Understanding Lifetime and Mixing Biases in Generated Events

Last Update: 30-Apr-04

Attempts to understand the bad lifetime fit quality of both Mixing ON and Mixing OFF samples.

Mixing ON (29-Apr-04): (Data-Fit)/Fit plot for a simple exponential fit to the generated t0 distribution.
Mixing OFF (29-Apr-04): (Data-Fit)/Fit plot for simple exponential fit to generated t0 distribution.

(Including final states with photons.)

Bad value of Time Ave. Mixing from Mixing ON Sample (29-Apr-04)
This comes from two effects.
- Asymmetry in mixed vs non-mixed events selected due to d0_mess selection of B_s(bar). Events selected:
  - B_s(bar) - B_x
  - B_x(bar) - B_s-->B_s(bar)
  - B_s(bar) - B_s-->B_s(bar)
  The last of these causes more B_s-->B_s(bar) to be written out than unmixed B_s.
- Stupid mistake in d0_mess cuts that allowed events with a B_s(bar) and any muon passing kinematic cuts to be written out. This allowed a larger number of potential event topologies to be written out
Lifetime Bias and Bad Fit Quality in Mixing ON sample (29-Apr-04)
This is largely due to the asymmetry in the number of mixed and unmixed final state B_s(bar) decays that are written out.
- N_tot(t) = N_unm^sel(t) + N_mix^sel(t)
  = <N^sel> exp(-t/τ) [1 + (ΔN^sel/2<N^sel>) cos(Δm.t)]
- with ΔN^sel = N_unm^sel - N_mix^sel non-zero because of the bias.
Lifetime Bias and Bad Fit Quality in Mixing OFF sample (29-Apr-04)
Not as bad as in the Mixing ON sample.
Note: not due to ommission/addition of radiative final states.