CLNS 95/1324 CLEO 95–3 March 6, 1995

Measurement of the Ratio of Branching Fractions B(D^{0} → π^{−}e^{+}ν_{e})/B(D^{0} → K^{−}e^{+}ν_{e})

F. Butler,^{1} X. Fu,^{1} B. Nemati,^{1} W.R. Ross,^{1} P. Skubic,^{1} M. Wood,^{1} M. Bishai,^{2} J. Fast,^{2}

E. Gerndt,^{2} J.W. Hinson,^{2} R.L. McIlwain,^{2} T. Miao,^{2} D.H. Miller,^{2} M. Modesitt,^{2} D. Payne,^{2} E.I. Shibata,^{2} I.P.J. Shipsey,^{2} P.N. Wang,^{2} L. Gibbons,^{3} Y. Kwon,^{3} S. Roberts,^{3}

E.H. Thorndike,^{3} T. Coan,^{4} J. Dominick,^{4} V. Fadeyev,^{4} I. Korolkov,^{4} M. Lambrecht,^{4} S. Sanghera,^{4} V. Shelkov,^{4} T. Skwarnicki,^{4} R. Stroynowski,^{4} I. Volobouev,^{4} G. Wei,^{4}

M. Artuso,^{5} M. Gao,^{5} M. Goldberg,^{5} D. He,^{5} N. Horwitz,^{5} G.C. Moneti,^{5} R. Mountain,^{5} F. Muheim,^{5} Y. Mukhin,^{5} S. Playfer,^{5} Y. Rozen,^{5} S. Stone,^{5} X. Xing,^{5} G. Zhu,^{5} J. Bartelt,^{6} S.E. Csorna,^{6} Z. Egyed,^{6} V. Jain,^{6} D. Gibaut,^{7} K. Kinoshita,^{7} P. Pomianowski,^{7} B. Barish,^{8}

M. Chadha,^{8} S. Chan,^{8} D.F. Cowen,^{8} G. Eigen,^{8} J.S. Miller,^{8} C. O’Grady,^{8} J. Urheim,^{8} A.J. Weinstein,^{8} F. Würthwein,^{8} D.M. Asner,^{9} M. Athanas,^{9} D.W. Bliss,^{9} W.S. Brower,^{9}

G. Masek,^{9} H.P. Paar,^{9} J. Gronberg,^{10} C.M. Korte,^{10} R. Kutschke,^{10} S. Menary,^{10} R.J. Morrison,^{10} S. Nakanishi,^{10} H.N. Nelson,^{10} T.K. Nelson,^{10} C. Qiao,^{10} J.D. Richman,^{10} D. Roberts,^{10} A. Ryd,^{10} H. Tajima,^{10} M.S. Witherell,^{10} R. Balest,^{11} K. Cho,^{11} W.T. Ford,^{11}

M. Lohner,^{11} H. Park,^{11} P. Rankin,^{11} J.G. Smith,^{11} J.P. Alexander,^{12} C. Bebek,^{12} B.E. Berger,^{12} K. Berkelman,^{12} K. Bloom,^{12} T.E. Browder,^{12}^{∗} D.G. Cassel,^{12} H.A. Cho,^{12} D.M. Coffman,^{12} D.S. Crowcroft,^{12} M. Dickson,^{12} P.S. Drell,^{12} D.J. Dumas,^{12} R. Ehrlich,^{12} R. Elia,^{12} P. Gaidarev,^{12} M. Garcia-Sciveres,^{12} B. Gittelman,^{12} S.W. Gray,^{12} D.L. Hartill,^{12}

B.K. Heltsley,^{12} S. Henderson,^{12} C.D. Jones,^{12} S.L. Jones,^{12} J. Kandaswamy,^{12} N. Katayama,^{12} P.C. Kim,^{12} D.L. Kreinick,^{12} Y. Liu,^{12} G.S. Ludwig,^{12} J. Masui,^{12}

J. Mevissen,^{12} N.B. Mistry,^{12} C.R. Ng,^{12} E. Nordberg,^{12} J.R. Patterson,^{12} D. Peterson,^{12} D. Riley,^{12} A. Soffer,^{12} P. Avery,^{13} A. Freyberger,^{13} K. Lingel,^{13} J. Rodriguez,^{13} S. Yang,^{13}

