Evidence for D⁰−D⁰ Mixing Using the CDF II Detector

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Reference

Evidence for D

−D

Mixing Using the CDF II Detector

CDF Collaboration

CLARK, Allan Geoffrey (Collab.), et al.

Abstract

We measure the time dependence of the ratio of decay rates for the rare decay D0→K+π− to the Cabibbo-favored decay D0→K−π+. A signal of 12.7×103 D0→K+π− decays was obtained using the Collider Detector at Fermilab II detector at the Fermilab Tevatron with an integrated luminosity of 1.5  fb−1. We measure the D0−D0 mixing parameters (RD,y′,x'2), and find that the data are inconsistent with the no-mixing hypothesis with a probability equivalent to 3.8 Gaussian standard deviations.

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Evidence for D

−D

Mixing Using the CDF II Detector. Physical Review. D , 2008, vol. 100, no. 12, p. 121802

DOI : 10.1103/PhysRevLett.100.121802

Available at:

http://archive-ouverte.unige.ch/unige:38508

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

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Evidence for D

D

Mixing Using the CDF II Detector

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Y. Zheng,^8,cand S. Zucchelli⁵ (CDF Collaboration)^a

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

14Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

15Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

16Duke University, Durham, North Carolina 27708

17Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA

18University of Florida, Gainesville, Florida 32611, USA

19Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

20University of Geneva, CH-1211 Geneva 4, Switzerland

21Glasgow University, Glasgow G12 8QQ, United Kingdom

22Harvard University, Cambridge, Massachusetts 02138, USA

23Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

121802-2

24University of Illinois, Urbana, Illinois 61801, USA

25The Johns Hopkins University, Baltimore, Maryland 21218, USA

26Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

27Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea;

Seoul National University, Seoul 151-742, Korea;

Sungkyunkwan University, Suwon 440-746, Korea;

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

Chonnam National University, Gwangju, 500-757, 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

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

43LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

44University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA

45Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy

46University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA

47Purdue University, West Lafayette, Indiana 47907, USA

48University of Rochester, Rochester, New York 14627, USA

49The Rockefeller University, New York, New York 10021, USA

50Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy

51Rutgers University, Piscataway, New Jersey 08855, USA

52Texas A&M University, College Station, Texas 77843, 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 11 December 2007; published 27 March 2008)

We measure the time dependence of the ratio of decay rates for the rare decay D⁰!K to the Cabibbo-favored decayD⁰!K. A signal of12:710³D⁰!Kdecays was obtained using the Collider Detector at Fermilab II detector at the Fermilab Tevatron with an integrated luminosity of 1:5 fb¹. We measure theD⁰D⁰mixing parametersR_D; y⁰; x⁰², and find that the data are inconsistent with the no-mixing hypothesis with a probability equivalent to 3.8 Gaussian standard deviations.

DOI:10.1103/PhysRevLett.100.121802 PACS numbers: 13.20.Fc, 13.25.Ft, 14.40.Lb

Since the discovery of the charm quark in 1974 [1,2], physicists have been searching for the oscillation of neutral charm mesons between particle and antiparticle states.

Such behavior is referred to as ‘‘mixing,’’ as first explained in 1955 [3] for the K⁰ meson in terms of quantum- mechanical mixed states. Mixing was next studied forB⁰ mesons in 1987 [4,5]. The years 2006 and 2007 have seen landmark new results on mixing: first time-dependent ob- servation ofB_smixing from the CDF experiment [6] and

evidence forD⁰mixing from theBABAR[7] and Belle [8]

experiments.

The recent evidence for D⁰ mixing comes from two different types of measurements. The Belle Collaboration found direct evidence for a longer and shorter lived D⁰ meson, in analogy to the well-known case forK⁰ mesons.

They found significantly different decay time distributions for D⁰ decays to the CP eigenstates KK and compared to that for the CP-mixed stateK. (In this

Letter, reference to a specific decay chain implicitly in- cludes the charge-conjugate decay.) No other experiment has confirmed the evidence for lifetime differences among these decays [9]. The evidence forD⁰ mixing found in the BABARexperiment is a difference in decay time distribu- tion forD⁰ !K compared to that for the Cabibbo- favored (CF) decayD⁰ !K. This same measurement was made in the Belle experiment [10], but evidence for mixing was not seen. In this Letter, we present a new measurement of the same D⁰ mixing process as used by BABARfor their evidence.

In the standard model, the decayD⁰ !Kproceeds through a doubly Cabibbo-suppressed (DCS) ‘‘tree’’ dia- gram, and may also result from a mixing process (D⁰ $ D⁰), if it exists, followed by a CF decay (D⁰!K).

The DCS decay rate depends on Cabibbo-Kobayashi- Maskawa quark-mixing matrix elements and on the mag- nitude of SU(3) flavor symmetry violation [11]. Mixing may occur through two distinct types of second-order weak processes. In ‘‘long-range’’ mixing, theD⁰ evolves into a virtual hadronic state such as, which subsequently evolves to aD⁰. The amplitude for long-range mixing has been estimated using strong interaction models [12], but has not been determined using a QCD calculation from first principles. ‘‘Short-range’’ processes [13] have a ‘‘box’’ or

‘‘penguin’’ topology, and are negligible in the standard model. However, exotic weakly interacting particles could enhance the short-range mixing and provide a signature of new physics [14–16].

The ratioRofD⁰ !KtoD⁰!Kdecay rates can be approximated [17,18] as a simple quadratic function oft=, wheretis the proper decay time andis the mean D⁰ lifetime. This form is valid assumingCPconservation and small values for the parameters xM=andy

=2, whereMis the mass difference between theD⁰ meson weak eigenstates,is the decay width difference, andis the average decay width of the eigenstates. Under the assumptions stated above,

Rt= R_D R_D

p y⁰t= x⁰²y⁰²

4 t=²; (1) whereR_Dis the squared modulus of the ratio of DCS to CF amplitudes,x⁰ xcosysin,y⁰ xsinycos, andis the strong interaction phase difference between the DCS and CF amplitudes. In the absence of mixing, x⁰ y⁰0andRt= R_D.

Our measurement uses data collected by the CDF II detector at the Fermilab Tevatron collider, from February 2002 to January 2007, corresponding to an integrated luminosity of 1:5 fb¹ for pp collisions at

ps 1:96 TeV. CDF II [19] is a multipurpose detector with a magnetic spectrometer surrounded by a calorimeter and a muon detector. The detector components pertinent to this analysis are the silicon microstrip vertex detector, the multiwire drift chamber (COT), and the 1.4 T magnet,

which together measure the trajectories and momenta of charged particles. The COT measures ionization energy loss for a charged particle, which is used for particle identification (PID).

Events are selected in real time with a trigger system developed for a broad class of heavy flavor decays. The trigger requirements used here are the same as those de- scribed for our previous measurement of the time- integrated value of R [20], which used a smaller data sample. The trigger selects events with a pair of oppositely charged particles that are consistent with originating from a secondary decay vertex separated from the beam line.

In the off-line analysis, we reconstruct the ‘‘right-sign’’

(RS) CF decay chainD!D⁰,D⁰ !K, and the

‘‘wrong-sign’’ (WS) decay chain D!D⁰, D⁰! K. The relative charges of the pions determine whether the decay chain is RS (like charge) or WS (oppo- site charge). The reconstruction method is similar to that used for our previous time-independent measurement.

Since the RS and WSDdecays have the same kinematics, we use the same selection criteria (cuts) for both the RS and WS decay modes to reduce systematic uncertainties.

Analysis cuts were optimized before the WS candidates were revealed.

The D⁰ candidate reconstruction starts with a pair of tracks from oppositely charged particles that satisfy the trigger requirements. The tracks are considered with both KandKinterpretations. A third ‘‘tagging’’ track, required to have p_T 0:3 GeV=c, is used to form a D candidate when considered as a pion and combined with theD⁰ candidate.

We apply two cuts to the WS signal to reduce the background from RS decays where the D⁰ decay tracks are misidentified because the kaon and pion assignments are mistakenly interchanged. As determined from the data, 96.4% of D⁰ decays with correct mass assignment are reconstructed with K invariant mass m_K within 20 MeV=c² of the D⁰ mass. The m_K distribution for misidentified D⁰ decays is much broader, and has only 22% of the events within the same mass range. We remove WS candidates that have a RS mass within that range. This cut excludes 96.4% of RS decays and retains 78% of the WS signal. We also impose a cut based on PID, which is used to distinguish pions from kaons for all three tracks in the decay chain. This cut, described in Ref. [20], further helps to reject misidentified decays.

We use a series of cuts based on the decay topology of signal events in which a D and its tagging pion are produced at the primary vertex, and the D⁰ travels a measurable distance before decay. The cuts reduce back- ground from combinations with one or more tracks not from theDdecay. We require the transverse decay length significance L_xy=_xy to be greater than 4, where L_xy

~rp~_T=p_T, ~ris the distance between the primary and D⁰ decay vertices, p~_T is the transverse component of the 121802-4

momentum of the D⁰ candidate with respect to the beam line, and_xy is the uncertainty onL_xy. The tagging pion track must have d₀<500m, where the transverse im- pact parameter d₀ is the distance of closest approach between a track and the primary vertex in the plane trans- verse to the beam line. The tagging pion must also have a point of closest approach to the primary vertex less than 1.5 cm along the beam line.

The ratio t= is determined for each D⁰ candidate by t=m_D0L_xy=p_T, where m_D0 1:8648 GeV=c² and 410:1 fs are the world average values for the D⁰ invariant mass and lifetime, respectively [21]. To study Rt=, we divide the data into 20 bins of t= ranging from 0.75 to 10.0, choosing bins of increasing size from

0.25 to 2.0 to reduce statistical uncertainty at larger times.

The bin sizes are larger than thet=resolution of0:16.

After RS and WS candidates are separately divided into t=bins, they are further divided into bins of mass differ- ence mm_Km_Km. For each m bin, we perform a binned maximum likelihood fit of the corre- sponding m_K distribution to determine the D⁰ signal yield. The distribution ofD⁰ signal yield versusmis fit using a least-squares method to get theDsignal for each time bin. The D fit procedure is illustrated by the time- integrated WSmdistribution shown in Fig.1(left).

The signal shapes for them_K andmdistributions are fixed from the RS time-integrated fits. For each m_K distribution, a parabola with floating parameters is used

τ t/

0 2 4 6 8 10

R

0.002 0.004 0.006 0.008 0.01

-3)

2 (10 x’

-0.5 0 0.5

)-3 y’ (10

-10 0 10 20

FIG. 2. (left) Ratio of promptD‘‘wrong-sign’’ to ‘‘right-sign’’ decays as a function of normalized proper decay time. The dashed curve is from a least-squares parabolic fit, which determines the parametersR_D,y⁰, andx⁰². The dotted line is the fit assuming no mixing. (right) Bayesian probability contours in thex⁰²y⁰parameter space corresponding to one through four equivalent Gaussian standard deviations. The closed circle shows the unconstrained fit values for the mixing parameters. The open diamond shows the values from the physically allowed fit (x⁰² 0). The cross shows the no-mixing point.

2) m (MeV/c

∆

0 10 20 30

2 Events / 0.5 MeV/c 5000

10000

µm)

0 ( d

0 100 200 300 400 500

mµEvents / 5

2000 4000 6000

FIG. 1. (left) Time-integrated distribution for ‘‘wrong-sign’’D⁰!Ksignal yield as a function ofm. Also shown is the result of a least-squares fit using an empirical function for the signal (dark shaded region) and a power law for the background (light shaded region). (right) Distribution of transverse impact parameterd0forD⁰mesons with5< t= <6for ‘‘right-sign’’Dmesons. The result of a binned maximum likelihood fit shows the narrow peak due to promptly produced D mesons (dark shaded) and the broad distribution due to nonpromptDmesons fromBdecay (light shaded).

to fit the background. The background shapes for all the m WS (RS) distributions are fixed to the shape deter- mined for the time-integrated WS (RS) distribution. The amplitudes of the signal and background shapes are deter- mined independently for all m_K and m fits. The RS distributions have similar amounts of background as the WS distributions, but the RS signal is about 250 times larger.

The D mesons that originate from beauty hadron (B) decays must be treated as background to avoid the com- plication of measuring the D⁰ decay length from the B decay point instead of the primary vertex. TheDmesons produced promptly at the primary vertex have a narrowd₀ distribution for their daughter D⁰ mesons, with a shape independent oft=. The background from nonpromptD mesons from the decay chainB!D!D⁰have a broad d₀ distribution, due to the decay length of theBhadrons.

The width of the broad distribution increases with increas- ing t=. An example d₀ distribution is shown in Fig. 1 (right). The shapes of the prompt and broad distributions are determined from RS data. The WS shapes are the same as the RS shapes. For each of the 20t=bins, the prompt WS (RS) signal is determined from the number of WS (RS) Dmesons and the shapes of thed₀distributions. The ratio of nonprompt to prompt signal is 0:02 at t=2 and increases with increasingt=due to the faster exponential falloff witht=forD⁰compared toB. Att=7, the ratio is1.

The time-integrated prompt D signals are 12:7 0:3 10³ WS events and 3:0440:002 10⁶ RS events. The ratios of prompt WS to RS signal for the 20 t= bins are shown in Fig.2 (left). The uncertainties for each bin include statistical and systematic contributions.

The significant systematic uncertainties are due to the background shapes for the m_K, m, and d₀ distribu- tions, which are described by parameters that are allowed to vary in the fitting procedure. We used simulation to confirm that our choice of decay time bins does not sys- tematically affect the result. The detector acceptances for RS and WS decays are nearly identical, and their dif- ference contributes a negligible systematic uncertainty in the ratio R. The bins at small and large t= with larger uncertainties are due to smaller numbers of signal events, due to the trigger turn-on and exponential decay rate, respectively.

