FitRebinned

Fitting rebinned asymmetries

• rebinning is a filter
• mujpy must show only chi2 referred to fit binning; chi2 referred to plot binning has no interest.
• should we rebin decay histograms and then recalculate asymmetry, {$A(R(N))$}, or rebin directly asymmetries {$R(A(N))$}?
  • The first, neglecting or subtracting backgrounds, and assuming the correct {$\alpha$} value, is equivalent to

{$$ \frac {\sum_i \exp(-t_i/\tau)A_i}{\sum_i \exp(-t_i/\tau)} \approx \left\langle \exp(-t/\tau) A(t)\right\rangle$$}

• the second is equivalent to

{$$\sum_{i=1}^n A_{j+i} /n \approx \left\langle A(t)\right\rangle$$}

• it is apparent therefore that the second is closer to the average of the instantaneous (time-differential, in {$\mu$}SR parlance) asymmetry.