\(\varepsilon_X=\frac{N_{after}^X}{N_{before}^X}\)
to estimate that efficiency, MC sample is used - the L0, L1 etc algorithms are applied to the simulated sample to count number of events before and after. so
\(D=\frac{\varepsilon_{L0}\varepsilon_{L1}\varepsilon_S}{\varepsilon_{L0}^\prime\varepsilon_{L1}^{\prime}\varepsilon_S^\prime}\cdot\frac{N_e}{N_{\mu}}\)
where \prime (denominator) corresponds to efficiencies of \(B\to KJ/\psi(ee)\) selections.
The problem is MC doesn’t model data well, so one have to apply reweighting to MC before calculating the efficiencies.
so the generic procedure is
- generate MC1, MC2
- get real data sample for both channels
- reweight both MC to match the data
- calculate efficiencies
- estimate \(N_e\)
- estimate \(N_{\mu}\)
- calculate the ratio \(D\)
unfortunately reweighting doesn't work well (potential discrepancies on other features) and one have to fix the simulation on deeper level.
Proposed solution
So the hypothesis is that incorrect MC simulation comes from improper simulation of \(\pi\) coming from the primary vertex that overlap with signal traces at the ECAL. the obvious test to falsify this hypothesis is to
- add condition (cut) to the data sample for (1) to have no \(\pi\) overlapping with \(e\) at ECAL
- update estimation of the ratio \(\hat{D}\). If the hypothesis is false, \(\hat{D} \approx D\) (within few percent accuracy)