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Measurement of the ratio of branching fractions <em>B(D<sup>0</sup>→K<sup>+</sup>π<sup>−</sup>)/B(D<sup>0</sup>→K<sup>−</sup>π<sup>+</sup>)</em> using the CDF II detector

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Article

Reference

Measurement of the ratio of branching fractions B(D

0

→K

+

π

)/B(D

0

→K

π

+

) using the CDF II detector

CDF Collaboration

CAMPANELLI, Mario (Collab.), et al .

Abstract

We present a measurement of RB, the ratio of the branching fraction for the rare decay D0→K+π− to that for the Cabibbo-favored decay D0→K−π+. Charge-conjugate decays are implicitly included. A signal of 2005±104 events for the decay D0→K+π− is obtained using the CDF II detector at the Fermilab Tevatron collider. The data set corresponds to an integrated luminosity of 0.35  fb−1 produced in pp collisions at s√=1.96  TeV. Assuming no mixing, we find RB=[4.05±0.21(stat)±0.11(syst)]×10−3. This measurement is consistent with the world average, and comparable in accuracy with the best measurements from other experiments.

CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the ratio of branching fractions B(D

0

→K

+

π

)/B(D

0

→K

π

+

) using the CDF II detector. Physical Review. D , 2006, vol.

74, no. 03, p. 031109

DOI : 10.1103/PhysRevD.74.031109

Available at:

http://archive-ouverte.unige.ch/unige:38359

Disclaimer: layout of this document may differ from the published version.

1 / 1

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Measurement of the ratio of branching fractions B D

0

! K

= B D

0

! K

using the CDF II detector

A. Abulencia,23D. Acosta,17J. Adelman,13T. Affolder,10T. Akimoto,55M. G. Albrow,16D. Ambrose,16S. Amerio,43 D. Amidei,34A. Anastassov,52K. Anikeev,16A. Annovi,18J. Antos,1M. Aoki,55G. Apollinari,16J.-F. Arguin,33 T. Arisawa,57A. Artikov,14W. Ashmanskas,16A. Attal,8F. Azfar,42P. Azzi-Bacchetta,43P. Azzurri,46N. Bacchetta,43 H. Bachacou,28W. Badgett,16A. Barbaro-Galtieri,28V. E. Barnes,48B. A. Barnett,24S. Baroiant,7V. Bartsch,30G. Bauer,32

F. Bedeschi,46S. Behari,24S. Belforte,54G. Bellettini,46J. Bellinger,59A. Belloni,32E. Ben Haim,44D. Benjamin,15 A. Beretvas,16J. Beringer,28T. Berry,29A. Bhatti,50M. Binkley,16D. Bisello,43R. E. Blair,2C. Blocker,6B. Blumenfeld,24 A. Bocci,15A. Bodek,49V. Boisvert,49G. Bolla,48A. Bolshov,32D. Bortoletto,48J. Boudreau,47A. Boveia,10B. Brau,10

C. Bromberg,35E. Brubaker,13J. Budagov,14H. S. Budd,49S. Budd,23K. Burkett,16G. Busetto,43P. Bussey,20 K. L. Byrum,2S. Cabrera,15M. Campanelli,19M. Campbell,34F. Canelli,8A. Canepa,48D. Carlsmith,59R. Carosi,46 S. Carron,15M. Casarsa,54A. Castro,5P. Catastini,46D. Cauz,54M. Cavalli-Sforza,3A. Cerri,28L. Cerrito,42S. H. Chang,27 J. Chapman,34Y. C. Chen,1M. Chertok,7G. Chiarelli,46G. Chlachidze,14F. Chlebana,16I. Cho,27K. Cho,27D. Chokheli,14

J. P. Chou,21P. H. Chu,23S. H. Chuang,59K. Chung,12W. H. Chung,59Y. S. Chung,49M. Ciljak,46C. I. Ciobanu,23 M. A. Ciocci,46A. Clark,19D. Clark,6M. Coca,15G. Compostella,43M. E. Convery,50J. Conway,7B. Cooper,30 K. Copic,34M. Cordelli,18G. Cortiana,43F. Cresciolo,46A. Cruz,17C. Cuenca Almenar,7J. Cuevas,11R. Culbertson,16

D. Cyr,59S. DaRonco,43S. D’Auria,20M. D’Onofrio,3D. Dagenhart,6P. de Barbaro,49S. De Cecco,51A. Deisher,28 G. De Lentdecker,49M. Dell’Orso,46F. Delli Paoli,43S. Demers,49L. Demortier,50J. Deng,15M. Deninno,5D. De Pedis,51

P. F. Derwent,16C. Dionisi,51J. R. Dittmann,4P. DiTuro,52C. Do¨rr,25S. Donati,46M. Donega,19P. Dong,8J. Donini,43 T. Dorigo,43S. Dube,52K. Ebina,57J. Efron,39J. Ehlers,19R. Erbacher,7D. Errede,23S. Errede,23R. Eusebi,16 H. C. Fang,28S. Farrington,29I. Fedorko,46W. T. Fedorko,13R. G. Feild,60M. Feindt,25J. P. Fernandez,31R. Field,17 G. Flanagan,48L. R. Flores-Castillo,47A. Foland,21S. Forrester,7G. W. Foster,16M. Franklin,21J. C. Freeman,28I. Furic,13

M. Gallinaro,50J. Galyardt,12J. E. Garcia,46M. Garcia Sciveres,28A. F. Garfinkel,48C. Gay,60H. Gerberich,23 D. Gerdes,34S. Giagu,51P. Giannetti,46A. Gibson,28K. Gibson,12C. Ginsburg,16N. Giokaris,14K. Giolo,48M. Giordani,54 P. Giromini,18M. Giunta,46G. Giurgiu,12V. Glagolev,14D. Glenzinski,16M. Gold,37N. Goldschmidt,34J. Goldstein,42

G. Gomez,11G. Gomez-Ceballos,11M. Goncharov,53O. Gonza´lez,31I. Gorelov,37A. T. Goshaw,15Y. Gotra,47 K. Goulianos,50A. Gresele,43M. Griffiths,29S. Grinstein,21C. Grosso-Pilcher,13R. C. Group,17U. Grundler,23 J. Guimaraes da Costa,21Z. Gunay-Unalan,35C. Haber,28S. R. Hahn,16K. Hahn,45E. Halkiadakis,52A. Hamilton,33 B.-Y. Han,49J. Y. Han,49R. Handler,59F. Happacher,18K. Hara,55M. Hare,56S. Harper,42R. F. Harr,58R. M. Harris,16

K. Hatakeyama,50J. Hauser,8C. Hays,15A. Heijboer,45B. Heinemann,29J. Heinrich,45M. Herndon,59D. Hidas,15 C. S. Hill,10D. Hirschbuehl,25A. Hocker,16A. Holloway,21S. Hou,1M. Houlden,29S.-C. Hsu,9B. T. Huffman,42 R. E. Hughes,39J. Huston,35J. Incandela,10G. Introzzi,46M. Iori,51Y. Ishizawa,55A. Ivanov,7B. Iyutin,32E. James,16

D. Jang,52B. Jayatilaka,34D. Jeans,51H. Jensen,16E. J. Jeon,27S. Jindariani,17M. Jones,48K. K. Joo,27S. Y. Jun,12 T. R. Junk,23T. Kamon,53J. Kang,34P. E. Karchin,58Y. Kato,41Y. Kemp,25R. Kephart,16U. Kerzel,25V. Khotilovich,53 B. Kilminster,39D. H. Kim,27H. S. Kim,27J. E. Kim,27M. J. Kim,12S. B. Kim,27S. H. Kim,55Y. K. Kim,13L. Kirsch,6

S. Klimenko,17M. Klute,32B. Knuteson,32B. R. Ko,15H. Kobayashi,55K. Kondo,57D. J. Kong,27J. Konigsberg,17 A. Korytov,17A. V. Kotwal,15A. Kovalev,45A. Kraan,45J. Kraus,23I. Kravchenko,32M. Kreps,25J. Kroll,45 N. Krumnack,4M. Kruse,15V. Krutelyov,53S. E. Kuhlmann,2Y. Kusakabe,57S. Kwang,13A. T. Laasanen,48S. Lai,33

S. Lami,46S. Lammel,16M. Lancaster,30R. L. Lander,7K. Lannon,39A. Lath,52G. Latino,46I. Lazzizzera,43 T. LeCompte,2J. Lee,49J. Lee,27Y. J. Lee,27S. W. Lee,53R. Lefe`vre,3N. Leonardo,32S. Leone,46S. Levy,13J. D. Lewis,16 C. Lin,60C. S. Lin,16M. Lindgren,16E. Lipeles,9A. Lister,19D. O. Litvintsev,16T. Liu,16N. S. Lockyer,45A. Loginov,36 M. Loreti,43P. Loverre,51R.-S. Lu,1D. Lucchesi,43P. Lujan,28P. Lukens,16G. Lungu,17L. Lyons,42J. Lys,28R. Lysak,1

E. Lytken,48P. Mack,25D. MacQueen,33R. Madrak,16K. Maeshima,16T. Maki,22P. Maksimovic,24S. Malde,42 G. Manca,29F. Margaroli,5R. Marginean,16C. Marino,23A. Martin,60V. Martin,38M. Martı´nez,3T. Maruyama,55 H. Matsunaga,55M. E. Mattson,58R. Mazini,33P. Mazzanti,5K. S. McFarland,49P. McIntyre,53R. McNulty,29A. Mehta,29 S. Menzemer,11A. Menzione,46P. Merkel,48C. Mesropian,50A. Messina,51M. von der Mey,8T. Miao,16N. Miladinovic,6 J. Miles,32R. Miller,35J. S. Miller,34C. Mills,10M. Milnik,25R. Miquel,28A. Mitra,1G. Mitselmakher,17A. Miyamoto,26 N. Moggi,5B. Mohr,8R. Moore,16M. Morello,46P. Movilla Fernandez,28J. Mu¨lmensta¨dt,28A. Mukherjee,16Th. Muller,25 R. Mumford,24P. Murat,16J. Nachtman,16J. Naganoma,57S. Nahn,32I. Nakano,40A. Napier,56D. Naumov,37V. Necula,17 C. Neu,45M. S. Neubauer,9J. Nielsen,28T. Nigmanov,47L. Nodulman,2O. Norniella,3E. Nurse,30T. Ogawa,57S. H. Oh,15

PHYSICAL REVIEW D74,031109(R) (2006)

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Y. D. Oh,27T. Okusawa,41R. Oldeman,29R. Orava,22K. Osterberg,22C. Pagliarone,46E. Palencia,11R. Paoletti,46 V. Papadimitriou,16A. A. Paramonov,13B. Parks,39S. Pashapour,33J. Patrick,16G. Pauletta,54M. Paulini,12C. Paus,32 D. E. Pellett,7A. Penzo,54T. J. Phillips,15G. Piacentino,46J. Piedra,44L. Pinera,17K. Pitts,23C. Plager,8L. Pondrom,59 X. Portell,3O. Poukhov,14N. Pounder,42F. Prakoshyn,14A. Pronko,16J. Proudfoot,2F. Ptohos,18G. Punzi,46J. Pursley,24

J. Rademacker,42A. Rahaman,47A. Rakitin,32S. Rappoccio,21F. Ratnikov,52B. Reisert,16V. Rekovic,37 N. van Remortel,22P. Renton,42M. Rescigno,51S. Richter,25F. Rimondi,5L. Ristori,46W. J. Robertson,15A. Robson,20

T. Rodrigo,11E. Rogers,23S. Rolli,56R. Roser,16M. Rossi,54R. Rossin,17C. Rott,48A. Ruiz,11J. Russ,12V. Rusu,13 H. Saarikko,22S. Sabik,33A. Safonov,53W. K. Sakumoto,49G. Salamanna,51O. Salto´,3D. Saltzberg,8C. Sanchez,3

L. Santi,54S. Sarkar,51L. Sartori,46K. Sato,55P. Savard,33A. Savoy-Navarro,44T. Scheidle,25P. Schlabach,16 E. E. Schmidt,16M. P. Schmidt,60M. Schmitt,38T. Schwarz,34L. Scodellaro,11A. L. Scott,10A. Scribano,46F. Scuri,46

A. Sedov,48S. Seidel,37Y. Seiya,41A. Semenov,14L. Sexton-Kennedy,16I. Sfiligoi,18M. D. Shapiro,28T. Shears,29 P. F. Shepard,47D. Sherman,21M. Shimojima,55M. Shochet,13Y. Shon,59I. Shreyber,36A. Sidoti,44P. Sinervo,33

A. Sisakyan,14J. Sjolin,42A. Skiba,25A. J. Slaughter,16K. Sliwa,56J. R. Smith,7F. D. Snider,16R. Snihur,33 M. Soderberg,34A. Soha,7S. Somalwar,52V. Sorin,35J. Spalding,16M. Spezziga,16F. Spinella,46T. Spreitzer,33 P. Squillacioti,46M. Stanitzki,60A. Staveris-Polykalas,46R. St. Denis,20B. Stelzer,8O. Stelzer-Chilton,42D. Stentz,38 J. Strologas,37D. Stuart,10J. S. Suh,27A. Sukhanov,17K. Sumorok,32H. Sun,56T. Suzuki,55A. Taffard,23R. Takashima,40

Y. Takeuchi,55K. Takikawa,55M. Tanaka,2R. Tanaka,40N. Tanimoto,40M. Tecchio,34P. K. Teng,1K. Terashi,50 S. Tether,32J. Thom,16A. S. Thompson,20E. Thomson,45P. Tipton,49V. Tiwari,12S. Tkaczyk,16D. Toback,53S. Tokar,14

K. Tollefson,35T. Tomura,55D. Tonelli,46M. To¨nnesmann,35S. Torre,18D. Torretta,16S. Tourneur,44W. Trischuk,33 R. Tsuchiya,57S. Tsuno,40N. Turini,46F. Ukegawa,55T. Unverhau,20S. Uozumi,55D. Usynin,45A. Vaiciulis,49 S. Vallecorsa,19A. Varganov,34E. Vataga,37G. Velev,16G. Veramendi,23V. Veszpremi,48R. Vidal,16I. Vila,11R. Vilar,11

T. Vine,30I. Vollrath,33I. Volobouev,28G. Volpi,46F. Wu¨rthwein,9P. Wagner,53R. G. Wagner,2R. L. Wagner,16 W. Wagner,25R. Wallny,8T. Walter,25Z. Wan,52S. M. Wang,1A. Warburton,33S. Waschke,20D. Waters,30 W. C. Wester III,16B. Whitehouse,56D. Whiteson,45A. B. Wicklund,2E. Wicklund,16G. Williams,33H. H. Williams,45

P. Wilson,16B. L. Winer,39P. Wittich,16S. Wolbers,16C. Wolfe,13T. Wright,34X. Wu,19S. M. Wynne,29A. Yagil,16 K. Yamamoto,41J. Yamaoka,52T. Yamashita,40C. Yang,60U. K. Yang,13Y. C. Yang,27W. M. Yao,28G. P. Yeh,16J. Yoh,16

K. Yorita,13T. Yoshida,41G. B. Yu,49I. Yu,27S. S. Yu,16J. C. Yun,16L. Zanello,51A. Zanetti,54I. Zaw,21F. Zetti,46 X. Zhang,23J. Zhou,52and S. Zucchelli5

(CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439, USA

3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

4Baylor University, Waco, Texas 76798, USA

5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy

6Brandeis University, Waltham, Massachusetts 02254, USA

7University of California, Davis, Davis, California 95616, USA

8University of California, Los Angeles, Los Angeles, California 90024, USA

9University of California, San Diego, La Jolla, California 92093, USA

10University of California, Santa Barbara, Santa Barbara, California 93106, USA

11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA

14Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

15Duke University, Durham, North Carolina 27708

16Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

17University of Florida, Gainesville, Florida 32611, USA

18Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

19University of Geneva, CH-1211 Geneva 4, Switzerland

20Glasgow University, Glasgow G12 8QQ, United Kingdom

21Harvard University, Cambridge, Massachusetts 02138, USA

22Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

23University of Illinois, Urbana, Illinois 61801, USA

A. ABULENCIAet al. PHYSICAL REVIEW D74,031109(R) (2006)

031109-2

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24The Johns Hopkins University, Baltimore, Maryland 21218, USA

25Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

26High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan

27Center for High Energy Physics: Kyungpook National University, Taegu 702-701; Seoul National University, Seoul 151-742;

and SungKyunKwan University, Suwon 440-746; Korea

28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

29University of Liverpool, Liverpool L69 7ZE, United Kingdom

30University College London, London WC1E 6BT, United Kingdom

31Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

32Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

33Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7

34University of Michigan, Ann Arbor, Michigan 48109, USA

35Michigan State University, East Lansing, Michigan 48824, USA

36Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

37University of New Mexico, Albuquerque, New Mexico 87131, USA

38Northwestern University, Evanston, Illinois 60208, USA

39The Ohio State University, Columbus, Ohio 43210, USA

40Okayama University, Okayama 700-8530, Japan

41Osaka City University, Osaka 588, Japan

42University of Oxford, Oxford OX1 3RH, United Kingdom

43University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

44LPNHE-Universite Pierre et Marie Curie-Paris 6, UMR7585, Paris F-75005 France; IN2P3-CNRS

45University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

46Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy

47University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

48Purdue University, West Lafayette, Indiana 47907, USA

49University of Rochester, Rochester, New York 14627, USA

50The Rockefeller University, New York, New York 10021, USA

51Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy

52Rutgers University, Piscataway, New Jersey 08855, USA

53Texas A&M University, College Station, Texas 77843, USA

54Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy

55University of Tsukuba, Tsukuba, Ibaraki 305, Japan

56Tufts University, Medford, Massachusetts 02155, USA

57Waseda University, Tokyo 169, Japan

58Wayne State University, Detroit, Michigan 48201, USA

59University of Wisconsin, Madison, Wisconsin 53706, USA

60Yale University, New Haven, Connecticut 06520, USA (Received 8 May 2006; published 28 August 2006)

We present a measurement ofRB, the ratio of the branching fraction for the rare decayD0!Kto that for the Cabibbo-favored decay D0!K. Charge-conjugate decays are implicitly included. A signal of 2005104 events for the decay D0!K is obtained using the CDF II detector at the Fermilab Tevatron collider. The data set corresponds to an integrated luminosity of0:35 fb1produced in

ppcollisions at ps

1:96 TeV. Assuming no mixing, we findRB 4:050:21stat 0:11syst 103. This measurement is consistent with the world average, and comparable in accuracy with the best measurements from other experiments.

DOI:10.1103/PhysRevD.74.031109 PACS numbers: 13.25.Ft, 14.40.Lb

The D0 can decay to K either through a doubly Cabibbo-suppressed (DCS) tree process or by oscillation (mixing) to aD0followed by a Cabibbo-favored (CF) tree process. The charge-conjugate decays, such as D0 ! K, are implied throughout this paper. The time- dependent decay ratertforD0 !K can be written in a compact form [1] taking into account the experimen- tally established facts that the rate for mixing is at least as small as that for the DCS decay, and that the effect ofCP violation is small. In this formalism, and assuming CP

conservation, rt /et

RD RD

p y0t x02y02 4 t2

: (1) The parameter RD is the squared modulus of the ratio of DCS to CF amplitudes. The parameters x0 and y0 are defined in terms of the parameters xm= and y

=2, where mis the difference in mass between the two mass eigenstates,is the difference in decay width between the two mass eigenstates, and is the average MEASUREMENT OF THE RATIO OF BRANCHING. . . PHYSICAL REVIEW D74,031109(R) (2006)

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decay width. The definitions are

x0xcosysin and y0 xsinycos;

(2) where is the strong phase difference between the DCS and CF amplitudes. The ratio of branching fractions,

RBBD0 !K=BD0!K (3) is given by the ratio of the time-integrals of the correspond- ing decay rates,

RBRD RD

p y0x02y02

2 : (4)

Thus, if the terms containingx0andy0are sufficiently small compared to RD, the mixing rate is small and the experi- mentally measurable quantityRBcan be interpreted as the theoretical parameterRD.

In the limit of flavor SU(3) symmetry, RD tan4C [2,3] where C is the Cabibbo angle, which is measured from kaon decays. The world average values [1], RD 3:620:29 103 and tan4C 2:880:27 103, are equal within their uncertainties, consistent with flavor SU(3) symmetry. However, symmetry violation of magnitude less than the current measurement accuracy is possible [4] if there are differences in the weak decay form factorsFD0 andFDK0 , or due to strong interaction resonant intermediate states following the charm quark decay.

There is no experimental evidence either forCPviola- tion inD0 decays or forD0-D0mixing; all measurements are consistent with x0y0 0. An upper limit on the contribution to RB from mixing can be derived from measured upper limits for x0; y03 102 [1] and the world average measurement ofRD. A simple estimate, by substituting these values into Eq. (4), gives a contribution toRBless than2:7 103, a limit which is comparable to the value ofRD.

In the standard model, theoretical predictions due to short-distance weak processes are x0; y06 107 [5].

However, strong interaction effects could result in larger values, of ordersin2C0:048times an unknown factor which describes the size of flavor SU(3) symmetry viola- tion. Thus, accurate measurement ofRD andCcan estab- lish the size of the symmetry violation factor and make possible the prediction of the standard model contribution to mixing. If the standard model contribution is small, then D0-D0 mixing measurements will be sensitive to new physics. Theories involving weak-scale supersymmetry or new strong dynamics at the TeV scale can accommodate large values ofx0andy0, up to the experimental limits [6], leaving open the possibility for indirect observation of new physics.

Until now, the most precise measurements ofRD were from the B factories. The BABAR collaboration [7] re- ported RD 3:590:20stat 0:27syst 103 with a DCS signal of 430 events, and the Belle collabora-

tion [8,9] reported RD 3:810:17stat 0:08 0:16syst 103 with a DCS signal of 845 events.

Both of these results are based on the assumption of no mixing and no CP violation, which is the convention chosen by the Particle Data Group. In this paper, using a DCS signal of 2005 events and assuming no mixing, we report a time-independent measurement of RD with com- parable precision to those ofBABARand Belle. As in those experiments, we reconstruct the decay chain D! D0, D0 !K, where the charge of the from Ddecay distinguishes theD0 from its antiparticle,D0.

Our measurement uses data collected by the CDF II detector at the Fermilab Tevatron collider, from October 2002 to August 2004. The data corresponds to an integrated luminosity of0:35 fb1produced inpp collisions at

ps 1:96 TeV. CDF II is a multipurpose detector with a mag- netic spectrometer surrounded by a calorimeter and a muon detector. The CDF II components pertinent to this analysis are described briefly below. A more detailed description is found in [10] and references therein. A cylindrical silicon microstrip vertex detector (SVX II) [11] and a cylindrical drift chamber (COT) [12], immersed in a 1.4 T axial magnetic field, allow reconstruction of tracks (trajectories of charged particles) in the pseudorapidity range jj 1:3, wheretanh1cosandis the angle measured from the beamline. The ionization signals from the COT provide a measurement of the specific energy loss for a charged particle, which is used for particle identification.

