Study of D0–D̄0 mixing and D0 doubly Cabibbo-suppressed decays

17 September 1998

Ž .Physics Letters B 436 1998 211–221

0 0Study of D –D mixingand D0 doubly Cabibbo-suppressed decays

ALEPH Collaboration

R. Barate a, D. Buskulic a, D. Decamp a, P. Ghez a, C. Goy a, J.-P. Lees a,A. Lucotte a, E. Merle a, M.-N. Minard a, J.-Y. Nief a, B. Pietrzyk a,

R. Alemany b, G. Boix b, M.P. Casado b, M. Chmeissani b, J.M. Crespo b,M. Delfino b, E. Fernandez b, M. Fernandez-Bosman b, Ll. Garrido b,1,E. Grauges b,`

A. Juste b, M. Martinez b, G. Merino b, R. Miquel b, Ll.M. Mir b,I.C. Park b,A. Pascual b, I. Riu b, F. Sanchez b, A. Colaleo c, D. Creanza c, M. de Palma c,

G. Gelao c, G. Iaselli c, G. Maggi c, M. Maggi c, S. Nuzzo c, A. Ranieri c, G. Raso c,F. Ruggieri c, G. Selvaggi c, L. Silvestris c, P. Tempesta c, A. Tricomi c,2,

G. Zito c, X. Huang d, J. Lin d, Q. Ouyang d, T. Wang d, Y. Xie d, R. Xu d, S. Xue d,J. Zhang d, L. Zhang d, W. Zhao d, D. Abbaneo e, U. Becker e, P. Bright-Thomas e,3,

D. Casper e, M. Cattaneo e, F. Cerutti e, V. Ciulli e, G. Dissertori e,H. Drevermann e, R.W. Forty e, M. Frank e, R. Hagelberg e, A.W. Halley e,

J.B. Hansen e, J. Harvey e, P. Janot e, B. Jost e, I. Lehraus e, P. Mato e, A. Minten e,L. Moneta e,4, A. Pacheco e, F. Ranjard e, L. Rolandi e, D. Rousseau e, D. Schlatter e,

M. Schmitt e,5, O. Schneider e, W. Tejessy e, F. Teubert e, I.R. Tomalin e,H. Wachsmuth e, Z. Ajaltouni f, F. Badaud f, G. Chazelle f, O. Deschamps f,A. Falvard f, C. Ferdi f, P. Gay f, C. Guicheney f, P. Henrard f, J. Jousset f,

B. Michel f, S. Monteil f, J-C. Montret f, D. Pallin f, P. Perret f, F. Podlyski f,J. Proriol f, P. Rosnet f, J.D. Hansen g, J.R. Hansen g, P.H. Hansen g, B.S. Nilsson g,

B. Rensch g, A. Waananen g, G. Daskalakis h, A. Kyriakis h, C. Markou h,¨¨ Ë. Simopoulou h, I. Siotis h, A. Vayaki h, A. Blondel i, G. Bonneaud i, J.-C. Brient i,

P. Bourdon i, A. Rouge i, M. Rumpf i, A. Valassi i,6, M. Verderi i, H. Videau i,É. Focardi j, G. Parrini j, K. Zachariadou j, M. Corden k, C. Georgiopoulos k,

D.E. Jaffe k, A. Antonelli l, G. Bencivenni l, G. Bologna l,7, F. Bossi l, P. Campana l,G. Capon l, V. Chiarella l, G. Felici l, P. Laurelli l, G. Mannocchi l,8, F. Murtas l,

G.P. Murtas l, L. Passalacqua l, M. Pepe-Altarelli l, L. Curtis m, J.G. Lynch m,P. Negus m, V. O’Shea m, C. Raine m, J.M. Scarr m, K. Smith m, P. Teixeira-Dias m,

0370-2693r98r$ - see front matter q 1998 Elsevier Science B.V. All rights reserved.Ž .PII: S0370-2693 98 00946-0

( )R. Barate et al.rPhysics Letters B 436 1998 211–221212

A.S. Thompson m, E. Thomson m, O. Buchmuller n, S. Dhamotharan n,¨C. Geweniger n, G. Graefe n, P. Hanke n, G. Hansper n, V. Hepp n, E.E. Kluge n,A. Putzer n, J. Sommer n, K. Tittel n, S. Werner n, M. Wunsch n, R. Beuselinck o,

D.M. Binnie o, W. Cameron o, P.J. Dornan o,9, M. Girone o, S. Goodsir o,E.B. Martin o, N. Marinelli o, A. Moutoussi o, J. Nash o, J.K. Sedgbeer o,

P. Spagnolo o, M.D. Williams o, V.M. Ghete p, P. Girtler p, E. Kneringer p,D. Kuhn p, G. Rudolph p, A.P. Betteridge q, C.K. Bowdery q,

P.G. Buck q, P. Colrain q, G. Crawford q, A.J. Finch q, F. Foster q, G. Hughes q,R.W.L. Jones q, N.A. Robertson q, M.I. Williams q, I. Giehl r, C. Hoffmann r,

K. Jakobs r, K. Kleinknecht r, G. Quast r, B. Renk r, E. Rohne r, H.-G. Sander r,P. van Gemmeren r, C. Zeitnitz r, J.J. Aubert s, C. Benchouk s, A. Bonissent s,

G. Bujosa s, J. Carr s,9, P. Coyle s, F. Etienne s, O. Leroy s, F. Motsch s, P. Payre s,M. Talby s, A. Sadouki s, M. Thulasidas s, K. Trabelsi s, M. Aleppo t, M. Antonelli t,

F. Ragusa t, R. Berlich u, V. Buscher u, G. Cowan u, H. Dietl u, G. Ganis u,¨G. Lutjens u, C. Mannert u, W. Manner u, H.-G. Moser u, S. Schael u, R. Settles u,¨ ¨

H. Seywerd u, H. Stenzel u, W. Wiedenmann u, G. Wolf u, J. Boucrot v, O. Callot v,S. Chen v, A. Cordier v, M. Davier v, L. Duflot v, J.-F. Grivaz v, Ph. Heusse v,

A. Hocker v, A. Jacholkowska v, D.W. Kim v,10, F. Le Diberder v, J. Lefrancois v,Ä.-M. Lutz v, M.-H. Schune v, E. Tournefier v, J.-J. Veillet v, I. Videau v,D. Zerwas v, P. Azzurri w, G. Bagliesi w,9, G. Batignani w, S. Bettarini w,T. Boccali w, C. Bozzi w, G. Calderini w, M. Carpinelli w, M.A. Ciocci w,

R. Dell’Orso w, R. Fantechi w, I. Ferrante w, L. Foa w,11, F. Forti w, A. Giassi w,`M.A. Giorgi w, A. Gregorio w, F. Ligabue w, A. Lusiani w, P.S. Marrocchesi w,

A. Messineo w, F. Palla w, G. Rizzo w, G. Sanguinetti w, A. Sciaba w,`G. Sguazzoni w, R. Tenchini w, G. Tonelli w,12, C. Vannini w, A. Venturi w,

P.G. Verdini w, G.A. Blair x, L.M. Bryant x, J.T. Chambers x, M.G. Green x,T. Medcalf x, P. Perrodo x, J.A. Strong x, J.H. von Wimmersperg-Toeller x,

D.R. Botterill y, R.W. Clifft y, T.R. Edgecock y, P.R. Norton y, J.C. Thompson y,A.E. Wright y, B. Bloch-Devaux z, P. Colas z, S. Emery z, W. Kozanecki z,

E. Lancon z,9, M.-C. Lemaire z, E. Locci z, P. Perez z, J. Rander z,J.-F. Renardy z, A. Roussarie z, J.-P. Schuller z, J. Schwindling z, A. Trabelsi z,

B. Vallage z, S.N. Black aa, J.H. Dann aa, R.P. Johnson aa, H.Y. Kim aa,N. Konstantinidis aa, A.M. Litke aa, M.A. McNeil aa, G. Taylor aa, C.N. Booth ab,S. Cartwright ab, F. Combley ab, M.S. Kelly ab, M. Lehto ab, L.F. Thompson ab,

K. Affholderbach ac, A. Bohrer ac, S. Brandt ac, C. Grupen ac, P. Saraiva ac,¨L. Smolik ac, F. Stephan ac, G. Giannini ad, B. Gobbo ad, G. Musolino ad,

J. Rothberg ae, S. Wasserbaech ae, S.R. Armstrong af, E. Charles af, P. Elmer af,D.P.S. Ferguson af, Y. Gao af, S. Gonzalez af, T.C. Greening af, O.J. Hayes af,´

( )R. Barate et al.rPhysics Letters B 436 1998 211–221 213

H. Hu af, S. Jin af, P.A. McNamara III af, J.M. Nachtman af,13, J. Nielsen af,W. Orejudos af, Y.B. Pan af, Y. Saadi af, I.J. Scott af, J. Walsh af,

Sau Lan Wu af, X. Wu af, G. Zobernig af

a ( )Laboratoire de Physique des Particules LAPP , IN2P3-CNRS, F-74019 Annecy-le-Vieux Cedex, Franceb ´ 14( )Institut de Fisica d’Altes Energies, UniÕersitat Autonoma de Barcelona, E-08193 Bellaterra Barcelona , Spain`

c Dipartimento di Fisica, INFN Sezione di Bari, I-70126 Bari, Italyd Institute of High-Energy Physics, Academia Sinica, Beijing, People’s Republic of China 15

e ( )European Laboratory for Particle Physics CERN , CH-1211 GeneÕa 23, Switzerlandf Laboratoire de Physique Corpusculaire, UniÕersite Blaise Pascal, IN2P3-CNRS, Clermont-Ferrand, F-63177 Aubiere, France´ `

g Niels Bohr Institute, DK-2100 Copenhagen, Denmark 16

h ( )Nuclear Research Center Demokritos NRCD , GR-15310 Attiki, Greecei Laboratoire de Physique Nucleaire et des Hautes Energies, Ecole Polytechnique, IN2P3-CNRS, F-91128 Palaiseau Cedex, France´

j Dipartimento di Fisica, UniÕersita di Firenze, INFN Sezione di Firenze, I-50125 Firenze, Italy`k Supercomputer Computations Research Institute, Florida State UniÕersity, Tallahassee, FL 32306-4052, USA 17,18

l ( )Laboratori Nazionali dell’INFN LNF-INFN , I-00044 Frascati, Italym Department of Physics and Astronomy, UniÕersity of Glasgow, Glasgow G12 8QQ, United Kingdom 19

n Institut fur Hochenergiephysik, UniÕersitat Heidelberg, D-69120 Heidelberg, Germany 2 0¨ ö Department of Physics, Imperial College, London SW7 2BZ, United Kingdom 19

p Institut fur Experimentalphysik, UniÕersitat Innsbruck, A-6020 Innsbruck, Austria 21¨ ¨q Department of Physics, UniÕersity of Lancaster, Lancaster LA1 4YB, United Kingdom 19

r Institut fur Physik, UniÕersitat Mainz, D-55099 Mainz, Germany 2 0¨ ¨s Centre de Physique des Particules, Faculte des Sciences de Luminy, IN2P3-CNRS, F-13288 Marseille, France´

t Dipartimento di Fisica, UniÕersita di Milano e INFN Sezione di Milano, I-20133 Milano, Italyù Max-Planck-Institut fur Physik, Werner-Heisenberg-Institut, D-80805 Munchen, Germany 2 0¨ ¨

v Laboratoire de l’Accelerateur Lineaire, UniÕersite de Paris-Sud, IN2P3-CNRS, F-91898 Orsay Cedex, France´ ´ ´ ´w Dipartimento di Fisica dell’UniÕersita, INFN Sezione di Pisa, e Scuola Normale Superiore, I-56010 Pisa, Italy`

x Department of Physics, Royal Holloway & Bedford New College, UniÕersity of London, Surrey TW20 OEX, United Kingdom 19

y Particle Physics Dept., Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 OQX, United Kingdom 19

z CEA, DAPNIArSerÕice de Physique des Particules, CE-Saclay, F-91191 Gif-sur-YÕette Cedex, France 22

aa Institute for Particle Physics, UniÕersity of California at Santa Cruz, Santa Cruz, CA 95064, USA 23

ab Department of Physics, UniÕersity of Sheffield, Sheffield S3 7RH, United Kingdom 19

ac Fachbereich Physik, UniÕersitat Siegen, D-57068 Siegen, Germany 2 0äd Dipartimento di Fisica, UniÕersita di Trieste e INFN Sezione di Trieste, I-34127 Trieste, Italyàe Experimental Elementary Particle Physics, UniÕersity of Washington, WA 98195 Seattle, USA

af Department of Physics, UniÕersity of Wisconsin, Madison, WI 53706, USA 24

Received 20 July 1998Editor: L. Montanet

Abstract

Using a sample of four million hadronic Z events collected in ALEPH from 1991 to 1995, the decays D)q™D0pq, withs0 y q q y Ž 0 q y. Ž 0 y q.D decaying to K p or to K p , are studied. The relative branching ratio B D ™K p rB D ™K p is

measured to be 1.84"0.59 stat. "0.34 syst. %. The two possible contributions to the D0 ™Kqpy decay, doublyŽ . Ž .Ž .0 0Cabibbo-suppressed decays and D –D mixing, are disentangled by measuring the proper-time distribution of the

reconstructed D0’s. Assuming no interference between the two processes, the upper limit obtained on the mixing rate is0.92% at 95% CL. The possible effect of interference between the two amplitudes is also assessed. q 1998 Elsevier ScienceB.V. All rights reserved.


1. Introduction

The D0 can produce a Kqpy system either via aŽ .doubly Cabibbo-suppressed decay DCSD or via the

0 0oscillation of the D into a D followed by the0 q yCabibbo-favoured decay D ™K p . The rate of

DCSD processes D0 ™Kqpy is expected to be of4 w xthe order of 2tan u ;0.6% 1 , where u is theC C

Cabibbo angle. Within the framework of the Stan-0 0dard Model the D –D mixing rate R is expectedmix

w xto be well below present experimental bounds 2,3 .While short distance effects from box diagrams are

Ž y10.known to give a small contribution R ;10mix

1 Permanent address: Universitat de Barcelona, 08208Barcelona, Spain.

2 Also at Dipartimento di Fisica, INFN, Sezione di Catania,Catania, Italy.

3 Now at School of Physics and Astronomy, Birmingham B152TT, U.K.

4 Now at University of Geneva, 1211 Geneva 4, Switzerland.5 Now at Harvard University, Cambridge, MA 02138, USA.6 Supported by the Commission of the European Communities,

contract ERBCHBICT941234.7 Also Istituto di Fisica Generale, Universita di Torino, Torino,`

Italy.8 Also Istituto di Cosmo-Geofisica del C.N.R., Torino, Italy.9 Also at CERN, 1211 Geneva 23, Switzerland.

10 Permanent address: Kangnung National University, Kang-nung, Korea.

11 Now at CERN, 1211 Geneva 23, Switzerland.12 Also at Istituto di Matematica e Fisica, Universita di Sassari,`

Sassari, Italy.13 Ž .Now at University of California at Los Angeles UCLA , Los

Angeles, CA 90024, USA.14 Supported by CICYT, Spain.15 Supported by the National Science Foundation of China.16 Supported by the Danish Natural Science Research Council.17 Supported by the US Department of Energy, contract DE-

FG05-92ER40742.18 Supported by the US Department of Energy, contract DE-

FC05-85ER250000.19 Supported by the UK Particle Physics and Astronomy Re-

search Council.20 Supported by the Bundesministerium fur Bildung, Wis-¨

senschaft, Forschung und Technologie, Germany.21 Supported by Fonds zur Forderung der wissenschaftlichen¨

Forschung, Austria.22 Supported by the Direction des Sciences de la Matiere, C.E.A.`23 Supported by the US Department of Energy, grant DE-FG03-

92ER40689.24 Supported by the US Department of Energy, grant DE-

FG0295-ER40896.

w x4 , long distance effects from second-order weakinteractions with mesonic intermediate states maygive a much larger contribution but are subject to

Ž y7 y3.large theoretical uncertainties R ;10 y10mixw x5 .

There are many extensions of the Standard Model0 0which allow a D –D mixing rate significantly larger

than the Standard Model prediction, for examplemodels with leptoquarks, with two-Higgs-doublet,with fourth quark generation and supersymmetric

w xmodels with alignment 6,7 . Experimental evidencefor mixing within the current experimental sensitiv-ity would therefore be an indication of new physics.

The search for DCSD or mixing necessitates theidentification of a change in the charm quantumnumber between production and decay of the D0.The method presented here consists of reconstructingthe D)q™D0pq decay where the charge of thes

0 0slow pion indicates whether a D or a D is pro-duced. The charge of the kaon in the subsequentD0 ™Kp decay tags the charm flavour at decay.The relative contributions of the DCSD process and

0 0the D –D mixing are assessed by studying theproper-time distribution of the reconstructed D0’s.

2. ALEPH detector and data selection

This analysis uses data collected in the vicinity ofthe Z peak from 1991 to 1995 with the ALEPHdetector at the LEP electron-positron storage ring.The data sample consists of about four million

w xhadronic Z decays that satisfy the criteria of Ref. 8 .A detailed description of the design and perfor-

w xmance of the apparatus can be found in Refs. 9,10 ,and only a brief summary of the features relevant tothis study is given here. A double-sided silicon

Ž .vertex detector VDET , surrounding the beam pipe,is installed close to the interaction region. The sin-gle-hit resolution for the rf and z projections is 12mm. Outside the vertex detector are an eight-layer

Ž .drift chamber, the inner tracking chamber ITC , andŽ .a large time projection chamber TPC . These three

detectors form the tracking system, which is im-mersed in a 1.5 T axial magnetic field. Using theVDET, ITC and TPC coordinates the particle mo-mentum transverse to the beam axis is measured


with a resolution of d p rp s6=10y4 p [5=T T Ty3 Ž .10 p in GeVrc .T

The TPC also provides up to 338 measurementsof the specific ionization of a charged particle. In thefollowing, the dErdx information is considered asavailable if more than 50 samples are present. Parti-cle identification is based on the dErdx estimators

Ž .x x , defined as the difference between thep K

measured and expected ionization expressed in terms

Ž .of standard deviations for the p K mass hypothe-sis. For charged tracks having momentum above2 GeVrc a pionrkaon separation of 2s is achieved.

( 0 H I) ( 03. Measurement of B D ™K p rrrrrB D ™I H)K p

Starting from the sample of hadronic Z decays theD) " are reconstructed as follows. Each pair of

Ž . )q 0 q 0 y q Ž .Fig. 1. Mass-difference distribution a for candidates of the decay channel D ™D p , D ™K p and b candidates of the decays

channel D)q™D0pq, D0 ™Kqpy. The dots with error bars are data while the hatched histogram represents the distribution of thes

combinatorial background.


oppositely-charged tracks is considered with the twomass assignments Kypq and pyKq and those with

Ž . 20NM Kp yM N-30 MeVrc are retained. If bothD

hypotheses satisfy the mass cut the event is rejected.In addition, the measured mean ionization of eachtrack is required to be closer, in terms of number ofstandard deviations, to the expectation for the as-sumed mass hypothesis than for the alternative hy-pothesis. The decay angle u ) of the kaon in the D0

K

rest frame is required to satisfy Ncosu ) NF0.8. OnlyK

combinations in which the two tracks form a com-mon vertex and each track has at least one VDET hitare kept.

