Vertex fitting
Contents
3.4.6. Vertex fitting#
Introduction#
In the broadest sense, we call vertex fitting a technique in which one uses prior knowledge on the nature of a decay to improve the measurement of its observables. The fits we are going to perform are of two main types:
Geometric Fitting: We use the fit to determine the decay vertex of the particle. Usually this is done by fitting together the tracks of its charged decay products, which we know originate from a common point. Additional information could be available — for example, if the particle is short lived, we can improve this by adding an IP constraint, i.e. fit the beam spot together with the tracks. If there’s only one track, using the beam spot is the only way to obtain a vertex.
Warning
If no vertex fit is performed, the corresponding variables for the vertex position will not be filled.
Kinematic Fitting: We use the fit to improve our knowledge of the particle kinematics. By default, composite particle kinematics are built off the decay products using 4-momentum conservation. If the particle we are reconstructing has a well defined mass (either stable, or a narrow resonance) it might make sense to apply a mass constraint to help reject combinatorial background.
Warning
If you apply a mass constraint, the invariant mass will be fixed to the nominal mass. This is problematic if you then want to use this variable, for example if you want to fit a peak. In that case, make sure you save the pre-fit mass separately.
Note
Several fitters exist. For this exercise we will focus on KFit
which is
the most basic one.
Exercise
Locate the documentation for vertex fitting functions and find KFit.
Hint
Solution
Basic Fitting#
This lesson assumes you successfully reconstructed your
Question
Which particles do you need to fit in order to reconstruct the
Hint
Answer
Exercise
Call the fit function with the correct parameters and save the output. Include the true vertex position from MC for comparison.
Hint
Solution
Exercise (optional)
Fit the
Exercise (optional)
Look up the documentation for TreeFitter
and fit the whole
Tag Vertex Fitting#
Since
We might be interested in knowing the decay position of this meson without
placing any requirements on its decay. This is done using the TagV
module.
TagV
performs a geometric fit over the tracks in the ROE to determine the
tag decay vertex. However, not all tracks will necessarily come from the tag
itself; consider for example our signal, where the pion tracks originate from a
long lived kaon vertex. TagV
is designed to iteratively downweight those tracks,
ultimately excluding them from the fit.
Exercise
Locate the TagV
documentation.
Solution
Question
By default, TagV only uses tracks with PXD hits. Why?
Solution
Exercise
Call the TagV
module and save the output.
Hint
Solution
Conclusion and Plotting#
Congratulations! Your steering file is ready! Time to run it and check the results.
Exercise
Run the steering file.
Solution
You can now plot some relevant vertex variables. In general, the choice would depend on what you need for your analysis. A few examples would include:
Vertex position in various coordinates, such as dz and dr.
P-value of the fit.
Resolution of the vertex fit (
) where x is each of the above variables. Pull (
).
As an exercise we will focus on the first two.
Exercise
Plot the
Hint: Variable names
Hint: Plot ranges
Solution
Fig. 3.26 Distribution of the fitted vertex position in Z#
Fig. 3.27 Distribution of the fit p-values.#
Exercises (optional)
Compare the
and Tag vertex positions and show that they are both compatible with being vertices.If you’ve fit the
vertex, compare its radial position with the . Is this what you expect?
Key points
Use
KFit
to fit simple vertices.Think carefully which vertex you need to fit, and whether it will need additional constraints.
Study the documentation if you need a different functionality, such as
TreeFitter
to fit complex trees.Use
TagV
to reconstruct a vertex from the ROE.
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Authors of this lesson
Francesco Tenchini