6.8.7. Continuum suppression

This page contains instructions on how to use the continuum suppression framework, with a focus on recent modifications. For a detailed description of the variables, please refer to Chapter 9 (Background suppression for B decays) of The Physics of the B Factories book

Example usage

In order to build continuum suppression variables, you need to first reconstruct a B on the signal side, then reconstruct the rest of event (ROE) buildRestOfEvent, and eventually build the continuum suppression variables buildContinuumSuppression.

Since the ROE can be affected by background and noise, a mask has to be provided to try to get rid of part of this background appendROEMasks. The mask defines a set of cuts which will be applied on ROE objects, and only the ROE objects passing the selection mask will be used to build the continuum suppression variables.

The generic interface is the following:

# build your signal ('B0')

buildRestOfEvent('B0', path=main)

cleanMask = ('cleanMask', '<Your selections for ROE>')
appendROEMasks('B0', [cleanMask], path=main)

buildContinuumSuppression('B0', 'cleanMask', path=main)

Where <Your selections for ROE> is a set of cuts on tracks and clusters of ROE which are in general analysis dependent. Some examples will be given below.

modularAnalysis.buildContinuumSuppression(list_name, roe_mask, path)[source]

Creates for each Particle in the given ParticleList a ContinuumSuppression dataobject and makes basf2 relation between them.

  • list_name – name of the input ParticleList

  • roe_mask – name of the ROE mask

  • path – modules are added to this path

The ROE mask cuts should be tuned for each individual physics analysis. However, it may be a good idea to always require a minimum of 1 CDC hit for the charged ROE particles to exclude VXD-only fake tracks. Here is a simple example that you can use as a starting point:

cleanMask = ('cleanMask', 'nCDCHits > 0 and useCMSFrame(p)<=3.2', 'p >= 0.05 and useCMSFrame(p)<=3.2')

The default CleoConeCS variable returns the cones calculated from all final state particles. It is now possible to construct CLEO Cones using only particles in the ROE. If you want to store the CleoCones constructed using only the ROE particles, you simply need to add ROE as a second argument to your variable:

variables = ['CleoCone(1)','CleoCone(1,ROE)']

Note that you can store both types of CleoClones in a single ntuple.

There is also the option to calculate the KSFW moments (KSFWVariables) constructed from the reconstructed B-mesons final state particles. In Belle, this was possible, but it was not often employed as the KSFW moments become analysis dependent which is not good for systematics. For this reason, the call to the KSFWVariables returns the variables calculated from the B-meson primary daughters. If you would like to store the KSFWVariables constructed from the B final state particles, you need to add FS1 as an additional argument (FS1 = final_state_1, from the Belle software):

variables = ['KSFWVariables(hso00)','KSFWVariables(hso00,FS1)']

Again, as shown in this example, you can store both cases in your ntuple.

Continuum Suppression variables

The Continuum Suppression variables are defined as following:

Thrust and thrust axis

For a set of \(N\) particles with momenta \(p_i\) the thrust axis \(\vec{T}\) is defined as the unit vector along which their total projection is maximal. The thrust scalar is \(T=\frac{\sum^N_{i=1} |\vec{T}\cdot \vec{p}_i|}{\sum^N_{i=1} |\vec{p}_i|}\),

CLEO Cones

The CLEO collaboration introduced variables based on the sum of the absolute values of the momenta of all particles within angular sectors around the thrust axis in intervals of 10 degrees, resulting in 9 concentric cones.

Fox-Wolfram moments

For a set of \(N\) particles with momenta \(p_i\), the l-th order Fox-Wolfram moment is defined as \(H_l = \sum^N_{i,j=1}|\vec{p}_i||\vec{p}_j| P_l (\cos{\theta_{i,j}})\), where \(P_l\) are Legendre polynomials and \(\theta_{i,j}\) is the angle between the particles

Deep Continuum Suppression

The Deep Continuum Suppression (DCS) employs additional detector-level variables describing nearly every track (cluster) in the event to increase the classification performance.

It is described in detail in this MsC thesis. Tutorial files are available in basf2 in analysis/examples/tutorials/.

There are two big differences when using the DCS instead of the Continuum Suppression:

1 Writing out of new variables, which describe single tracks and clusters instead of the whole shape of the event.

2 Using Deep Neural Networks as MVA methods to increase performance and to deal with the large number of new variables.

This following section provides additional information about the DCS, which supplements the information in the tutorials.

Adversarial Networks

Due to the new variables in the DCS, correlations between the classifier output and quantities like Mbc and \(\Delta{Z}\) are much more likely to occur.

Using Adversarial Networks during training can reduce such correlations to a minimum. This is achieved by using additional networks for signal and background distributions of each quantity to train against the regular Neural network used for classification.

In the DCS, the impact on these additional Adversarial Networks can be regularized with the parameter \(\lambda\).

This parameter is highly dependent on the given problem and can vary in orders of magnitude.

Please note that in most cases either the signal or continuum distribution of a quantity is correlated.

While in the DCS tutorial there is an Adverserial Network for every signal and background distribution for every quantity (which is put in as a spectator), one should limit the number of Adversarial Networks to only those distributions which are correlated.