Unfolding

For the low mass Drell-Yan analysis in 1D the purities are very high so unfolding can be done using a bin by bin method. However when measuring in 2D dimensions the purities are lower and other methods may be needed. For this preliminary study I have split a monte carlo in half to use one half as MC for corrections and the other half as pseudo data to be corrected. Then a bias was created in the reconstruction to see if the correction methods are sufficient. For the three variables two bias terms were added, one proportional to the variable and and one just as a number. For mass and Pt there was a 5% increase proportional to the mass or pt and 1GeV additional term. For rapidity there was again a 5% increase proportional to the rapidity but now with a 0.1 increase in rapidity.

1fb Binning Scheme

The bin by bin unfolding for the mass, rapidity and pt spectrums are shown for the 1fb binning scheme below.

• Mass Spectrum
• Rapidity Spectrum
• Pt Spectrum

With the corrections applied to each bin showed here

• Mass Corrections
• Rapidity Corrections
• Pt Corrections

Using the in built class TUnfold a chi squared minimisation method can be used to unfold the data an the resulting spectrums are given below

• Mass Spectrum
• Rapidity Spectrum
• Pt Spectrum

Smaller Binning scheme

The bin by bin unfolding for the mass, rapidity and pt spectrums are shown for the smaller binning scheme below.

• Mass Spectrum
• Rapidity Spectrum
• Pt Spectrum

With the corrections applied to each bin showed here

• Mass Corrections
• Rapidity Corrections
• Pt Corrections

The TUnfold unfolding is show below

• Mass Spectrum
• Rapidity Spectrum
• Pt Spectrum

Varying the Regularisation Parameter

One of the inputs into the TUnfold function is a regularisation parameter. The regularisation parameter determines the relative weight placed on the data, compared to the MC truth used for the response matrix. Small values of tau bias the unfolded distribution towards the data and large values bias it towards the MC truth scaled by another parameter the bias scale.

For the mass spectrum three unfolded distributions with varying taus have been plotted below

• Mass Spectrum (varying tau)

Most of whats happing in the plot cannot be seen due to the distributions lying on top of each other. For Tau = 1E-2 the distribution lies exactly on top of the MC truth. The distributions for Tau = 1E-6 and 1E-10 are on top of each other as well, apart from the high mass part of the spectrum. As you tend to one from tau = 1E-2 the distribution just matches the MC truth more perfectly. As you tend to zero from tau = 1E-10 the distribution doesn't change.

The effect of varying tau on the Pt spectrum is even less pronounced and is shown below.

• Pt Spectrum (varying tau)

Again the Tau = 1E-10 distribution is hidden by the Tau = 1E-06 distribution and the Tau = 1E-02 matches almost perfectly with the truth distribution

Varying Tau Within Individual Bins

The value of Tau was plotted against the number events for the mass bins 14-16 and 50-52 GeV. For Tau = 1 the truth value of the MC is plotted as this is how the data should be biased. The statistical error in the bins vs tau is also shown.

• Varying tau in specific bins

-- RobertHickling - 31-Oct-2011