Primary Vertex Selection

In collaboration with Meenakshi Narain

Goal:

For each reconstructed vertex (PVRECO), we want to provide a table with the following information:

Principal Component Analysis

• sum(pt)
• sum[Log(pT)]
• highest pT track
• second highest pT track
• multiplicity

We look for a new set of a small number of variables (first components) which allow us to caracterize the distributions for signal and background.

• Variable distributions

  Next table shows the 6 variables used in the PCA for different physics samples.

  ttbar	sum(pt) and multiplicity	sum(log(pt))	highest(pt)
  zbbar	sum(pt) and multiplicity	sum(log(pt))	highest(pt)
  ztautau

• Variances

  The PCA consists of diagonalize the covariance matrix of the 6 variables. The matrix of eigenvectors correspond to the transformation towards the principal component variables (PC) and the eigenvalues correspond to their variances.
  PC with small variances could be rejected from the analysis since they don't provide much information.

  Next table shows the eigenvalues (variances) for the diagonalization of signal (primary) and background (min bias) independently

  ttbar	primary vertex	min bias
  zbbar	primary vertex	min bias
  ztautau

  Since we are interestred on discriminate signal from background, we have to apply the same transformation to both kind of vertices and look at the PC's which give us the greatest discrimination.

  Next table shows the variance (eigenvalues) for signal and the variance for the background which results by using the same transformation used for the signal.

  ttbar	variance	difference
  zbbar	variance	difference
  ztautau

  The same plots using the min bias transformation are shown in next table:

  ttbar	variance	difference
  zbbar	variance	difference
  ztautau

• Principal components

  Netx table shows the PC's for signal and background using the PV transformation.

  ttbar	PC 1	PC 2	PC 3	PC 4	PC 5
  zbbar	PC 1	PC 2	PC 3	PC 4	PC 5
  ztautau

  Netx table shows the PC's for signal and background using the MB transformation.

  ttbar	PC 1	PC 2	PC 3	PC 4	PC 5
  zbbar	PC 1	PC 2	PC 3	PC 4	PC 5
  ztautau

  Neural Network Analysis

  We trained an ANN using JETNET package to obtain the PV probablity for a given vertex. The 5 input variables used, for zbb are shown inthe next plots:
  • sum(logPt), highest(pT), second highest(pT), average pT
  • multiplicity
  Next plot shows the neural network output for 700 PV hard vertices and 700 Min Bias vertices:
  • NN output