeen extensively checked with MC simulations, as wellas the statistical uncertainty of f L ( B s → D ∗− s ρ + ), whichlies near the limit of the physically allowed range (0 − S ) → B ∗ s ¯ B ∗ s mode is con-firmed. For better precision, we therefore extract thebranching fractions (BF) using only the yields in thismode. Table II shows the values obtained with the re-lations B = N S / ( N B s × ε ), for the B s → D ∗− s π + and B s → D − s ρ + modes. The values for B ( B s → D ∗− s ρ + )and f L = 1 . +0 . − . (stat . ) +0 . − . (syst . ) are obtained byfloating these two parameters in a fit where the lon-gitudinal (transverse) yield is replaced by the relation N B s × B × f L × ε L ( N B s × B × (1 − f L ) × ε T ), with N B s , ε T and ε L being fixed. Since the transverse yield fluctu-ated to a negative central value, f L >
1. The commonsystematic uncertainties on the BF are due to the errorson the integrated luminosity (1.3%), σ Υ(5 S ) b ¯ b (4.6%), f s (15.0%), f B ∗ s ¯ B ∗ s (4.3%), the D − s BF (6.4%), the R cut FIG. 1: Left (right): M bc (∆ E ) distributions for the B s → D ∗− s π + (top) and B s → D − s ρ + (bottom) candidateswith ∆ E ( M bc ) restricted to the ± . σ B ∗ s ¯ B ∗ s signal region.The blue solid curve is the total PDF, while the green (black)dotted curve is the peaking (continuum) background and thered dashed curve is the signal. -0.8 -0.4 0 0.4 0.8 -0.8 -0.4 0 0.4 0.8 FIG. 2: Distributions for the B s → D ∗− s ρ + candidates. Top: M bc and ∆ E distributions, as in Fig. 1. Bottom: helicitydistributions of the D ∗− s (left) and ρ + (right) with M bc and∆ E restricted to the B ∗ s ¯ B ∗ s kinematic region. The compo-nents of the total PDF (blue solid line) are shown separately:the black-dotted curve is the background and the two red-dashed curve are the signal. The large (small) signal shapecorresponds to the longitudinal (transverse) component. (2.0%), the tracking efficiency (4.0%) and the charged-particle identification (5.4%). In addition, uncertaintiesdue to the MC statistics (1.6%, 2.3%, 1.5%), the neutral-particle identification (8.8%, 5.4%, 8.8%) and the PDFshapes (4.6%, 4.7%, 4.3%) depend on the ( B s → D ∗− s π + , B s → D − s ρ + , B s → D ∗− s ρ + ) mode. The systematic er-rors on f L are due to the uncertainties in PDF shapes.Our values for the BF are in good agreement with pre-dictions based on HQET and the factorization approxi-mation [11]. The large value of f L ( B s → D ∗− s ρ + ) is con-sistent with the value measured for B → D ∗− ρ decays[29] and with the predictions of Refs. [9, 30]. TABLE II: Top: measured BF values with statistical, sys-tematic (without f s ) and f s uncertainties, and HQET pre-dictions from the factorization hypothesis [11]. Bottom: BFratios where several systematic uncertainties cancel out. Weuse our previous measurement of B ( B s → D − s π + ) [5].Mode B (10 − ) HQET (10 − ) B s → D ∗− s π + . +0 . − . ± . ± . . B s → D − s ρ + . +1 . − . ± . ± . . B s → D ∗− s ρ + . +2 . − . ± . ± . . B ( B s → D ∗− s π + ) / B ( B s → D − s π + ) = 0 . +0 . − . ± . B ( B s → D − s ρ + ) / B ( B s → D − s π + ) = 2 . ± . ± . B ( B s → D ∗− s ρ + ) / B ( B s → D − s π + ) = 3 . ± . ± . B ( B s → D ∗− s ρ + ) / B ( B s → D − s ρ + ) = 1 . ± . ± . In summary, we report the first observation of threeCKM-favored exclusive B s decay modes, we extract theirbranching fractions, and, for B s → D ∗− s ρ + , we measurethe longitudinal polarization fraction. Our results areconsistent with theoretical predictions based on HQET[11] and are similar to analogous B decay branchingfractions. 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