Search For D～0-(?)～0 Mixing In D～0�'K～+π～- Decay And Measurements Of B～+�'J/ψ(?)～0 π+ And B～0�'J/ψ(?)～0 Decays

We report the results of a search for D⁰-(D|ˉ)⁰ mixing based on 400 fb^-1 of data accumulated by the Belle detector at the KEKB asymmetric-energy e⁺e^- collider. The parameters that describe D⁰-(D|ˉ)⁰ mixing, x' and y', are measured by studying a proper-time evolution of the wrong-sign decay process D⁰ → K⁺Ï€^-.In the analysis, D⁰ are selected from continuum c(c|ˉ) events. We reconstruct D⁰ from the decay chain D^·+→π_s⁺D⁰,D⁰→K⁺Ï€^-. The charge of the soft pion Ï€_s is used to tag the flavor of the neutral D at production. The right-sign decay D⁰→K^-Ï€⁺ is also reconstructed for R_WS measurement and as a reference channel, where R_WS is the rate of wrong-sign to right-sign decay. We obtain the D⁰ decay and production vertices by three dimensional vertex fit, to calculate the proper time and its uncertainty.We use huge amounts of background Monte Carlo (MC) to study background sources. The background can be categorized into random slow Ï€⁺, D⁰≥3 body, D₍₃₎⁺ and combinatorial. The mass and time distribution characteristics of these four types of backgrounds are well understood. Besides, their two dimensional mass distributions are carefully parameterized. Two dimensional fits to the right-sign and wrong-sign distributions yield 1073993±1108 D⁰→K^-Ï€⁺ and 4024±88 D⁰→K⁺Ï€^- signal events, which result in R_WS=(0.375 ±0.008)%. The ratio of wrong-sign signal to background is improved to be 1.1, due to the optimized selection criteria. By using the information of data events outside signal region, the selection criteria are obtained to maximum the figure of merit, as which can minimize the statistical uncertainty of mixing parameters.An unbinned maximum likelihood method is used in the lifetime fit with event-by-event resolution functions. The probability density function (PDF) is constructed from the time distributions of signal and backgrounds and the relations among time, time uncertainty, mass, and mass difference variables. In the fit, the two dimensional mass fit merged with time-uncertainty PDF is used to calculate the fraction of signal or backgrounds in the PDF for each of events. The background distributions are fully modeled with different functions, whose parameters are obtained from fitting to the mass sideband events (few parameters from MC). A sum of three Gaussians is used to describe the detector resolution function of signal. The right-sign data fit yields the resolution function and a D⁰ lifetime 409.9±0.7 ps, in good agreement with the world average value.The timing fit to the wrong-sign events can proceed when the detector resolution function and the background contributions are studied clearly and fixed. Before the data fit, large Toy and full MC samples are used to check the correctness of the whole analysis processes and the statistical and systematic behavior of the result. For five sets of full MCs generated at nine (y', x^'2) points each, the fits recover the input values well within the statistical uncertainty. Due to large difference in time-uncertain distributions between signal and backgrounds, if the time uncertainty is not merged in the fraction of signal or backgrounds, which was used in the former...