To build the D) " candidate the surviving trackpairs are combined with an extra charged track, the

Ž .‘‘soft pion’’ p , of low momentum, typically lesssw x Žthan 4 GeVrc 11 the limits on momentum are

.fixed by kinematics and resolution effects . In orderto reduce the combinatorial background, the energyof the D) " candidate is required to be greater thanhalf the beam energy.

0 0The Cabibbo-favoured decays of the D and Dare contained in the sample for which the two pions

Ž .have the same sign right-sign sample , while theDCSDs and mixing candidates are contained in thesample for which the two pions have opposite signŽ . 0 0wrong-sign sample . The DMsM yM dis-p D Ds

tributions of the right-sign and wrong-sign samplesare shown in Fig. 1 together with the estimatedcombinatorial background. The shape of this combi-natorial background is assumed to be the same asthat obtained from events in the sideband region ofthe D0 invariant mass distribution above 2.1GeVrc2, and is normalised to the number of candi-dates having DM)160 MeVrc2.

Within a DM mass window from 143.5 MeVrc2

to 147.5 MeVrc2 the numbers of events in theright-sign and the wrong-sign samples after the com-binatorial background is subtracted are

N s1038.8"32.5 stat. "4.3 syst. ,Ž . Ž .RS

N s21.3"6.1 stat. "3.4 syst. ,Ž . Ž .WS

respectively. The systematic error is due to the lim-ited statistics used to determine the combinatorialbackground.

Monte Carlo studies show that, although thephysics background contamination in the right-sign

sample is negligible, a small contribution fromphysics backgrounds must be subtracted from thewrong-sign sample. Four decay modes are found to

0 y qŽ 0 . 0contribute, namely: D ™ K p p , D ™

pymqn , D0 ™pqpyp 0 and D0 ™KyKq. Theym

contribute because of misidentification of one orboth tracks or because of missing neutrinos or p 0s.

To demonstrate that the peak appearing in Fig. 1bis not related to combinatorial background, eventsare selected in the DM mass window and the cut onŽ .M Kp for the wrong-sign sample is not applied.

Ž .The resulting M Kp distribution is shown inFig. 2. A narrow peak at the nominal D0 massŽ 2 .0M s1864.5 GeVrc is present. The peak on theD

left, due to D0 ™KyKq decays, is outside the D0

mass window.Rather than relying on the Monte Carlo estimates

for the physics background subtraction, the data areused to estimate the contribution of the dominant

0 y qŽ 0 .D ™ K p p physics background to thewrong-sign sample. This is achieved by repeating theselection, with the dErdx requirement reversed, i.e.

Ž .the ionization of the kaon pion candidate has to be

Fig. 2. Mass distribution for candidates of the decay channelD)q™D0pq, D0 ™Kqpy. A narrow peak at the nominal D0

sŽ 2 .0mass M s1864.5 GeVrc is present. The peak on the left isD

due to the decays D0 ™Ky Kq and is fitted taking the shapefrom Monte Carlo.


Table 1Physics background estimated from the Monte Carlo with thestandard and reversed dErdx cuts

Channel dErdx dErdx0 y q 0Ž .D ™K p p 1.56"1.08 26.48"4.160 y q 0D ™p p p 0.36"0.36 0.36"0.360 y qD ™p m n 0.16"0.16 0.16"0.16m0 y qD ™K K 0.12"0.12 0.12"0.120 y qD ™K e n – 3.16"1.20e0 y qD ™K m n – 0.84"0.64m

Ž .closer to the expectation for a pion kaon . Thissample is hereafter called dErdx. In this sample the

0 y qŽ 0.D ™K p p contribution is strongly enhancedwhile the DCSDrmixing signal is suppressed by thesame factor. The contributions from the other decaychannels remain the same, since the cut is symmetricwhen the mass hypotheses are reversed.

According to Monte Carlo studies, the dErdxsample also contains some small additional physicsbackgrounds, from semileptonic D0 decay channels,and these must also be taken into account. Table 1shows the number of expected physics backgroundcandidates for the dErdx and dErdx samples, calcu-lated from the Monte Carlo efficiencies and assum-

w xing the Particle Data Group 12 branching ratios.The expected contributions after the subtraction of

the combinatorial background to the number of can-didates of the wrong-sign sample, N , and theWS

d Erd xnumber of candidates of the dErdx sample, N ,WS

can be written as

N sN 0 ™ q yqN 0 qNWS D K p Kp Žp . symm

1d Erd x

0 q y 0N s N ™ qrN qN qN ,WS D K p Kp Žp . symm otherr1Ž .

where the various quantities are explicited hereafter.Ø N 0 q y is the unknown number of eventsD ™ K p

attributed to the DCSDrmixing signal in thewrong-sign sample.

Ø N 0 is the unknown number of events at-Kp Žp .0 y qŽ 0 .tributed to the dominant D ™ K p p

physics background in the wrong sign sample.Ø r is the known enhancement factor for the D0 ™

y qŽ 0 .K p p contribution obtained when thedErdx cut is reversed. This is measured in the

data to be rs46.1"11.8, by applying the re-versed dErdx cuts to the right-sign sample andnoting the reduction in the size of the peak fromthe Cabibbo-favoured D0 decay.

Ø N is the estimate of the sum of the back-symm

grounds which are symmetric upon reversal of thedErdx cut, i.e. the D0 ™ pypqp 0, D0 ™

pymqn and D0 ™KyKq backgrounds. Nm symm

is assumed to be rN 0 P f , where f isKp Žp . symm symm

the fraction of symmetric events with respect theŽ 0.number of Kp p events in the Monte Carlo

dErdx sample. The error on this number is takento be 100% to take into account the differences,compatible with statistical fluctuations, found bothfor the dErdx and dErdx samples in MonteCarlo.

Ø N is the additional backgrounds expected inother0 y qthe dErdx sample coming from D ™K e ne

and D0 ™Kymqn decays. It is assumed to bem

rN 0 P f , where f is also taken fromKp Žp . other other

the Monte Carlo estimate. The uncertainties aredue to the limited statistics and to the errors onthe branching ratios.

Ž .Using the values N s 21.3 " 6.1 stat. "WSd Erd xŽ . Ž . Ž .3.4 syst. , N s 56.4 " 8.1 stat. " 2.3 syst.WS

Ž . Ž .measured in the data, Eqs. 1 and 2 yield

N 0 s1.03"0.15 stat. "0.27 syst. ,Ž . Ž .Kp Žp .

N 0 q ys19.1"6.1 stat. "3.5 syst. .Ž . Ž .D ™ K p

Ž .0The total physical background N qN isKp Žp . symm

2.2"1.0 and is consistent with the Monte Carloexpectation of 2.2"1.2 from Table 1. The system-atic uncertainties for N 0 q y are listed in TableD ™ K p

2 and are derived by varying the following quantities

Table 2Systematic uncertainties for the measurement of the number ofD0 ™Kqpy decays

Source Systematics

Syst. error on N "3.4WSd Er d xStat. error on N "0.3WSd Er d xSyst. error on N "0.1WS

Ž . Ž .r s effic. dErdx reffic. dErdx "0.3Fractions of physics background "0.9

Total "3.5


Ž .by one standard deviation: i the systematic uncer-tainty on N due to the combinatorial backgroundWS

Ž .subtraction, ii the statistical and systematic uncer-d Erd x Ž .tainties on the N sample, iii the statisticalWS

Ž .uncertainty on r and finally iv the uncertainties onthe physics background processes as discussed previ-ously.

Dividing N 0 q y by the number of signalD ™ K p

Ž .events in the right-sign sample N yields a rela-RS

tive branching ratio of

B D0 ™Kqpy rB D0 ™KypqŽ . Ž .s 1.84"0.59 stat. "0.34 syst. % .Ž . Ž .Ž .

4. Proper time distribution

Assuming small mixing and neglecting CP-violat-ing terms, the time evolution for the signal in thewrong sign sample is expected to have the following

w xform 13 :

0 q yN t A R q 2 R R trt cosfŽ . (D ™ K p DCSD mix DCSD

21 yt rtqR trt e , 2Ž . Ž .mix 2

where R is the ratio of doubly Cabibbo-sup-DCSD

pressed over Cabibbo-favoured decays, R is themix0 0 q y 0 y qŽ . Ž .ratio B D ™D ™K p rB D ™K p and

cosf is the phase angle parametrizing the interfer-ence between the two processes. The first term, dueto the DCSD decay, has the conventional exponentialproper time dependence with a decay constant givenby the D0 lifetime. The third term is the contributionfrom the mixed events and peaks at trts2. Thesecond term accounts for possible interference be-tween both processes. The significant differences inthe structure of the proper time distributions for theDCSD and the mixing signals allow their respectivecontributions to be estimated.

M 0The proper time ts ll of a D candidate isp

calculated from the decay length ll , defined as thedistance between the primary vertex and the D0

decay vertex projected along the direction of flightof the D0, and the reconstructed momentum p andmass M of the candidate. The average resolution onthe proper time is f0.1 ps and is dominated by theuncertainty on the position of the D0 vertex.

The distributions of proper time in the signalregion for the wrong-sign sample observed in thedata is shown in Fig. 3a. The result of a binnedmaximum likelihood fit is also shown. The followingcontributions are included in the probability densityof the likelihood function:

0Ø A direct cc™D X component, which has theŽ .proper time dependence given by Eq. 2 convo-

luted with the detector resolution. The number ofevents attributed to the DCSD signal and themixing signal are left free in the fit. Variousassumptions for the phase of the interference termare investigated.The fraction of the signal which is attributed to

0 0Žcc™D X, rather than the bb™cc™D X dis-. K pcussed next is f s 77.0 " 2.7 stat .Ž .Žc

Ž .."0.5 syst. %. It is extracted from the data us-ing a likelihood fit to the proper time dependenceof the right-sign sample. This fit is essentially thesame as the fit to the wrong-sign sample exceptthat proper time dependence of the Cabibbo-favoured events is assumed to be exponential, asexpected for small mixing, and the contributionaccounting for the physics background is notnecessary. The result of this fit is shown in Fig.3b.

0Ø An indirect bb™cc™D X component, whichhas the same proper time dependence as the directcomponent of the signal, but modified to take intoaccount the effect of the additional flight distanceof the B meson. The exact shape for this compo-nent is taken from Monte Carlo after appropriatereweighting for the world average B hadron and

0 w xD lifetimes 12 .Ø A physics background contribution for which the

proper time dependence is assumed to be expo-nential with a decay constant given by the D0

lifetime. The number of events attributed to thisprocess is 2.2"1.0, as determined in Section 3.

Ø A combinatorial background contribution, forwhich the proper time dependence is measured inthe data from the sideband regions of the DMplot. The number of events attributed to thisprocess is 15.7"3.4 events.For all the above contributions, except the combi-

natorial background, an additional proper timeŽ .smearing of 29"12 % is applied to take into ac-

count that the proper time resolution measured in the


Ž . 0 q y Ž . 0 y qFig. 3. Proper time distribution for a the D ™K p candidates, and b for the D ™K p candidates. The dots with error bars arethe data. The histograms are the contributions of cc, bb and combinatorial background events resulting from the unconstrained fit when nointerference is assumed.

data is slightly worse than that predicted by theMonte Carlo. This Monte Carlordata comparison isperformed by selecting candidates from the sideband of the Kp mass distribution both in MonteCarlo and data and comparing the width of a Gauss-ian fit to the negative proper time distribution ofthese events. To enhance the fraction of tracks in thissample coming from the interaction point the con-tamination from cc and bb events is suppressed by

applying to the opposite hemisphere the lifetime tagw xveto described in Ref. 14 .

Ž .Setting the interference term to zero cosfs0 ,the result of the fit to the proper time distribution ofthe wrong-sign sample is

N s20.8q8 .4 stat. "4.0 syst. ,Ž . Ž .DCSD y7.4

N sy2.0"4.4 stat. "1.1 syst. .Ž . Ž .mix


Table 3List of systematic uncertainties contributing to N and NDCSD mix

for the case of no interference. The constrained fit results areobtained with N constrained to be non-negativemix

Source of uncertainty Unconstrained fit Constrained fit

N N Nmix DCSD DCSD

Resolution -0.1 "0.1 -0.10D lifetime -0.1 -0.1 -0.1

Comb. back. distribution "0.7 "1.4 "1.1Comb. back. rate "0.8 "3.6 "2.8Charm fraction "0.4 "0.3 "0.1Phys. back. rate "1.0 "1.0

Total "1.1 "4.0 "3.2

The fitted value for N is outside the physicalmix

region, thus no mixing is observed. Table 3 sum-marises all the sources of systematic uncertaintyconsidered. They are computed by varying by onestandard deviation on the fit the additional propertime smearing, the D0 lifetime, the charm fractionand the combinatorial and physical background rates.The systematic uncertainties due to the combinatorial

Fig. 4. Proper time distribution of the D0 ™Kqpy over D0 ™

Kypq candidates with the background subtracted. The dots witherror bars are data. The errors are the sum in quadrature ofstatistical and systematic uncertainties due to combinatorial back-ground subtraction. The solid curve is the fit result with nointerference, the dotted and dashed curves are the fit resultsassuming fully constructive and destructive interference, respec-tively.

Fig. 5. Likelihood of the fit as a function of R calculated bymix

leaving free the R parameter and constraining all the externalDCSD

parameters within their uncertainties in order to take the system-atic errors into account. The solid line represents the fit resultswith no interference, the dotted line is the likelihood for fullypositive interference and the dashed line for fully negative inter-ference.

background proper time shape is evaluated by repeat-ing the fit many times with a new combinatorialbackground shape, obtained by randomly varying thecontents of each proper time bin according to aPoisson distribution.

Fig. 4 shows the time dependence of the ratio ofwrong-sign over the right-sign candidates after thebackground subtraction.

If N is constrained to be non-negative, themix

result is

N s18.4q6 .2 stat. "3.2 syst. ,Ž . Ž .DCSD y5.8

q1 .4q3.0N s0 stat. syst.Ž . Ž .mix

which translates to

R s 1.77q0 .60 stat. "0.31 syst. % .Ž . Ž .Ž .DCSD y0.56

In this case the systematic uncertainty on N ismix

obtained by adding to the likelihood used to fit thedata, additional Gaussian terms for the extra smear-ing on the time resolution, the D0 lifetime, the charmfraction and the physical background rate, and Pois-sonian terms for the combinatorial background rateand shape. Fig. 5 shows the resulting likelihood as afunction of the assumed mixed fraction. By integrat-


ing the resulting likelihood over the allowed regionan upper limit of N -9.6 at 95% confidence levelmix

is obtained, corresponding to

R -0.92% at 95% CL.mix

The effect of interference has been studied byŽ .fitting the data with fully constructive cosfsq1

Ž .and fully destructive interference cosfsy1 ; therespective upper limits are R -0.96% at 95% CLmix

and R -3.6% at 95% CL. For the case cosfsmixq12.1Ž . Ž .y1 N s14.8 stat. "3.3 syst. .mix y13.3

5. Conclusion

The D0 ™Kqpy decay is studied to determineŽ 0 q y. Ž 0the branching ratio B D ™ K p rB D ™

y q.K p . The method consists in reconstructing theD)q™D0pq decay where the D0 can subsequentlys

decay to Kqpy or Kypq. The numbers of recon-structed decays observed after background subtrac-tion give

B D0 ™Kqpy rB D0 ™KypqŽ . Ž .s 1.84"0.59 stat. "0.34 syst. % .Ž . Ž .Ž .

w xThis is 1.4 standard deviations from the CLEO 15Ž 0 q y. Ž 0 y q.measurement B D ™ K p rB D ™ K p

s 0.77"0.25 stat. "0.25 syst. %.Ž . Ž .Ž .In order to distinguish the two possible contribut-

ing processes, the fraction of doubly Cabibbo-sup-0 0pressed decays R and D –D mixing rate R ,DCSD mix

the proper time distribution is analysed, yielding

R s 1.77q0 .60 stat. "0.31 syst. % ,Ž . Ž .Ž .DCSD y0.56

R -0.92% at 95% CL ,mix

assuming no interference between the two processes.The fit is improved if destructive interference isallowed.

This can be compared with the results obtainedw xby the E691 Collaboration 16 : R -1.5% atDCSD

90% CL based on the number of observed eventsN s 1.8 " 13.2, and R - 0.5% at 90%DCSD mix

w xCL. The E791 collab. 17 finds R D CSD

s 0.68q0 .34 stat. "0.07 syst. %, for R s0,Ž . Ž .Ž .y0 .33 mix

in agreement within 1.5 standard deviations with our

result, and sets a limit R -0.85% at 90% CL al-mix

lowing CP violation in the interference term.

Acknowledgements

We wish to congratulate our colleagues in theCERN accelerator divisions for successfully operat-ing the LEP storage ring. We are grateful to theengineers and technicians in all our institutions fortheir contribution towards ALEPH’s success. Thoseof us from non-member countries thank CERN forits hospitality.

References

w x Ž .1 I. Bigi, A.I. Sanda, Phys. Lett. B 171 1986 320; L.L. Chau,Ž .H.Y. Cheng, Phys. Lett. B 333 1994 514; I. Hincliffe, T.A.

Ž .Kaeding, Phys. Rev. D 54 1996 914; F. Buccella, M.Ž .Lusignoli, A. Pugliese, Phys. Lett. B 379 1996 249.

w x Ž .2 H. Georgi, Phys. Lett. B 297 1992 353; T. Ohl, G. Riccia-Ž .rdi, E.H. Simmons, Nucl. Phys. B 403 1993 603.

w x3 G. Burdman, Charm mixing and CP violation in the StandardModel in: Proceedings of the Charm 2000 Workshop, FER-MILAB-Conf-94r190, Fermilab, June 7–9, 1994.

w x Ž .4 M.K. Gaillard, B.W. Lee, Phys. Rev. D 10 1974 897; A.Ž .Datta, Phys. Lett. B 154 1985 287; A. Datta, M. Kham-

Ž .bkhar, Z. Phys. C 27 1985 515; A.A. Petrov, Phys. Rev. DŽ .56 1997 1685.

w x Ž .5 L. Wolfenstein, Phys. Lett. B 164 1985 170; J. Donoghue,E. Golowich, B.R. Holstein, J. Trampetic, Phys. Rev. D 33Ž .1986 179.

w x Ž .6 T.E. Browder, S. Pakvasa, Phy. Lett. B 383 1996 475.w x Ž .7 Y. Nir, N. Seiberg, Phys. Lett. B 309 1993 337; M. Leurer,

Ž .Y. Nir, N. Seiberg, Nucl. Phys. B 420 1994 468.w x Ž .8 ALEPH Collaboration, Z. Phys. C 53 1992 1.w x Ž .9 ALEPH Collaboration, Nucl. Instr. and Meth. A 294 1990

121.w x Ž .10 ALEPH Collaboration, Nucl. Instr. and Meth. A 360 1995

481.w x Ž .11 ALEPH Collaboration, Z. Phys. C 62 1994 1.w x Ž .12 R.M. Barnett et al., Phys. Rev. D 54 1996 1.

0 0w x13 T. Liu, An Overview of D –D Mixing Search Techniques:Current Status and Future Prospects, hep-phr9508415, Pre-sented at the t-charm Factory Workshop, Argonne NationalLaboratory, June 20–23, 1995.

w x Ž .14 ALEPH Collaboration, Phys. Lett. B 401 1997 150.w x Ž .15 CLEO Collaboration, Phys. Rev. Lett. 72 1994 1406.w x Ž .16 E691 Collaboration, Phys. Rev. Lett. 60 1988 1239.w x Ž .17 E791 Collaboration, Phys. Rev. D 57 1998 13.

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Study of D0–D̄0 mixing and D0 doubly Cabibbo-suppressed decays