Simple 1D fit
12.2.1. Simple 1D fit#
Unbinned likelihood fit to the beam-constrained mass distribution of \(B^{0}\to K^{*}\gamma\) decay candidates reconstructed in simulation, to determine the fraction of signal decays.
The input data is provided by the ROOT ntuple BtoKstG
contained in the file example-data/fitme.root
. The branch of the tree corresponding to the beam-constrained mass is B0_mbc
.
To find the maximum of the likelihood, the following quantity is minimized:
where the index \(i\) runs over the data candidates, \(m_i\) is the observed beam-constrained mass for candidate \(i\), which PDF depends on some unknown parameters identified by the vector \(\vec{\theta}\).
The fit model assumes a signal component peaking at the nominal \(B^{0}\) mass, described by a Crystal Ball distribution with \(n=15\)
and a background component, described by an Argus distribution
Each PDF is normalized in the fit range that goes from 5.2 GeV/\(c^{2}\) up to the threshold corresponding to \(m_0\). The total PDF is sum of the signal and background PDFs weighted by the signal fraction \(f_\mathrm{sgn}\)
The fit is developed using the following frameworks: