Lifetime 2D fit
12.2.3. Lifetime 2D fit#
Unbinned likelihood fit to the 2D joint distribution of decay time
The input data is provided by the ROOT ntuple ntp
contained in the file example-data/lifetime.root
. The branches of the tree corresponding to the decay time and decay-time uncertainty are Dz_t
and Dz_t_err
, respectively.
To find the maximum of the likelihood, the following quantity is minimized:
where the index
The fit assumes no background contamination. The 2D joint PDF is written as a conditional PDF of the decay time given the value of the decay-time uncertainty as
The decay-time PDF is written as the convolution between the exponential decay and the experimental resolution function
where
The decay-time uncertainty PDF is parametrized by a Johnson’s SU distribution
and is normalized in the range
The fit is developed using the following frameworks: