Article
Reference
Measurement of the moments of the hadronic invariant mass distribution in semileptonic B decays
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
Using 180 pb−1 of data collected with the CDF II detector at the Tevatron, we measure the first two moments of the hadronic invariant mass-squared distribution in charmed semileptonic B decays. From these we determine the nonperturbative Heavy Quark Effective Theory parameters Λ and λ1 used to relate the B meson semileptonic branching ratio to the CKM matrix element |Vcb|. For a minimum lepton momentum of 0.7 GeV/c in the B rest frame we measure the first two moments of the D**→D(*)π component to be
⟨m2D**⟩=(5.83±0.16stat±0.08syst) GeV2/c4 and
⟨(m2D**−⟨m2D**⟩)2⟩=(1.30±0.69stat±0.22syst) GeV4/c8. Combining these with the discrete mass terms from the D and D∗ mesons, we find the total moments to be
⟨M2Xc⟩−m2D=(0.467±0.038stat±0.068syst) GeV2/c4 and
⟨(M2Xc−⟨M2Xc⟩)2⟩=(1.05±0.26stat±0.13syst) GeV4/c8, where mD is the spin-averaged D mass. The systematic error is dominated by the uncertainties in the world-average branching ratios used to combine the D, D∗, and D** contributions. The analysis makes no assumptions about the shape or resonant structure of the [...]
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the moments of the hadronic invariant mass distribution in semileptonic B decays. Physical Review. D , 2005, vol.
71, no. 05, p. 051103
DOI : 10.1103/PhysRevD.71.051103
Available at:
http://archive-ouverte.unige.ch/unige:38305
Disclaimer: layout of this document may differ from the published version.
1 / 1
Measurement of the moments of the hadronic invariant mass distribution in semileptonic B decays
D. Acosta,16J. Adelman,12T. Affolder,9T. Akimoto,54M. G. Albrow,15D. Ambrose,43S. Amerio,42D. Amidei,33 A. Anastassov,50K. Anikeev,15A. Annovi,44J. Antos,1M. Aoki,54G. Apollinari,15T. Arisawa,56J-F. Arguin,32 A. Artikov,13W. Ashmanskas,15A. Attal,7F. Azfar,41P. Azzi-Bacchetta,42N. Bacchetta,42H. Bachacou,28W. Badgett,15 A. Barbaro-Galtieri,28G. J. Barker,25V. E. Barnes,46B. A. Barnett,24S. Baroiant,6M. Barone,17G. Bauer,31F. Bedeschi,44
S. Behari,24S. Belforte,53G. Bellettini,44J. Bellinger,58E. Ben-Haim,15D. Benjamin,14A. Beretvas,15A. Bhatti,48 M. Binkley,15D. Bisello,42M. Bishai,15R. E. Blair,2C. Blocker,5K. Bloom,33B. Blumenfeld,24A. Bocci,48A. Bodek,47
G. Bolla,46A. Bolshov,31P. S. L. Booth,29D. Bortoletto,46J. Boudreau,45S. Bourov,15B. Brau,9C. Bromberg,34 E. Brubaker,12J. Budagov,13H. S. Budd,47K. Burkett,15G. Busetto,42P. Bussey,19K. L. Byrum,2S. Cabrera,14 M. Campanelli,18M. Campbell,33A. Canepa,46M. Casarsa,53D. Carlsmith,58S. Carron,14R. Carosi,44M. Cavalli-Sforza,3
A. Castro,4P. Catastini,44D. Cauz,53A. Cerri,28L. Cerrito,23J. Chapman,33C. Chen,43Y. C. Chen,1M. Chertok,6 G. Chiarelli,44G. Chlachidze,13F. Chlebana,15I. Cho,27K. Cho,27D. Chokheli,13J. P. Chou,20M. L. Chu,1S. Chuang,58
J. Y. Chung,38W-H. Chung,58Y. S. Chung,47C. I. Ciobanu,23M. A. Ciocci,44A. G. Clark,18D. Clark,5M. Coca,47 A. Connolly,28M. Convery,48J. Conway,6B. Cooper,30M. Cordelli,17G. Cortiana,42J. Cranshaw,52J. Cuevas,10 R. Culbertson,15C. Currat,28D. Cyr,58D. Dagenhart,5S. Da Ronco,42S. D’Auria,19P. de Barbaro,47S. De Cecco,49
G. De Lentdecker,47S. Dell’Agnello,17M. Dell’Orso,44S. Demers,47L. Demortier,48M. Deninno,4D. De Pedis,49 P. F. Derwent,15C. Dionisi,49J. R. Dittmann,15C. Do¨rr,25P. Doksus,23A. Dominguez,28S. Donati,44M. Donega,18 J. Donini,42M. D’Onofrio,18T. Dorigo,42V. Drollinger,36K. Ebina,56N. Eddy,23J. Ehlers,18R. Ely,28R. Erbacher,6
M. Erdmann,25D. Errede,23S. Errede,23R. Eusebi,47H.-C. Fang,28S. Farrington,29I. Fedorko,44W. T. Fedorko,12 R. G. Feild,59M. Feindt,25J. P. Fernandez,46C. Ferretti,33R. D. Field,16G. Flanagan,34B. Flaugher,15
L. R. Flores-Castillo,45A. Foland,20S. Forrester,6G. W. Foster,15M. Franklin,20J. C. Freeman,28Y. Fujii,26I. Furic,12 A. Gajjar,29A. Gallas,37J. Galyardt,11M. Gallinaro,48M. Garcia-Sciveres,28A. F. Garfinkel,46C. Gay,59H. Gerberich,14
D. W. Gerdes,33E. Gerchtein,11S. Giagu,49P. Giannetti,44A. Gibson,28K. Gibson,11C. Ginsburg,58K. Giolo,46 M. Giordani,53M. Giunta,44G. Giurgiu,11V. Glagolev,13D. Glenzinski,15M. Gold,36N. Goldschmidt,33D. Goldstein,7
J. Goldstein,41G. Gomez,10G. Gomez-Ceballos,31M. Goncharov,51O. Gonza´lez,46I. Gorelov,36A. T. Goshaw,14 Y. Gotra,45K. Goulianos,48A. Gresele,4M. Griffiths,29C. Grosso-Pilcher,12U. Grundler,23M. Guenther,46 J. Guimaraes da Costa,20C. Haber,28K. Hahn,43S. R. Hahn,15E. Halkiadakis,47A. Hamilton,32B-Y. Han,47R. Handler,58 F. Happacher,17K. Hara,54M. Hare,55R. F. Harr,57R. M. Harris,15F. Hartmann,25K. Hatakeyama,48J. Hauser,7C. Hays,14 H. Hayward,29E. Heider,55B. Heinemann,29J. Heinrich,43M. Hennecke,25M. Herndon,24C. Hill,9D. Hirschbuehl,25 A. Hocker,47K. D. Hoffman,12A. Holloway,20S. Hou,1M. A. Houlden,29B. T. Huffman,41Y. Huang,14R. E. Hughes,38
J. Huston,34K. Ikado,56J. Incandela,9G. Introzzi,44M. Iori,49Y. Ishizawa,54C. Issever,9A. Ivanov,47Y. Iwata,22 B. Iyutin,31E. James,15D. Jang,50J. Jarrell,36D. Jeans,49H. Jensen,15E. J. Jeon,27M. Jones,46K. K. Joo,27S. Y. Jun,11 T. Junk,23T. Kamon,51J. Kang,33M. Karagoz Unel,37P. E. Karchin,57S. Kartal,15Y. Kato,40Y. Kemp,25R. Kephart,15
U. Kerzel,25V. Khotilovich,51B. Kilminster,38D. H. Kim,27H. S. Kim,23J. E. Kim,27M. J. Kim,11M. S. Kim,27 S. B. Kim,27S. H. Kim,54T. H. Kim,31Y. K. Kim,12B. T. King,29M. Kirby,14L. Kirsch,5S. Klimenko,16B. Knuteson,31 B. R. Ko,14H. Kobayashi,54P. Koehn,38D. J. Kong,27K. Kondo,56J. Konigsberg,16K. Kordas,32A. Korn,31A. Korytov,16
K. Kotelnikov,35A. V. Kotwal,14A. Kovalev,43J. Kraus,23I. Kravchenko,31A. Kreymer,15J. Kroll,43M. Kruse,14 V. Krutelyov,51S. E. Kuhlmann,2S. Kwang,12A. T. Laasanen,46S. Lai,32S. Lami,48S. Lammel,15J. Lancaster,14 M. Lancaster,30R. Lander,6K. Lannon,38A. Lath,50G. Latino,36R. Lauhakangas,21I. Lazzizzera,42Y. Le,24C. Lecci,25 T. LeCompte,2J. Lee,27J. Lee,47S. W. Lee,51R. Lefe`vre,3N. Leonardo,31S. Leone,44S. Levy,12J. D. Lewis,15K. Li,59
C. Lin,59C. S. Lin,15M. Lindgren,15E. Lipeles,8T. M. Liss,23A. Lister,18D. O. Litvintsev,15T. Liu,15Y. Liu,18 N. S. Lockyer,43A. Loginov,35M. Loreti,42P. Loverre,49R-S. Lu,1D. Lucchesi,42P. Lujan,28P. Lukens,15G. Lungu,16
L. Lyons,41J. Lys,28R. Lysak,1D. MacQueen,32R. Madrak,15K. Maeshima,15P. Maksimovic,24L. Malferrari,4 G. Manca,29R. Marginean,38C. Marino,23A. Martin,24M. Martin,59V. Martin,37M. Martı´nez,3T. Maruyama,54 H. Matsunaga,54M. Mattson,57P. Mazzanti,4K. S. McFarland,47D. McGivern,30P. M. McIntyre,51P. McNamara,50
R. NcNulty,29A. Mehta,29S. Menzemer,31A. Menzione,44P. Merkel,15C. Mesropian,48A. Messina,49T. Miao,15 N. Miladinovic,5L. Miller,20R. Miller,34J. S. Miller,33R. Miquel,28S. Miscetti,17G. Mitselmakher,16A. Miyamoto,26
Y. Miyazaki,40N. Moggi,4B. Mohr,7R. Moore,15M. Morello,44P. A. Movilla Fernandez,28A. Mukherjee,15 M. Mulhearn,31T. Muller,25R. Mumford,24A. Munar,43P. Murat,15J. Nachtman,15S. Nahn,59I. Nakamura,43I. Nakano,39
A. Napier,55R. Napora,24D. Naumov,36V. Necula,16F. Niell,33J. Nielsen,28C. Nelson,15T. Nelson,15C. Neu,43 M. S. Neubauer,8C. Newman-Holmes,15T. Nigmanov,45L. Nodulman,2O. Norniella,3K. Oesterberg,21T. Ogawa,56
S. H. Oh,14Y. D. Oh,27T. Ohsugi,22T. Okusawa,40R. Oldeman,49R. Orava,21W. Orejudos,28C. Pagliarone,44 E. Palencia,10R. Paoletti,44V. Papadimitriou,15S. Pashapour,32J. Patrick,15G. Pauletta,53M. Paulini,11T. Pauly,41 C. Paus,31D. Pellett,6A. Penzo,53T. J. Phillips,14G. Piacentino,44J. Piedra,10K. T. Pitts,23C. Plager,7A. Pomposˇ,46 L. Pondrom,58G. Pope,45X. Portell,3O. Poukhov,13F. Prakoshyn,13T. Pratt,29A. Pronko,16J. Proudfoot,2F. Ptohos,17
G. Punzi,44J. Rademacker,41M. A. Rahaman,45A. Rakitine,31S. Rappoccio,20F. Ratnikov,50H. Ray,33B. Reisert,15 V. Rekovic,36P. Renton,41M. Rescigno,49F. Rimondi,4K. Rinnert,25L. Ristori,44W. J. Robertson,14A. Robson,41 T. Rodrigo,10S. Rolli,55L. Rosenson,31R. Roser,15R. Rossin,42C. Rott,46J. Russ,11V. Rusu,12A. Ruiz,10D. Ryan,55 H. Saarikko,21S. Sabik,32A. Safonov,6R. St. Denis,19W. K. Sakumoto,47G. Salamanna,49D. Saltzberg,7C. Sanchez,3
A. Sansoni,17L. Santi,53S. Sarkar,49K. Sato,54P. Savard,32A. Savoy-Navarro,15P. Schlabach,15E. E. Schmidt,15 M. P. Schmidt,59M. Schmitt,37L. Scodellaro,10A. Scribano,44F. Scuri,44A. Sedov,46S. Seidel,36Y. Seiya,40F. Semeria,4
L. Sexton-Kennedy,15I. Sfiligoi,17M. D. Shapiro,28T. Shears,29P. F. Shepard,45D. Sherman,20M. Shimojima,54 M. Shochet,12Y. Shon,58I. Shreyber,35A. Sidoti,44J. Siegrist,28M. Siket,1A. Sill,52P. Sinervo,32A. Sisakyan,13
A. Skiba,25A. J. Slaughter,15K. Sliwa,55D. Smirnov,36J. R. Smith,6F. D. Snider,15R. Snihur,32A. Soha,6 S. V. Somalwar,50J. Spalding,15M. Spezziga,52L. Spiegel,15F. Spinella,44M. Spiropulu,9P. Squillacioti,44H. Stadie,25
B. Stelzer,32O. Stelzer-Chilton,32J. Strologas,36D. Stuart,9A. Sukhanov,16K. Sumorok,31H. Sun,55T. Suzuki,54 A. Taffard,23R. Tafirout,32S. F. Takach,57H. Takano,54R. Takashima,22Y. Takeuchi,54K. Takikawa,54M. Tanaka,2
R. Tanaka,39N. Tanimoto,39S. Tapprogge,21M. Tecchio,33P. K. Teng,1K. Terashi,48R. J. Tesarek,15S. Tether,31 J. Thom,15A. S. Thompson,19E. Thomson,43P. Tipton,47V. Tiwari,11S. Tkaczyk,15D. Toback,51K. Tollefson,34 T. Tomura,54D. Tonelli,44M. To¨nnesmann,34S. Torre,44D. Torretta,15S. Tourneur,15W. Trischuk,32J. Tseng,41 R. Tsuchiya,56S. Tsuno,39D. Tsybychev,16N. Turini,44M. Turner,29F. Ukegawa,54T. Unverhau,19S. Uozumi,54 D. Usynin,43L. Vacavant,28A. Vaiciulis,47A. Varganov,33E. Vataga,44S. Vejcik III,15G. Velev,15V. Veszpremi,46 G. Veramendi,23T. Vickey,23R. Vidal,15I. Vila,10R. Vilar,10I. Vollrath,32I. Volobouev,28M. von der Mey,7P. Wagner,51
R. G. Wagner,2R. L. Wagner,15W. Wagner,25R. Wallny,7T. Walter,25T. Yamashita,39K. Yamamoto,40Z. Wan,50 M. J. Wang,1S. M. Wang,16A. Warburton,32B. Ward,19S. Waschke,19D. Waters,30T. Watts,50M. Weber,28 W. C. Wester III,15B. Whitehouse,55A. B. Wicklund,2E. Wicklund,15H. H. Williams,43P. Wilson,15B. L. Winer,38 P. Wittich,43S. Wolbers,15M. Wolter,55M. Worcester,7S. Worm,50T. Wright,33X. Wu,18F. Wu¨rthwein,8A. Wyatt,30 A. Yagil,15C. Yang,59U. K. Yang,12W. Yao,28G. P. Yeh,15K. Yi,24J. Yoh,15P. Yoon,47K. Yorita,56T. Yoshida,40I. Yu,27
S. Yu,43Z. Yu,59J. C. Yun,15L. Zanello,49A. Zanetti,53I. Zaw,20F. Zetti,44J. Zhou,50A. Zsenei,18and S. Zucchelli4 (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
4Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
5Brandeis University, Waltham, Massachusetts 02254, USA
6University of California at Davis, Davis, California 95616, USA
7University of California at Los Angeles, Los Angeles, California 90024, USA
8University of California at San Diego, La Jolla, California 92093, USA
9University of California at Santa Barbara, Santa Barbara, California 93106, USA
10Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
11Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 , USA
12Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
14Duke University, Durham, North Carolina 27708
15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
16University of Florida, Gainesville, Florida 32611, USA
17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
18University of Geneva, CH-1211 Geneva 4, Switzerland
19Glasgow University, Glasgow G12 8QQ, United Kingdom
20Harvard University, Cambridge, Massachusetts 02138, USA
21The Helsinki Group: Helsinki Institute of Physics; and Division of High Energy Physics, Department of Physical Sciences, University of Helsinki, FIN-00044, Helsinki, Finland
D. ACOSTA et al. PHYSICAL REVIEW D71,051103 (2005)
051103-2
22Hiroshima University, Higashi-Hiroshima 724, Japan
23University of Illinois, Urbana, Illinois 61801, USA
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
31Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
32Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7
33University of Michigan, Ann Arbor, Michigan 48109, USA
34Michigan State University, East Lansing, Michigan 48824, USA
35Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
36University of New Mexico, Albuquerque, New Mexico 87131, USA
37Northwestern University, Evanston, Illinois 60208, USA
38The Ohio State University, Columbus, Ohio 43210, USA
39Okayama University, Okayama 700-8530, Japan
40Osaka City University, Osaka 588, Japan
41University of Oxford, Oxford OX1 3RH, United Kingdom
42University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
44Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 Pisa, Italy
45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
46Purdue University, West Lafayette, Indiana 47907, USA
47University of Rochester, Rochester, New York 14627, USA
48The Rockefeller University, New York, New York 10021, USA
49Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University di Roma ‘‘La Sapienza,’’ I-00185 Roma, Italy
50Rutgers University, Piscataway, New Jersey 08855, USA
51Texas A&M University, College Station, Texas 77843, USA
52Texas Tech University, Lubbock, Texas 79409, USA
53Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy
54University of Tsukuba, Tsukuba, Ibaraki 305, Japan
55Tufts University, Medford, Massachusetts 02155, USA
56Waseda University, Tokyo 169, Japan
57Wayne State University, Detroit, Michigan 48201, USA
58University of Wisconsin, Madison, Wisconsin 53706, USA
59Yale University, New Haven, Connecticut 06520, USA (Received 1 February 2005; published 18 March 2005)
Using 180pb1of data collected with the CDF II detector at the Tevatron, we measure the first two moments of the hadronic invariant mass-squared distribution in charmed semileptonicBdecays. From these we determine the nonperturbative Heavy Quark Effective Theory parametersand1used to relate the B meson semileptonic branching ratio to the CKM matrix element jVcbj. For a minimum lepton momentum of 0.7 GeV/cin the B rest frame we measure the first two moments of the D!D component to be hm2Di 5:830:16stat0:08systGeV2=c4 and hm2D hm2Di2i 1:30 0:69stat0:22systGeV4=c8. Combining these with the discrete mass terms from theDandDmesons, we find the total moments to be hM2X
ci m2D 0:4670:038stat0:068systGeV2=c4 and hM2X
c
hM2X
ci2i 1:050:26stat0:13systGeV4=c8, wheremDis the spin-averagedDmass. The systematic error is dominated by the uncertainties in the world-average branching ratios used to combine theD,D, andDcontributions. The analysis makes no assumptions about the shape or resonant structure of the D!Dinvariant mass distribution.
DOI: 10.1103/PhysRevD.71.051103 PACS numbers: 13.20.He, 12.15.Hh, 12.39.Hg
I. INTRODUCTION
In order to constrain the length of the side opposite the anglein the Cabibbo-Kobayashi-Maskawa (CKM) uni- tarity triangle, a precise measurement of the ratio
jVubj=jVcbjis needed. The matrix elementjVcbjis gener- ally extracted from semileptonic B decays. Currently, the most precise method is based on the measurement of the inclusive semileptonic partial width into charm,
sl B!Xcll. The Operator Product Expansion (OPE) applied to Heavy Quark Effective Theory (HQET) relates the experimental determination ofsltojVcbj[1,2].
The relationship takes the form of an expansion in inverse powers of theBmass,mB. At each order in the expansion, new free nonperturbative parameters enter: one () at order 1=mB, two (1 and2) at order1=m2B, six at order 1=m3B, etc. In order to extractjVcbjfromslsome external information on these parameters is needed.
The same theoretical framework that predicts the value of sl predicts the value of any weighted integral of the differential ratedsl=dsH, provided the weight is a smooth function ofsH MX2
c. Using weight functionssHm2D andsH hsHi2, withmD 0:25mD0:75mD, one can define the first two moments of the hadronic mass distri- bution:
M1 ZsmaxH
sminH
dsHsHm2D 1 sl
dsl dsH;
M2 ZsmaxH
sminH
dsHsH hsHi2 1 sl
dsl dsH ;
(1)
which are simply the shifted mean and variance of theM2X
c
distribution in semileptonic charmed decays ofBmesons.
The moments are not sensitive tojVcbj, but they are more sensitive to the nonperturbative parameters of HQET than slitself is. Therefore, measuring the moments provides a useful constraint on the HQET parameters which improves the overall precision onjVcbjas determined fromsl. This is the purpose of this analysis. Since2is well determined from the values of the hyperfine mass splittings in theB andDmeson systems [2], onlyand1 are studied here.
ThesHdistribution inB!X0clldecays can be split into three contributions corresponding to Xc0 D0; D0; D0. Here D0 stands for any neutral charmed state, resonant or not, other thanD0,D0. The differential mass-squared spectrum can be written as:
1 sl
dsl dsH
0
slsH m2D0
slsHm2D0
10
sl
sl
fsH; (2) whereslis now the inclusiveBsemileptonic width,0 and are the exclusiveB partial widths toD0lland D0llrespectively, and fsH is the normalized had- ronic invariant mass-squared distribution in theD0chan- nel. We use world-average values of 0=sl,=sl, mD0 andmD0from the Particle Data Group [3] and concentrate on measuringfsH. In this way, we have only to mea- sure the invariant mass distribution for theD0component without having to determine theD0,D0components or the relative normalizations between those and theD0 chan- nel. TheD0 spectrum is not well known, and includes, at
least, two narrow and two wide states, together with a possible nonresonant Dn contribution. The measure- ment of theD0spectrum is the main task of this analysis.
We assume that the Dlldecays of B saturate the difference between its inclusive semileptonic decay rate and the sum of its exclusive decay rates to D0ll and D0ll. We neglect all modes with additional pions in the final state, as well asD0 !Ds K.
Only D decays (charge conjugated channels are implicitly included throughout the paper) are recon- structed. Contributions to thesH distribution from decays with neutral particles are included by applying isospin factors to the charged modes. Feed-down from one channel to another due to unmeasured neutral particles is subtracted statistically using the data themselves and isospin rela- tions, as explained in Sec. III.
II. DATA ANALYSIS
The analysis uses a data sample ofppcollisions at ps 1:96 TeVwith an integrated luminosity of about180 pb1, collected between February 2002 and August 2003 with the upgraded Collider Detector at the Fermilab Tevatron (CDF II). A description of the detector can be found in [4].
The relevant components for this analysis include a track- ing system composed of a silicon strip vertex detector (SVX II) surrounded by an open cell drift chamber system (COT). The SVX II detector comprises five concentric layers of double-sided sensors located at radii between 2.5 and 10.6 cm, while the COT provides 96 measurements (including axial and stereo) out to a radius of 132 cm. The central tracking system is immersed in a 1.4 T solenoidal magnetic field. Two sampling calorimeters surround the magnetic coil. A set of proportional chambers inside the electromagnetic calorimeter provides information on the shower profile for use in electron identification. Muon candidates are identified with two sets of multilayer drift chambers, one located outside the calorimeters and the other behind an additional 60 cm-thick iron shield.
DecaysB!DlX, wherelstands for electron or muon, were recorded using a trigger that requires a leptonl and a track displaced from the interaction point [5]. The lepton and the displaced track must have transverse mo- mentumpTin excess of 4 GeV/cand 2 GeV/crespectively.
The displaced track’s impact parameter with respect to the beamline has to exceed 120 m and be below 1 mm.
Events which pass the trigger are recorded for further analysis. Only well-reconstructed tracks with pT 0:4 GeV=c are retained. Track parameters are corrected for the ionization energy loss appropriate to the mass hypothesis under consideration. A Monte Carlo sample of B!Dll events based on the ISGW2 [6] and Goity-Roberts [7] matrix elements and including a detailed simulation of the CDF II detector based on the GEANT [8]
package has been used throughout the analysis. In accor-
D. ACOSTA et al. PHYSICAL REVIEW D71,051103 (2005)
051103-4
dance with our assumption, onlyD!Ddecays are generated.
Events withD!D0l andDl combinations are reconstructed in the decay channels D0 ! K; K; K0 and D!K. Tracks with the appropriate charge combination are re- quired to be consistent with a common vertex in three dimensions. One of the tracks in the vertex must fulfill the displaced trigger requirements. Suitable ranges are selected in the D0 (1.84 –1.89 GeV/c2) and D (1.84 – 1.89 GeV/c2) mass distributions. For theDchannel, an additional charged track () is required, such that the MD0 MD0 mass-difference lies between 0.142
and 0.147 GeV/c2. TheD0 !K0 channel is recon- structed from the satellite peak in the K mass distri- bution (1.50 –1.70 GeV/c2). In this case the MK MK mass-difference is required to be between 0.142 and 0.155 GeV/c2. Duplicate removal is performed in theD0!Kchannel: when two Dcandidates share all five tracks, differing only in the kaon mass assignment, the candidate with the K mass closer to the nominal D0 mass is re- tained. No attempt has been made to further identify kaons and pions.
After the selection of Dl and Dl combi- nations, we obtain 389063,299457,663898and
2) m* (GeV/c
∆
0.14 0.15 0.16 0.17 0.18
)2 events / (0.5 MeV/c
0 500 1000 1500 2000 2500
2) m* (GeV/c
∆
0.14 0.15 0.16 0.17 0.18
)2 events / (0.5 MeV/c
0 500 1000 1500 2000 2500
π+
D0
→ D*+
π+
π -
π+
, K-
π+
K-
→ D0
) π0
( π+
K-
→ D0
CDF Run II L=180pb-1
- X
+l
→ D*
B
sideband
2) ) (GeV/c π+
π+
m(K-
1.7 1.8 1.9 2
)2 events / (0.5 MeV/c
0 1000 2000 3000 4000 5000
2) ) (GeV/c π+
π+
m(K-
1.7 1.8 1.9 2
)2 events / (0.5 MeV/c
0 1000 2000 3000 4000 5000
π+
π+
K-
→ D+
CDF Run II L=180pb-1 - X
+l
→ D B
sideband sideband
FIG. 1. Left: Mass-differencem MD0 MD0in theD0!KandD0!Kchannels (narrow peak) and m MK MKin theD0!K0 channel (broad peak). Right: Mass distribution for theD!K channel. The signal areas are shaded; side-band regions are also indicated.
