Effects of K-Factor and Mis-Tag on Fits

Version Information

• Dates covered: up to 26-Mar-04
• Uses only B_s final states without gammas

Conclusions & Questions

1. Using <K> in the fits causes biases in fitted parameters.
   • τ : 2.5 * RMS
   • Δm : 0.3 * RMS(m_s) -- 0.7 * RMS(m_d)
   • P(mis-tag) : 12 * RMS(m_s) -- 1.1 * RMS(m_d)
2. <K> fits have large mismatches between fit parameter rms's and average fit errors. These disappear in K-PDF fits.
   • Δm_s: RMS(Δm) = 0.562 -- <Error> = 0.096
   • Δm_d: RMS(Δm) = 0.096 -- <Error> = 0.027

Effects of Mis-Tag and K-Factor on mixing distributions

• Δ(ms): Plots of N(evts) vs ct0 or λ Unmixed Events | Mixed Events
• Δ(md): Plots of N(evts) vs ct0 or λ Unmixed Events | Mixed Events
• a) plot vs. ct0(true) -- Prob(mis-tag) = 0
• b) plot vs. ct0(true) -- Prob(mis-tag) = 0.2
• c) plot vs. λ -- Prob(mis-tag) = 0
• d) plot vs. ct0 -- Prob(mis-tag) = 0
• e) plot vs. λ -- Prob(mis-tag) = 0.2

Lifetime Fits Tested

1. χ² fit on ct0 histogram
2. log-L fit to true ct0
3. log-L fit to λ using <K>
4. log-L fit to λ using convolution over K-factor histogram

Mixing Fits Tested

1. log-L fit to true ct0-distrib & Prob(mis-tag) = 0
2. log-L fit to λ-distrib using <K>
3. log-L fit to λ-distrib using convolution over K-factor histogram