A least-squares parabolic fit of the data in Fig.2(left) to Eq. (1) determines the values and uncertainties for the parameters R_D, y⁰, and x⁰², which are listed in Table I.

Since the value of x⁰² is unphysical (less than zero), but consistent with zero, we also fit the data with the constraint x⁰² 0. The values ofR_D andy⁰ are consistent with and without the constraint. The values and precision of the parameters measured by CDF are comparable to those from the best previous measurements, as shown in TableII.

To determine the consistency of our data with the no- mixing hypothesis, we compute Bayesian contours con- taining the region with the highest posterior probability.

The probability density is calculated as the product of a likelihoodLand a prior, divided by a normalization factor.

The likelihood isLexp²=2, where²is computed from the data in Fig. 2 (left) for a particular set of fit parameters. A flat prior is used for all three parameters, and R_D is treated as a Bayesian nuisance parameter. The contours are insensitive to modest changes in the prior. The contours in thex⁰²-y⁰plane are shown in Fig.2(right). The no-mixing point lies on the contour, which excludes a region containing a probability of 1:510⁴, equivalent to 3.8 Gaussian standard deviations. We also computed contours with the constraintx⁰² 0and find a probability for no-mixing consistent with the value obtained without the constraint.

We tried alternate procedures to determine the probabil- ity for no mixing. We fit the data in Fig.2(left) with the constraint y⁰ x⁰²0, with results as given in Table I.

The change in log likelihood (2 lnL) between the un- constrained and no-mixing fits has an approximately chi- square distribution for 2 degrees of freedom. From TableI, 2 lnL17:6, which corresponds to a probability of 1:610⁴. We also made a frequentist check using en- sembles of simulated Rt=measurements without mix- ing. The probability for a simulation to have a value of 2 lnL 17:6 is 1:310⁴. The probabilities from both of these checks are consistent with that obtained using Bayesian contours.

In conclusion, our data show evidence for D⁰D⁰ mixing in theKchannel, providing the first confirma- tion of the evidence in this channel from the BABAR experiment. The mixing could be due to standard model long-range intermediate states or due to new physics.

Improved reliability of standard model calculations and

TABLE I. Fit results for the Rt= distribution. The uncertainties include statistical and systematic components. The correlation coefficient between y⁰ andx⁰² for the unconstrained fit is0:98. The no-mixing fit is consistent with our previous time-independent result [20].

Fit type R_D10³ y⁰10³ x⁰²10^{3 2}=d:o:f:

Unconstrained 3:040:55 8:57:6 0:120:35 19:2=17

Physically allowed 3:220:23 6:01:4 0 19:3=18

No mixing 4:150:10 0 0 36:8=19

121802-6

future measurements of mixing signatures with improved precision are needed to explain this phenomenon.

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 Founda- tion; 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 Science and Technology Facilities Coun- cil and the Royal Society, U.K.; the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Comisio´n Interministerial de Ciencia y Tecnologı´a, Spain; the European Community’s Human Potential Programme;

the Slovak R&D Agency; and the Academy of Finland.

aWith visitors from:

bUniversity of Athens, 15784 Athens, Greece.

cChinese Academy of Sciences, Beijing 100864, China.

dUniversity of Bristol, Bristol BS8 1TL, United Kingdom.

eUniversity Libre de Bruxelles, B-1050 Brussels, Belgium.

fUniversity of California Irvine, Irvine, CA 92697, USA.

gUniversity of California Santa Cruz, Santa Cruz, CA 95064, USA.

hCornell University, Ithaca, NY 14853, USA.

iUniversity of Cyprus, Nicosia CY-1678, Cyprus.

jUniversity College Dublin, Dublin 4, Ireland.

kUniversity of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.

lUniversity of Heidelberg, D-69120 Heidelberg, Germany.

mUniversidad Iberoamericana, Mexico D.F., Mexico.

nUniversity of Manchester, Manchester M13 9PL, United Kingdom.

oNagasaki Institute of Applied Science, Nagasaki, Japan.

pUniversity de Oviedo, E-33007 Oviedo, Spain.

qQueen Mary, University of London, London E1 4NS, England.

rTexas Tech University, Lubbock, TX 79409, USA.

sIFIC (CSIC–Universitat de Valencia), 46071 Valencia, Spain.

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TABLE II. Comparison of the CDF result with recent measurements. All results useD⁰!Kdecays and fits assuming noCP violation. The uncertainties include statistical and systematic components. The significance for no mixing is given in terms of the equivalent number of Gaussian standard deviations.

Experiment R_D10³ y⁰10³ x⁰²10³ Mixing Signif.

CDF 3:040:55 8:57:6 0:120:35 3.8

BABAR[7] 3:030:19 9:75:4 0:220:37 3.9

Belle [10] 3:640:17 0:64:03:9 0:180:210:23 2.0