2) ) (GeV/c π**
m(D*+
2 2.2 2.4 2.6 2.8 3 3.2 3.4
)2 yield / (20 MeV/c
0 10 20 30 40 50
- **
π D*+
right-sign l- +
π**
D*+
wrong-sign l- CDF Run II L=180pb-1
- X
**l π D*+
→ B
2) ) (GeV/c π**
m(D+
2 2.2 2.4 2.6 2.8 3 3.2 3.4
)2 yield / (20 MeV/c
-5 0 5 10 15 20 25 30
- **
π D+
right-sign l- +
π**
D+
wrong-sign l- CDF Run II L=180pb-1
- X
**l π D+
→ B
FIG. 2. Side-band-subtracted invariant mass distribution for theDchannels (left) and for theDchannel (right). The mass regions shown are limited at 3.5 GeV=c2for illustration only. No explicit mass cut is applied in the analysis.
14416202 signal events in the K, K, K0 and K channels, respectively.
Combinatorial backgrounds, estimated from side-bands of the MD and MD0 MD0 distributions, have been subtracted. The quoted yield in theD channel has been rescaled by a factor 0.96 to account for the background fromDs !KK decays where theK is assigned the pion mass. Figure 1 shows on the left the MD0 MD0 distributions for D0 decaying into either K or K, and for D0 !K0 , while theD!K mass distribution is plotted on the right.
The Dl vertex (the B vertex) is reconstructed in three dimensions and required to be at least 500m away from the beam line. An additional pion () is then added to create fullDlcandidates. The’s trajectory is required to be at most 2.5 standard deviations away from theBvertex, and at least 3 standard deviations away from the beam line. These cuts were optimized using theB! DllMonte Carlo for the signal, and wrong-signl combinations in data for the background. The measured mass distributions in theDandDchannels are shown in Fig. 2.
III. BACKGROUND AND EFFICIENCY CORRECTIONS
The most important background sources are combinato- rial background under theDandD mass peaks, prompt tracks (from fragmentation or the underlying event) that fake candidates, and feed-down from D!D0 decays into the D channel. Data side-bands are used to assess combinatorial background under theD mass and D–D0 mass-difference peaks, and wrong-sign l combinations in data to characterize the prompt back- ground to thecandidates. The wrong-sign pion-lepton sample is subtracted from the right-sign sample, after performing side-band subtraction in both. A possible dif- ference between the rate of prompt background with the right and the wrongcharge has been studied with a sample of fully reconstructed B decays (B ! J=K; B0!D; B !D0) and found to be at most4%. This has been included in the systematic error.
The bias in the background subtraction introduced by using the same wrong-sign sample for both the optimization of the selection and the final background subtraction has been studied using bootstrap [9] copies of the data and found to be smaller than15%of the statistical error on the moments.
This upper bound on the bias has been added as an addi- tional systematical error.
Since we do not reconstruct neutral particles, events with a decay B!Dll with the D decaying into D0 constitute an irreducible background to the signal channel B !Dll. Using isospin symmetry, the background rate andDinvariant mass can be obtained
from theD0 invariant mass inB!Dllde- cays withD!D0, which we fully reconstruct, after correcting for the relative efficiency using Monte Carlo. A small physics background (around 1% in rate), coming mostly from B!Ds D decays with theDs decaying semileptonically, is subtracted using Monte Carlo predic- tions. Background from tracks faking a lepton has been studied by looking at wrong-signDlcombinations. It has been found that the background subtraction procedure outlined above effectively removes any such background.
Finally, the background from B!D decays has been studied with Monte Carlo and found to have a negli- gible effect on the determination of the moments.
Since only the shape of the mass-squared distribution for theDcomponent (fsHin Eq. (2)) is being measured, the relevant efficiency corrections are those that can bias the mass-squared distribution, along with the relative effi- ciency for theDandD components of theD piece.
Both efficiencies are obtained, as a function of the mass MD, from the Monte Carlo simulation. We have checked the Monte Carlo relative efficiency predictions as a function of thetransverse momentum by applying the selection cuts to decay tracks from D and D mesons. The efficiency variation in the data agrees well with the simulation. Where small differences have been found, corrections have been derived from these Monte Carlo –data comparisons.
To compare the moments with theoretical predictions, they must be measured with a well defined cut onpl, the lepton momentum in the B rest frame. Since we do not attempt to measure the boost of theB, we cannot accesspl directly in data. Instead, acceptance corrections are derived from Monte Carlo that turn our gradual trigger turn-on as a function of pl into a sharp threshold atpl 0:7 GeV/c, thereby correcting our measurement of the moments to a cut pl >0:7GeV/c. The value 0:7 GeV/cwas chosen in order to minimize the correction. Because of the negative correlation between lepton momentum in theBrest frame and D mass, the correction itself can depend on the detailed D mass spectrum in Monte Carlo. In order to assess the possible systematic error, the default B decay model has been compared to a naı¨ve phase-spaceBsemi- leptonic decay model. The differences in the ensuing cor- rection factors as a function of MDare considered as systematic errors.