J. Yelton,^{13} G. Brandenburg,^{14} D. Cinabro,^{14} T. Liu,^{14} M. Saulnier,^{14} R. Wilson,^{14} H. Yamamoto,^{14} T. Bergfeld,^{15} B.I. Eisenstein,^{15} J. Ernst,^{15} G.E. Gladding,^{15}

G.D. Gollin,^{15} M. Palmer,^{15} M. Selen,^{15} J. J. Thaler,^{15} K.W. Edwards,^{16} K.W. McLean,^{16} M. Ogg,^{16} A. Bellerive,^{17} D.I. Britton,^{17} E.R.F. Hyatt,^{17} R. Janicek,^{17} D.B. MacFarlane,^{17}

P.M. Patel,^{17} B. Spaan,^{17} A.J. Sadoff,^{18} R. Ammar,^{19} P. Baringer,^{19} A. Bean,^{19} D. Besson,^{19} D. Coppage,^{19} N. Copty,^{19} R. Davis,^{19} N. Hancock,^{19} M. Kelly,^{19} S. Kotov,^{19}

I. Kravchenko,^{19} N. Kwak,^{19} H. Lam,^{19} Y. Kubota,^{20} M. Lattery,^{20} M. Momayezi,^{20} J.K. Nelson,^{20} S. Patton,^{20} R. Poling,^{20} V. Savinov,^{20} S. Schrenk,^{20} R. Wang,^{20} M.S. Alam,^{21} I.J. Kim,^{21} Z. Ling,^{21} A.H. Mahmood,^{21} J.J. O’Neill,^{21} H. Severini,^{21} C.R. Sun,^{21} F. Wappler,^{21} G. Crawford,^{22} R. Fulton,^{22} D. Fujino,^{22} K.K. Gan,^{22}

K. Honscheid,^{22} H. Kagan,^{22} R. Kass,^{22} J. Lee,^{22} M. Sung,^{22} C. White,^{22} A. Wolf,^{22} and M.M. Zoeller^{22}

(CLEO Collaboration)

1University of Oklahoma, Norman, Oklahoma 73019 2Purdue University, West Lafayette, Indiana 47907 3University of Rochester, Rochester, New York 14627 4Southern Methodist University, Dallas, Texas 75275 5Syracuse University, Syracuse, New York 13244 6Vanderbilt University, Nashville, Tennessee 37235

7Virginia Polytechnic Institute and State University, Blacksburg, Virginia, 24061 8California Institute of Technology, Pasadena, California 91125 9University of California, San Diego, La Jolla, California 92093 10University of California, Santa Barbara, California 93106 11University of Colorado, Boulder, Colorado 80309-0390 12Cornell University, Ithaca, New York 14853 13University of Florida, Gainesville, Florida 32611 14Harvard University, Cambridge, Massachusetts 02138 15University of Illinois, Champaign-Urbana, Illinois, 61801

16Carleton University, Ottawa, Ontario K1S 5B6 and the Institute of Particle Physics, Canada 17McGill University, Montréal, Québec H3A 2T8 and the Institute of Particle Physics, Canada

18Ithaca College, Ithaca, New York 14850 19University of Kansas, Lawrence, Kansas 66045 20University of Minnesota, Minneapolis, Minnesota 55455 21State University of New York at Albany, Albany, New York 12222 22Ohio State University, Columbus, Ohio, 43210

(March 6, 1995)

Abstract

Using 3.0 fb^{−1} of data collected with the CLEO-II detector, we study the Cabibbo-suppressed decay D^{0} → π^{−}e^{+}ν_{e}. The ratio of the branching fractions B(D^{0} → π^{−}e^{+}ν_{e})/B(D^{0} → K^{−}e^{+}ν_{e}) is measured to be (10.3 ± 3.9 ± 1.3)%, corresponding to an upper limit of 15.6% at the 90% confidence level.

13.20.Fc,13.65.+i,14.40.Jz

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∗Permanent address: University of Hawaii at Manoa

Semileptonic decays of D mesons provide important information about the structure of hadrons containing a heavy quark. The differential decay rate for D → πℓν is

\frac{dΓ}{dq^{2}} = \frac{G^{2}}{24π^{3}} |V_{cd}|^{2} P_{π}^{3} [f_{+}^{π}(q^{2})]^{2} ,  (1)

where q^{2} = m^{2}(ℓν) and P_{π} is the momentum of the pion in the D rest frame. The wave functions of the initial and final state mesons determine the single vector form factor f_{+}^{π}(q^{2}). Measuring the branching fraction B(D^{0} → π^{−}ℓ^{+}ν) determines the normalization of the form factor, f^{π}(0), which can be compared with predictions from lattice qauge techniques, quark models, and quark sum rules. This knowledge also improves our understanding of the similar form factor in the decay B → πℓν.

The variable q^{2} is directly related to the energy of the pion in the D frame; q_{min}^{2} ≈ 0 corresponds to maximum energy for the pion, and the form factor is conventionally normalized at this value. There are experimental and theoretical advantages in measuring the ratio of the form factor for D^{0} → π^{−}ℓ^{+}ν to the well-measured form factor for D^{0} → K^{−}ℓ^{+}ν. The ratio of the branching fractions R_{0} = \frac{B(D^{0}→π^{−}ℓ^{+}ν)}{B(D^{0}→K^{−}ℓ^{+}ν)} can be expressed as

R_{0} = C_{πK} \begin{matrix}|V_{cd}f_{+}^{π}(0)| & 2 \\ |V_{cs}f_{+}^{K}(0)| & 2 \end{matrix} ,  (2)

where the factor C_{πK} is given by the expression

C_{πK} = \frac{∫ P_{π}^{3} |\frac{f_{+}^{π}(q^{2})}{f_{+}^{π}(0)} |^{2} dq^{2}}{∫ P_{K}^{3} |\frac{f_{+}^{K}(q^{2})}{f_{+}^{K}(0)} |^{2} dq^{2}} .  (3)

The ratio |V_{cd}/V_{cs}| is determined well from unitarity of the CKM matrix, so the measurement of B(D^{0} → π^{−}ℓ^{+}ν)/B(D^{0} → K^{−}ℓ^{+}ν) determines the ratio of the form factors, f_{+}^{π}(0)/f_{+}^{K}(0).

Mark III established the existence of the decay D^{0} → π^{−}ℓ^{+}ν when they observed 7 events. This observation yields B(D^{0} → π^{−}ℓ^{+}ν) = (0.39_{−0.11}^{+0.23} ± 0.04)%, corresponding to R_{0} = (11.5_{−3.7}^{+7.3} ± 1.8)% [1]. CLEO II observed about 30 events of D^{∗+} → π^{0}D^{+}, D^{+} → π^{0}ℓ^{+}ν, corresponding to B(D^{+} → π^{0}ℓ^{+}ν)/B(D^{+} → \overline{K}^{0}ℓ^{+}ν) = (8.5 ± 2.7 ± 1.4)% [2]. Since isospin invariance requires Γ(D^{+} → π^{0}ℓ^{+}ν)/Γ(D^{0} → π^{−}ℓ^{+}ν) = 1/2, this result implies R_{0} = (17.0 ± 5.4 ± 2.8)%. The theoretical calculations for R_{0} are in the range 5-10% [3–7]. In this paper we report a new measurement of the ratio of the branching fractions B(D^{0} → π^{−}e^{+}ν_{e})/B(D^{0} → K^{−}e^{+}ν_{e}).

This analysis is closely related to that used to study D^{0} → K^{−}ℓ^{+}ν [8]. To reduce backgrounds, we use the decay D^{∗+} → π_{s}^{+}D^{0} to tag D^{0} mesons, where π_{s} refers to the “slow” pion, which has a momentum of only 40 MeV/c in the D^{∗+} rest frame. (The charge conjugate mode is implicitly included throughout the paper.) The process D^{∗+} → D^{0}π^{+}, D^{0} → π^{−}e^{+}ν_{e} gives a small average value of δm = m_{π_{f} eπ_{s}} −m_{π_{f} e}, where π_{f} is the “fast” pion from the D^{0} decay. In addition, the distribution in δm is reasonably narrow, which helps in suppressing backgrounds. The signal is extracted by fitting the two-dimensional distribution of the variables δm and m_{π_{f} e}, which is shown in figure 1 for a Monte Carlo sample of D^{0} → π^{−}e^{+}ν_{e} decays. We also show Monte Carlo events for the largest background source, D^{0} → K^{−}e^{+}ν_{e} decays in which the kaon is misidentified as a pion. The distributions are very similar, except that the misidentified D^{0} → K^{−}e^{+}ν_{e} decay distribution is offset to lower m_{π_{f} e} by about 100 MeV. To reduce the kaon contamination, we use information on the energy loss (dE/dx) and the time-of-flight (TOF) of the fast pion.

The analysis uses a sample of 3 million e^{+}e^{−} → c \overline{c} events collected with the CLEO-II detector [9] at the Cornell Electron Storage Ring (CESR). The integrated luminosity is 2.1 fb^{−1} at the Υ(4S) energy and 0.9 fb^{−1} in the continuum just below the resonance. We first select events containing a possible π_{f}^{−}e^{+}π_{s}^{+} combination, including requirements for good tracks and for a clean electron. The spherical B\overline{B} events are suppressed by requiring that the ratio of Fox-Wolfram moments [10], H_{2}/H_{0} > 0.2; the combinatoric backgrounds are reduced by demanding that the momentum P_{π_{f} e} > 1.8 GeV/c. We also impose an upper limit on the tranverse momentum of the eν combination relative to the thrust axis to reduce background combinations.

Only electrons from kinematic regions in which the efficiency is well known are used in the analysis. This leads to the requirements P_{e} > 0.7 GeV/c and |cosθ| < 0.81, where θ is the angle of the electron momentum relative to the beam line. We do not use muons because the probability of a hadron faking a muon is significantly higher than the probability of it faking an electron.

Since D^{0} → K^{−}e^{+}ν_{e} is the major background, kaon and pion separation is of special importance in this analysis. Because we need to model the TOF and dE/dx distributions very accurately, we use data, rather than Monte Carlo events, to determine cuts and measure efficiencies. In particular, D^{0} → K^{−}π^{+} events provide a clean sample of identified kaons and pions in a kinematic region very similar to that needed for the semileptonic decay.

The variable used to select pions by time-of-flight is δ(t) ≡ (t − t_{π})/σ(t), where t is the measured TOF, t_{π} is the mean TOF for a pion, and σ(t) is the resolution in the TOF. Thus, the δ(t) distribution should be centered at zero with a standard deviation of one. Figure 2(a) shows this distribution for pions and kaons for the momentum region 0.5−1.2 GeV/c, where there is substantial separation. We require δ(t) < 1.0 for p = 0.5−1.2 GeV/c, and δ(t) < 0.5 for p = 1.2 − 1.5 GeV/c, where the separation is somewhat less, but is still useful.

The corresponding variable containing dE/dx information from the drift chamber is δ(dE/dx) ≡ (dE/dx − dE/dx_{π})/σ(dE/dx). Figure 2(b) shows the δ(dE/dx) distribution for pions and kaons in the momentum region p > 1.5 GeV/c. We require δ(dE/dx) > −1.0 for p > 1.5 GeV/c, and δ(dE/dx) > −0.5 for p = 1.2 − 1.5 GeV/c, where the separation is somewhat less. In table I we list the efficiencies for the combination of TOF and dE/dx cuts, with errors, for six momentum bins.

Besides the background from D^{0} → K^{−}e^{+}ν_{e}, the other significant background comes from random combinations of pions and electrons. We parameterize the shape for this combinatoric background using a wrong-sign sample consisting of π_{f}^{−}e^{+}π_{s}^{−}, π_{f}^{+}e^{+}π_{s}^{−}, and π_{f}^{+}e^{+}π_{s}^{+} combinations, plus charge conjugates. A detailed study of the major components of the backgrounds in the D^{0} → K^{−}e^{+}ν_{e} analysis [8] showed that this wrong-sign sample gives a good representation of the smooth shape in the two-dimensional space. The wrong-sign sample is not used to normalize the background, however. It is important to understand whether there are any significant backgrounds from D^{0} decays other than K^{−}e^{+}ν_{e} that would peak in the kinematic region of the signal but would not show up in the wrong-sign data.

Contamination from D^{0} → K^{−}π^{+} would lie in the critical region of the two-dimensional plot just above the upper limit for D^{0} → K^{−}e^{+}ν_{e} decays. Because the D^{0} → K^{−}π^{+} events form a narrow peak in the two-dimensional δm − m_{π_{f} e} space, we fit for this component explicitly in the data, and find 0 ± 3 events. For three-body hadronic decays of the D^{0} in which one particle is missed and another particle is misidentified as an electron, the invariant mass m_{π_{f} e} is low enough that very few events feed into the mass region used in this analysis. We also studied the level of contamination from semileptonic decays such as D → K^{∗}eν and D → ηeν and found it to be negligible.