Events were selected in real time using a three-level trigger system with requirements developed for a broad class of heavy flavor decays. At level 1, tracks are recon- structed in the COT in the plane transverse to the beamline by a hardware processor (XFT) [13]. Two oppositely charged tracks are required, each with transverse momen- tum greater than2 GeV=c. In addition, the scalar sum of the two transverse momenta must be greater than 5:5 GeV=c. The opening anglebetween the two tracks in the transverse plane must be less than 135. At level 2, the silicon vertex tracker (SVT) [14] attaches SVX II hits to each of the two XFT tracks to increase the measurement accuracy. The transverse impact parameterd0is defined as the distance of closest approach, in the transverse plane, of a track to the beamline. Each of the two tracks is required to satisfy120md0 1:0 mm. The opening angle cut is tightened (compared to level 1) to290. The track pair forms a long-lived particle candidate which is required to have a decay lengthLxy>200m, whereLxy is the transverse distance from the beam line to the candi- date’s vertex, projected along the total transverse momen- tum of the candidate. At level 3, a conventional computer processor confirms the selection with a full event reconstruction.

The analysis method for determining the ratio of branch- ing fractions requires reconstruction of the decay chains D!D0, D0 !K (CF), and D!D0,

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D0 !K (DCS). The D0 candidate reconstruction starts with a pair of oppositely charged tracks that satisfy the trigger requirements. The tracks are considered with both K and K interpretations. A third track, which is required to have pT 0:3 GeV=c, is used to form a D candidate when combined as a pion with the D0 candidate. The charge of this ‘‘tagging pion’’ deter- mines whether theD0 candidate decay is CF or DCS.

To reduce systematic uncertainty, the same set of cuts is employed for both the CF and DCS decay modes. The offline analysis cuts were chosen to maximize the signifi- cance of the DCS signal determined from a study of the CF signal and the DCS background. The optimization was performed without using DCS candidates and before the candidates were revealed. The DCS signal was estimated by scaling the CF signal by the world average forRD. The DCS background was estimated from candidates in a con- trol region ofD invariant mass, outside a region contain- ing the signal. In the optimization study, the same algorithms for data analysis were followed as for the DCS signal determination.

We apply two cuts to reduce the background to the DCS signal from CF decays where the D0 decay tracks are misidentified. Misidentification occurs when the kaon and pion assignments are mistakenly interchanged. This background is characterized by a K mass distribution with width about 10 times that of the signal peak. A DCS candidate that is consistent with being a CF decay, with K invariant mass within 20 MeV=c2 of the D0 mass, is excluded from the DCS signal. This cut rejects 97.5% of misidentified decays, while retaining 78% of the signal. Since the analysis procedure is the same for DCS and CF decays, a CF candidate that is consistent with being a DCS decay is excluded from the CF signal.

A cut based on particle identification from specific ionization in the COT also helps to reject misidentified decays, but with a smaller improvement to DCS signal significance than from the cut based on invariant mass. A variableZis defined as the ratio of logarithms of measured to predicted charge deposition for a single track. The prediction is based on the ionization expected for a particle with the measured momentum and a specific hypothesis for mass. For a pair of particles, we define

SK ZK

K 2

Z

2

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where the subscriptsKandindicate the particle hypoth- eses for the first and second track of the pair, andK, are the corresponding Gaussian resolutions on Z. The particle identification for the pair is chosen by the smaller ofSKandSK. This selection is correct 80.2% of the time, as measured using the CF signal that survives the invariant mass cut.

We apply four cuts to reduce combinatoric background from prompt particle production or from improper combi-

nations of tracks in events containing heavy flavor parti- cles. These cuts retain most of the signal, with a small improvement in the signal significance. Since theD0has a long enough mean lifetime to have an observable decay length, the decay vertex should be displaced, on average, from the production point. We require the transverse decay length significance Lxy=xy>5, where Lxy was defined earlier andxyis the uncertainty onLxy. TheDhas a short enough mean lifetime so that it should appear to decay at its production point. The tagging pion and theD0candidate must be consistent with coming from a common point based on a 2 measure in the transverse plane. For the D vertex, we also require jLxy=xyj<15. Furthermore, the tagging pion track must have an impact parameterd0<

800m.

The K mass distribution for CF decays has been re- ported in a recent CDF II publication on singly Cabibbo- suppressed decays [15]. TheKmass distribution for DCS candidates is illustrated by the histogram in Fig. 1 for candidates satisfying 5 MeV=c2< m <7 MeV=c2,

where mmK mK m. Four

categories of K combinations contribute to the distri- bution. The first category (signal) is DCS signal fromD, with the correct D0 !K interpretation. The second category (random pion) is background from CFD0decays, where a randomly selected particle, usually from the pri- mary interaction, is used as the tagging pion to form theD candidate. The third category (mis-id D0) is background fromDdecays where theKandassignments from the CF D0 decay are mistakenly interchanged. The last cate- gory is combinatoric background, where one or both tracks

2

) ) (GeV/c π

m(K

1.8 1.85 1.9

2

Events per 2 MeV/c 200

400

1.8 1.85 1.9

200 400

data signal random pion mis-id D0

combinatoric

FIG. 1. K invariant mass distribution for candidates recon- structed as D0!K (DCS), requiring 5 MeV=c2< m <

7 MeV=c2. The shaded regions are projections from the overall fit onto this distribution. This mass plot illustrates the relative contributions from the DCS signal and the three types of background, as described in the text.

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do not belong to a D!K decay. Background from singly Cabibbo-suppressed decays D0!KK and D0 ! that are misreconstructed asK are ex- cluded by limiting the mass range from 1:80–1:93GeV=c2.

To determine the signal and background, candidates are divided into 60 slices of m, each slice of width 0:5 MeV=c2. (The distribution in Fig. 1 is for a 2 MeV=c2 wide slice for purpose of illustration.) For each slice, the Kmass distribution is fit using a binned likelihood method with a predetermined D0 shape and a linear function for the combinatoric background. TheD0 peak includes events from bothDsignal and random pion background. TheD0 shape is determined from a fit to the CF K distribution, which has a negligible background compared to the signal. The amplitudes of theD0 and the combinatoric parameters are fit independently for each slice. The amplitude and shape of the mis-idD0 contribu- tion is determined from the CF signal, by interchanging the pion and kaon assignments.

To determine the amount of DCSDsignal and random pion background, theD0yields for the slices are plotted as a function ofm, as shown in Fig.2. This distribution is fit using a least-squares method with a signal shape predeter- mined from the CF m distribution and a background function of the form AmBeCm. The amplitudes of the signal and background terms and the background shape parameters B and C are determined from the fit. The fit results are2005104DCS signal and495172907CF signal; their ratio givesRB 4:050:21 103.

Most of the detector properties that affect the DCS and CF signals are common and hence do not affect the ratio.

Thus, there are no systematic uncertainties due to geomet- ric acceptance, particle identification, and trigger effi- ciency. While the number of background events is similar for the DCS and CF candidates, the size of the DCS signal is much smaller. Thus, systematic uncertainty in the DCS background which affects the DCS signal estimate also affects the ratio. There are three such significant sources of systematic uncertainty, as summarized in TableI.

To estimate the uncertainty due to the assumed combi- natoric background shape in the DCS K slice fits, we comparedRBresults for two shapes. The nominal shape is linear and gives a good fit. We also tried a quadratic form and assigned the change inRBas a systematic uncertainty.

To estimate the uncertainty due to the assumed mback- ground shape, we comparedRBresults for two shapes. The nominal shape is given by the function described earlier and gives a good fit. We also tried a function with an additional parameter and assigned the change in RB as a systematic uncertainty. In fitting the DCSKslice fits, the amplitude of the mis-idD0 background is fixed from the CF signal. A simulation of the fitting procedure is used to propagate the statistical uncertainty on the background amplitude to a systematic uncertainty onRB.

We considered other sources of systematic uncertainty that we found to be negligible. These include effects due to small differences in detection efficiencies for K versus Kandversus, which are reported in [15]. We tried alternative fits to the DCS Kdistributions by extending the upper limit of the mass range from 1.80 to 2:00 GeV=c2. This study required adding an explicit term for background from D0!decays.

In conclusion, we find RB 4:050:21stat 0:11syst 103. The difference between this value and the world average value fortan4Cis1:170:34 103, a3:4deviation from zero. If not a statistical fluc- tuation, this difference could be due to violation of flavor SU(3) symmetry causingRDtan4C, or could be a result of mixing. If mixing is non-negligible, our observed value ofRB would depend on the mixing parameters andRD as well as the acceptance, which is nonuniform in proper time. For negligible mixing, the proper time dependence of the acceptance does not affect our observed value ofRB. While we cannot rule out the possibility of mixing from our result alone, our result is consistent with the scenario of modest symmetry violation and negligible mixing. As shown in Fig. 3, our measured value of RB is in fact

2) m (MeV/c δ

0 10 20 30

2 Events per 0.5 MeV/c

500 1000 1500

FIG. 2. The number ofD0!K (DCS) decays as a func- tion ofm. The data points and statistical uncertainty bars are taken from theKslice fits. The shaded regions are determined from a least-squares fit and show the contributions from signal (dark gray) and random tagging pion background (light gray) as explained in the text.

TABLE I. Dominant systematic uncertainties for RB. The sources lead to uncertainties in the DCS signal estimate.

Source Uncertainty ( 103)

Kcombinatoric background shape 0.09 mrandom pion background shape 0.06 Kmis-IDD0background amplitude 0.01

A. ABULENCIAet al. PHYSICAL REVIEW D74,031109(R) (2006)

031109-6

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consistent with the world average and the most accurate

individual measurements ofRDobtained fromBABAR[7]

and Belle [8]. Using the technique we have established to extract the D0!K signal, we can perform a time- dependent analysis using a larger data sample than re- ported here, to separately measure RD and the mixing parametersx0andy0.

We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.

This work was supported by the U.S. Department of Energy and National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A. P. Sloan Foundation; the Bundesministerium fu¨r Bildung und Forschung, Germany; the Korean Science and Engineering Foundation and the Korean Research Foundation; the Particle Physics and Astronomy Research Council and the Royal Society, UK; the Russian Foundation for Basic Research; the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain; in part by the European Community’s Human Potential Programme under contract HPRN-CT- 2002-00292; and the Academy of Finland.

[1] S. Eidelman et al. (Particle Data Group), Phys. Lett. B 592, 1 (2004), review by D. Asner onD0D0 mixing;

ibid.review by E. Blucher and W. J. Marciano onVud,Vus, the Cabibbo angle, and CKM Unitarity.

[2] R. L. Kingsley, S. B. Trieman, F. Wilczek, and A. Zee, Phys. Rev. D11, 1919 (1975).

[3] M. B. Voloshin, V. I. Zakharov, and L. B. Okun, Pis’ma Zh.

Eksp. Teor. Fiz. 21, 403 (1975) [JETP Lett. 21, 183 (1975)].

[4] M. Gronau and J. L. Rosner, Phys. Lett. B500, 247 (2001).

[5] E. Golowich and A. A. Petrov, Phys. Lett. B 625, 53 (2005).

[6] G. Burdman and I. Shipsey, Annu. Rev. Nucl. Part. Sci.53, 431 (2003). See section 2.3.

[7] B. Aubertet al.(BABARCollaboration), Phys. Rev. Lett.

91, 171801 (2003).

[8] K. Abe et al.(Belle Collaboration), Phys. Rev. Lett. 94, 071801 (2005).

[9] After our paper was submitted, we learned of a recent result with statistical and systematic errors about half of the result presented: L. M. Zhang et al. (Belle Collab-

oration), Phys. Rev. Lett.96, 151801 (2006).

[10] D. Acosta et al.(CDF Collaboration), Phys. Rev. D71, 032001 (2005).

[11] A. Sillet al., Nucl. Instrum. Methods Phys. Res., Sect. A 447, 1 (2000).

[12] T. Affolderet al., Nucl. Instrum. Methods Phys. Res., Sect.

A526, 249 (2004).

[13] E. J. Thomson et al., IEEE Trans. Nucl. Sci. 49, 1063 (2002).

[14] W. Ashmanskaset al., Nucl. Instrum. Methods Phys. Res., Sect. A518, 532 (2004).

[15] D. Acostaet al.(CDF Collaboration), Phys. Rev. Lett.94, 122001 (2005).

[16] E. M. Aitalaet al.(E791 Collaboration), Phys. Rev. D57, 13 (1998).

[17] R. Godanget al.(CLEO Collaboration), Phys. Rev. Lett.

84, 5038 (2000).

[18] J. M. Linket al.(FOCUS Collaboration), Phys. Rev. Lett.

86, 2955 (2001).

[19] J. M. Link et al. (FOCUS Collaboration), Phys. Lett. B 618, 23 (2005).

R

D 0.002 0.003 0.004 0.005 0.006 0.007

CDF BELLE BABAR FOCUS CLEO E791

R

D 0.002 0.003 0.004 0.005 0.006 0.007

CDF BELLE BABAR FOCUS CLEO E791

PDG Average

Included in PDG Average

Not in PDG Average 2001

2005

FIG. 3 (color online). Comparison of this measurement ofRD with other recent results. All the experimental fits assume no mixing orCPviolation. The inner set of bars indicate statistical uncertainty; the outer set indicates the quadratic sum of statis- tical and systematic uncertainties. The shaded region spans the PDG average and uncertainty [1]. That average includes mea- surements from E791 [16], CLEO [17], FOCUS(2001) [18], and BABAR[7]. The Belle [8], FOCUS(2005) [19] and current CDF measurements are not included in the PDG average.

MEASUREMENT OF THE RATIO OF BRANCHING. . . PHYSICAL REVIEW D74,031109(R) (2006)

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