Measurement of and determination of |Vcb|
Introduction
In the Standard Model of electroweak interactions, the elements of the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix [1] are constrained by unitarity. Therefore, experimental measurements of the precise values of the CKM matrix elements are important to understand the phenomenology of weak interactions.
In the framework of Heavy Quark Effective Theory (HQET) [2], the semileptonic decay is amongst the cleanest modes that can be used to measure the CKM matrix element |Vcb|. The differential decay rate for can be expressed as [3] where GF is the Fermi coupling constant, and and mD+ are the masses of the and D+ mesons, respectively. The variable y denotes the inner product of the and D+ meson four-velocities, which is related to q2, the mass squared of the lepton–neutrino system: and FD(y) is the form factor. By extrapolating the measured |Vcb|FD(y) to the point of zero recoil of the D+ meson, |Vcb| can be determined using a theoretical prediction of FD(1). In this Letter p represents the four-momentum vector of the particle in subscript, while denotes the three-momentum vector in the center of mass (CM) frame and is the three-momentum vector in the laboratory frame.
|Vcb| measurements made using decays are less precise than those made using , due to the suppressed decay rate near the point of zero recoil, substantial feed down from and the large combinatoric background from fake D mesons. Nevertheless, the measurement provides a consistency check, and allows a test of heavy-quark symmetry [4] through the precise measurement of the form factor. Furthermore, this decay has one experimental advantage over as there is no slow pion involved.
The decay is preferred to because it has much less feed-down background from excited charm meson states. Good particle identification and vertexing capabilities allow effective reduction of the combinatoric background.
In this Letter we report measurements of the branching fraction of the semileptonic decay , the CKM matrix element |Vcb| and the form factor FD(y). The lepton ℓ can be either an electron or a muon, and the use of the charge-conjugate mode is implied.
The data sample used in this analysis was collected with the Belle detector [5] at KEKB [6], an asymmetric e+e− collider. The data sample has an integrated luminosity of 10.2 fb−1 and contains 10.8×106 pairs. Another data sample with an integrated luminosity of 0.6 fb−1 was taken at an energy 60 MeV below the ϒ(4S) resonance, and is used as a control sample to check the continuum background determination.
Section snippets
Belle detector
Belle is a large solid-angle spectrometer based on a 1.5 T superconducting solenoid magnet. Charged particle tracking is provided by a silicon vertex detector (SVD) and a central drift chamber (CDC) that surround the interaction region. The SVD consists of three approximately cylindrical layers of double-sided silicon strip detectors; one side of each detector measures the z coordinate and the other the r–φ coordinate. The CDC has 50 cylindrical layers of anode wires; the inner three layers
Event selection
For hadronic event selection, we require that each event have at least 5 well-reconstructed charged tracks, a total visible energy of at least 0.15 times the CM energy and an event vertex that is consistent with the known interaction point. Continuum background events are suppressed by requiring the normalized second Fox–Wolfram moment [8] to be less than 0.4.
This analysis is based on the neutrino reconstruction method, which exploits the hermeticity of the detector and the near zero value of
Measurement of
The uncertainty on the reconstructed value of y is dominated by the error on the measurement of the neutrino four-momentum. We denote the reconstructed value as ỹ. The resolution is improved by making the correction to the momentum measurement by the factor α given in Eq. (9). Using a MC simulation, the resolution of y is found to be accurately modeled by a symmetric Gaussian with σ=0.03.
Fig. 3 shows the ỹ distribution for data and the estimated backgrounds. After all backgrounds are
Systematic uncertainty
The systematic uncertainties are given in Table 3. The dominant uncertainty is the imperfection of the detector simulation for the neutrino reconstruction, which is determined by varying a number of simulation parameters including the track finding efficiency, the track momentum resolution, the fraction of incorrectly reconstructed tracks, the photon finding efficiency, the photon energy resolution, the charged kaon identification efficiency, the charm semileptonic decay fraction and the KL0
Summary
Using the missing energy and momentum to extract kinematic information about the undetected neutrino in the decay, we have measured the decay rate, |Vcb|FD(1) and the form factor parameters for a number of different parametrizations. These results, with statistical errors, are summarized in Table 2. We have evaluated systematic errors of 12.5%, 12.6% and 18.2% on |Vcb|FD(1), and Γ, respectively. Using the Caprini et al. parametrization, we find the decay rate of ,
Acknowledgements
We thank Benjamin Grinstein for useful discussions. We wish to thank the KEKB accelerator group for the excellent operation of the KEKB accelerator. We acknowledge support from the Ministry of Education, Culture, Sports, Science, and Technology of Japan and the Japan Society for the Promotion of Science; the Australian Research Council and the Australian Department of Industry, Science and Resources; the Department of Science and Technology of India; the BK21 program of the Ministry of
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2014, International Journal of Modern Physics A