V b. (u,c,t) d. d W. (u,c,t)

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1 CHU Karene Mattison Tom of British Columbia University Congress CAP Measuring B 0 Meson Mixing Rate, Lifetime, and Lepton Energy Spectra a Feasibility Study June 19, 2001

2 Outline 1. Motivation 2. What Happens at the Experiment 3. Simple Time Independent Model 4. Simple Time Dependent Model 5. Conclusion

3 V cb : using the B meson inclusive semileptonic branching 1. and lifetime ratio Traditionally, these measurements are done using only events by high-momentum leptons tagged" We are studying the feasibility of using all leptons in the data, just high momentum leptons. not Motivation Determination of the CKM matrix elements 2. V td : using the B 0 B 0 mixing rate, m b V qb (u,c,t) V * 0 0 B W W B qd d b B V Qb W (u,c,t) * V 0 0 qd (u,c,t) d B d V* Qd (u,c,t) V Qb b d * V Qd W V qb b

4 The B! `ν D" and D! `ν K" branching ratios are about while the B! D"X branching ratio is about , There is no way to tell directly whether a given lepton is from decay or from D decay, but the momentum spectra are B What Happens in the Experiments e + e (4s) B B 0 l ν l + ν K ( ) + l D ( ) 20 ν l ν K ( ) 20 D ( )+ The following interaction occurs: There are up to 4 leptons per (4s) event rather different

5 PEP-II and KEK-B colliders use unequal beam energies (9 so electrons and 3 GeV positrons) GeV In the lab frame, the B mesons have a momentum of about 3 and the decay vertices can be resolved by the silicon GeV, Observables for a dilepton event: 2 lepton energies and in decay length, z separation At Asymmetric B factories The B mesons are produced nearly at rest in the (4s) frame, vertex detectors. (4s) 0 B B 0 ν l + D ( ) ν l D ( )+ K ( ) ν K ( ) ν z l l +

6 S ij : Number of events with one lepton in energy bin i and 2. of same sign in energy bin j another D ij : Number of events with one lepton in energy bin i and 3. of different sign in energy bin j another a ij : Probability of B 0! X`+` with leptons in energy bins 4. and j i Simple Time Independent Model Assume no background from B + B events and no mixing Observables 1. L i : Total number of leptons in energy bin i Parameters: 1. N: Number of BB events 2. b i : Probability of (B 0! `+ν) with ` in energy bin i 3. c i : Probability of (B 0! DX! ` ν) with ` in energy bin i

7 1. Use 10 bins of b i and c i from CLEO, and a ij = b i c j + b j c i 2. Calculate L i, S ij, and D ij for N = 10 7 Simple Time Independent Model (cont.) The Fitting Functions: 1. L i = 2N (b i + c i ) 2. S ij = N (b i c j + b j c i ) 3. D ij = N (b i b j + c i c j + a ij ) Test: 3. Fit for b i, c j, a ij, and N using Minuit (76 parameters)

8 0.1 Results with Simulated Data Energy (GeV) Magenta: True bi; Blue: True ci; Black points with error bars: Fit results of respective spectrum; Red: True bi + ci with errors calculated from p N on L distribution NOTE: Errors multiplied by 40 times to make them visible

9 Ratio of Errors from Other Methods parameter numbers Red: Simulated Tag Analysis: Run the fit using only events with at least one high momentum lepton above 1.5 GeV Blue: Magic" analysis: all lepton sources known from truth"

10 Add k-index to dilepton spectra, representing separation along beam direction of the lepton origin points the + (b i c j + b j c i )Z bc Simple Time Dependent Model Fitting Functions: 1. L i = 2N(b i + c i ) S ijk = N[(b i c j + b j c i )Z bc k (1 W k) 2. (b i b j Z bb k + c jc i Z cc k )W k] + D ijk = N[(b i b j Z bb k 3. c jc i Z cc k )(1 W k) + k W k + a ij Z a k ]

11 Z k functions are the probability of observing dileptons from sources with separation in the beam direction of bin k various W k function is the probability of B 0 B 0 oscillation for lepton in bin k separation Z and W functions bb k (fi B) = exp( t k fi Z ) B bc(fi B) = 2exp( t k fi Z ) exp( t k fi ) D k B cc(fi B) = 2exp( t k fi Z ) exp( t k fi ) D k B a k (fi B) = exp( t k fi Z ) D Z k functions are all normalized to 1 in the k direction W k ( m) = 1 2 (1 cos( m t k))

12 Composition of S ijk and D ijk Above Axis: Composition of ± ij D ijk ; Below: Composition of ± ij S ijk Time (ps) Lepton Sources: Red: bb; Blue: cc; Magenta: bc; Green: a; Black: Sum NOTE: Mixed contributions are multiplied by 10 times to make them visible

13 Results for Time Dependent Parameter A: Fractional Error B: Fractional Error Ratio (A/B) Simulated Tag Anal. Our Anal. m 3: : fi B 2: : Simulate Tag Analysis: Run the fit using only dilepton events with both leptons above 1.0 GeV

14 It is Possible to measure the time dependent parameters and lepton energy spectra at the same time. the Errors on the first few bins of the lepton energy spectra are by a factor of compared to errors from the improved Use Monte Carlo Data to generate the Z and W 2. including resolution effects distributions, Conclusions simulated tag analysis. Many more things to do: 1. Add in another parameter to allow for B + B background 3. Data: correct for lepton misidentification and non BB events