To extract the size of the D^{0} → π^{−}e^{+}ν_{e} signal, we fit the two dimensional distribution in (δm, m_{π_{f} e}) with three components:

n(δm, m_{π_{f} e}) = N_{π}f_{π} + N_{K}f_{K} + N_{bg}f_{bg}.  (4)

The N_{i} represent the number of events in each component, and the values are varied in the fit; the f_{i} are fixed shapes for each component. The three components are D^{0} → π^{−}e^{+}ν_{e}, D^{0} → K^{−}e^{+}ν_{e}, and combinatoric background. The shapes for the two semileptonic decays are taken from Monte Carlo samples weighted by the measured particle identification efficiency. The shape of the combinatoric background is parameterized using the wrong-sign sample. The fit yields N_{π} = 87 ± 33, N_{K} = 227 ± 36, and N_{bg} = 259 ± 20. We have measured the quality of the fit by comparing its likelihood with that of a set of test samples, and find that the confidence level is about 70%. The amount of πeν signal is determined primarily by the excess of events above background in the critical region near the maximum allowed value of m_{π_{f} e} for a given δm, as shown in figure 1. In this region, the contributions from the three components in the fit are about equal. Figure 3 shows the result of the two-dimensional fit projected on the m_{π_{f} e} axis for events with δm < 0.16. Such a plot does not display all of the information used by the fit to separate the components, but it gives some idea of the quality of the fit.

We use the yield for D^{0} → K^{−}e^{+}ν_{e} from reference [8] to normalize the branching ratio, correcting for the ratio of luminosities. The yield for D^{0} → K^{−}e^{+}ν_{e} from the present analysis is less precisely measured, since the particle identification cuts are designed to suppress it. The ratio of branching ratios is therefore

R_{0} = \frac{N_{π}/ϵ_{π}}{N_{K}/ϵ_{K}} = \frac{(4484 ± 1700)}{(43505 ± 1045)} = (10.3 ± 3.9)%.  (5)

By normalizing to this mode we minimize our systematic errors, since the tracking and electron identification efficiencies almost cancel. Only the errors on the kaon and pion identification are effectively uncorrelated, and they are 4.5% and 2.7%, respectively. The systematic errors on the fit include the statistical error on the Monte Carlo samples used for the shape of the semileptonic components (7.5%), the uncertainty in the background function (5%), the uncertainty in the signal shape (6%) and the uncertainty in the D^{0} → K^{−}π^{+} component (5%). We estimate the error due to the uncertainty in the number of lepton fakes to be less than 1%. Combining these errors in quadrature we assign a total systematic error of ±13%. The final result is

R_{0} = (10.3 ± 3.9 ± 1.3)%.  (6)

To evaluate the ratio C_{πK} defined in equation 3, we assume that each form factor factor has a pole shape, f_{+}(q^{2}) = f_{+}(0)/(1 − q^{2}/m_{V}^{2} ), where m_{V}, the mass of the vector pole, is taken as the mass of the D^{∗+}(D_{s}^{∗+}) for the πeν(Keν) decay. Using the result C_{πK} = 1.97 from

this calculation and the measured value of R_{0}, we get |\frac{V_{cd}}{V_{cs}} |^{2} |\frac{f_{+}^{π}(0)}{f_{+}^{K}(0)} |^{2} = 0.052 ± 0.020 ± 0.007.

Unitarity constraints on the CKM matrix yield a value of 0.051 ± 0.001 for |\frac{V_{cd}}{V_{cs}} |^{2} [11]; using

this value we obtain |\frac{f_{+}^{π}(0)}{f_{+}^{K}(0)} | = 1.01 ± 0.20 ± 0.07.

In conclusion, we have measured the branching ratio of the Cabibbo-suppressed decay D^{0} → π^{−}e^{+}ν_{e} relative to the Cabibbo-favored decay D^{0} → K^{−}e^{+}ν_{e} to be (10.3±3.9±1.3)%, corresponding to an upper limit of 15.6% at the 90% confidence level. This result agrees well with the theoretical predictions listed in table II. It also agrees with the Mark III measurement, but has a somewhat smaller error. It has a lower central value than that implied by the CLEO D^{∗+} → π^{0}D^{+}, D^{+} → π^{0}ℓ^{+}ν_{e} measurement, but is consistent at the 1σ level. We calculate the world average of all three measurements to be (12.1 ± 2.9)%.

We gratefully acknowledge the effort of the CESR staff in providing us with excellent luminosity and running conditions. J.P.A., J.R.P., and I.P.J.S. thank the NYI program of the NSF, G.E. thanks the Heisenberg Foundation, I.P.J.S. and T.S. thank the K.K.G., M.S., H.N.N., T.S., and H.Y. thank the OJI program of DOE, J.R.P thanks the A.P. Sloan Foundation, S.M.S. thanks the Islamic Development Bank, and A.W. thanks the Alexander von Humboldt Stiftung for support. This work was supported by the National Science Foundation, the U.S. Dept. of Energy and the Natural Sciences and Engineering Research Council of Canada.

REFERENCES

[1] J. Adler et al. (Mark III), Phys. Rev. Lett. 62, 1821 (1989). To calculate R_{0}, we used the measurement B(D^{0} → K^{−}ℓ^{+}ν) = (3.4 ± 0.5 ± 0.4)% from the same publication, and assumed uncorrelated errors.

[2] M.S. Alam et al. (CLEO), Phys. Rev. Lett. 71, 1311 (1993).

[3] M. Wirbel et al. Z. Phys. C29, 637 (1985).

[4] N. Isgur et al., Phys. Rev. D39, 799 (1989).

[5] C.A. Dominguez and N. Paver, Phys. Lett. B207, 499 (1988).

[6] S.Narison, Phys. Lett. B337, 163(1994). To calculate R_{0}, we used the value C_{πK} = 1.97.

[7] V. Lubicz et al., Phys. Lett. B274, 415 (1992).

[8] A. Bean et al., Phys. Lett. B317, 647 (1993).

[9] Y. Kubota et al., Nucl. Instrum. Methods A320, 66(1992).

[10] G. Fox and S. Wolfram, Phys. Rev. Lett. 41, 1581 (1978).

[11] “Review of Particle Properties,” Particle Data Group, Phys. Rev. D50, 1173 (1994).

FIGURES

FIG. 1. Distribution in δm vs m_{π_{f} e} for Monte Carlo samples of πeν and Keν. The normalizations are chosen arbitrarily for the purposes of display.

FIG. 2. The distributions of (a) δt for pions and kaon with momentum between 0.5 and 1.2 GeV/c and (b) δ(dE/dx) for pions and kaons with momentum above 1.5 GeV/c. The variables are defined in the text. In each plot,the pion distribution is the solid histogram, the kaon distribution is the dotted.

FIG. 3. The result of the two-dimensional fit projected on the m_{π_{f} e} axis for events with δm < 0.16. The data are shown with error bars, the fit in the upper solid histogram. The components of the fit are also shown: D^{0} → π^{−}e^{+}ν_{e} (solid), D^{0} → K^{−}e^{+}ν_{e} (dashed), and other background (dotted).

TABLES

TABLE I. The efficiency of the hadron identification cuts for pions and kaons in six momentum bins. The column labeled “fraction” gives the fraction of accepted πeν events that lie in each bin. The averages reported in the table are weighted with this fraction.

momentum (GeV/c)  ε_{π}  ε_{K}  fraction
0.5–0.7  0.683±0.026  0.080±0.009  0.06
0.7–1.0  0.556±0.019  0.048±0.006  0.15
1.0–1.2  0.583±0.024  0.135±0.012  0.12
1.2–1.5  0.480±0.018  0.177±0.011  0.13
1.5–2.0  0.610±0.016  0.250±0.010  0.27
2.0– —  0.607±0.011  0.145±0.005  0.27
Ave.  0.595 ±0.016  0.176±0.008

TABLE II. Theoretical predictions for R_{0}.

Technique  Group  R_{0}(%)
Quark Models  WSB [3]  8.8
ISGW [4]  5.3
QCD Sum Rules DP [5] 9.3
Narison [6]  8.3
Lattice QCD  LMS [7]  8.6