IV. RESULTS
TheD mass distribution is shown in Fig. 3 after background subtraction and efficiency and acceptance cor- rections. The first and second moments of theDcompo- nent of the mass-squared distribution, m1 and m2, are determined by simply computing the mean and variance of the distribution shown in Fig. 3, without any assumption
D. ACOSTA et al. PHYSICAL REVIEW D71,051103 (2005)
051103-6
about the shape or rate of its several components:
m1 hm2Di 5:830:16stat0:08systGeV2=c4 m2 hm2D hm2Di2i
1:300:69stat0:22syst GeV4=c8;
with a61%positive correlation. The full moments of the hadronic mass-squared distribution,M1andM2, are deter- mined by combiningm1andm2with theDandDpieces, obtained from world-average values [3]:
M1 hM2X
ci m2D
0:4670:038stat0:019exp0:065BRGeV2=c4 M2 hM2X
c hMX2
ci2i
1:050:26stat0:08exp0:10BRGeV4=c8; with a69%positive correlation betweenM1andM2. Here
‘‘BR’’ refers to the uncertainty coming from the branching ratios needed for the combination of the D, D and D pieces. For the exclusive branching ratios toDandD, all available information [3] coming from charged and neutral B decays has been combined using isospin invariance, leading to0=sl 0:2030:015and=sl 0:550 0:026 with about 30% positive correlation. The isospin- related partial widths (not the branching ratios) ofBand B0 are assumed to be identical.
Finally, using the predictions in [2], the HQET parame- tersand1are determined. After applying constraints on the other HQET parameters coming from the knownBand D hyperfine mass splittings we find, in the pole scheme:
pole 0:3970:078stat0:027exp0:064BR
0:058theo GeV and pole1 0:1840:057stat 0:017exp0:022BR0:077theoGeV2, with a 79%nega- tive correlation. Similarly, we extract the equivalent HQET parameters in the 1S scheme: m1Sb M$=21S 4:6540:078stat0:027exp0:064BR0:089theoGeV and 1S1 0:2770:049stat0:017exp0:022BR 0:094theo GeV2, with a77%positive correlation.
The statistical and systematic errors in the extraction of the D moments, the full moments, and the HQET pa- rameters in the pole-mass scheme are presented in Table I.
Statistical errors dominate the measurements ofm1andm2 while experimental systematic errors are all smaller. The main experimental systematics are computed from the differences in the results when we apply or omit a correc- tion for the60 MeV=c2mass resolution in theK0 channel or the MD-dependent efficiency correction from data. Similarly, we considered the difference in re- sults obtained using Monte Carlo efficiency and accep- tance corrections calculated with ISGW2 and Goity- Roberts matrix elements or phase-space as a systematic error. Other experimental systematics include uncertainties on the level of the prompt background (studied with a fully reconstructedBsample), a possible bias due to having used the same data sample to model the background in the optimization process and to subtract the background from the data (studied by repeating the optimization on boot- strap copies of the data), and uncertainties onDbranching fractions used in the analysis.
Uncertainties in the inclusive and exclusive semilep- tonicBbranching ratios become important when combin- ingm1andm2with theD0andD0pieces to obtainM1and M2, the moments of the entire charm mass distribution.
Theoretical uncertainties become dominant in the extrac- tion of the HQET parameters and1. The largest con- tribution to the theoretical systematic error is that estimated by varying the unknown third order HQET pa- rameters in the ranges 1 120:5 GeV3120:5 GeV3, Ti 0:0 GeV3 0:5 GeV3. Finally, acceptance cor- rections have been computed for two alternative pl cuts, 0.5 and 0.9 GeV/c. The moments obtained this way are different physical quantities and numerically different from those obtained for the default pl cut at 0.7 GeV/c.
However, if HQET describes the data, they should all lead to compatible values of the HQET parameters. The three sets of parameters are found to be equal within errors.
Differences between them have been considered as addi- tional systematic uncertainties.
In summary, we have presented a measurement of the first two moments of the hadronic mass-squared distribu- tion in semileptonic Bdecays to charm by combining our measurement of the D mass spectrum with the known masses and branching ratios toDlandDltaken from the Particle Data Group compilation [3]. These chan- nels together are assumed to fully account for the inclusive semileptonic decay width ofBmesons to charm. The mo-
2) ) (GeV/c π -
m(D(*)+
2 2.5 3 3.5 4 4.5 5
)2 yield / (20 MeV/c
-20 0 20 40 60 80
CDF Run II L=180pb-1
νl
l -
π -
*)+
D( - → B
FIG. 3. Fully corrected invariant mass distribution mD. The number of events in each bin has been back- ground subtracted and corrected for mass-dependent andD=D relative efficiency corrections. The plotted errors take into account all corrections and subtractions.
