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Binned and Unbinned Transverse Single Spin Asymmetry Extraction, including Background Subtraction and Unfolding

S. F Pate, H. Arachchige, C. Kuruppu, D. Nawarathne

Abstract

The determination of transverse single-spin asymmetries in experiments involving polarized targets and/or beams may encounter challenges when (1) the magnitude of the polarization varies greatly with time, (2) the polarization magnitude is not the same for each spin state, (3) different integrated luminosities occur for different spin states or different target materials, and/or (4) some kinematic variables require unfolding; these are just a few examples. We present general methods of determining the asymmetry based on both binned analysis and unbinned maximum likelihood optimization, incorporating the unfolding of kinematic variables that are smeared by detector effects, and also including the possibility of background subtraction.

Binned and Unbinned Transverse Single Spin Asymmetry Extraction, including Background Subtraction and Unfolding

Abstract

The determination of transverse single-spin asymmetries in experiments involving polarized targets and/or beams may encounter challenges when (1) the magnitude of the polarization varies greatly with time, (2) the polarization magnitude is not the same for each spin state, (3) different integrated luminosities occur for different spin states or different target materials, and/or (4) some kinematic variables require unfolding; these are just a few examples. We present general methods of determining the asymmetry based on both binned analysis and unbinned maximum likelihood optimization, incorporating the unfolding of kinematic variables that are smeared by detector effects, and also including the possibility of background subtraction.
Paper Structure (15 sections, 28 equations, 5 figures, 6 tables)

This paper contains 15 sections, 28 equations, 5 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Binned Estimation of the Asymmetry: without Unfolding
  3. Unbinned Estimation of the Asymmetry: without Unfolding
  4. Experimental Weights Correcting for Luminosity and/or Polarization Imbalances
  5. Approximation of the Log-Likelihood for Small Asymmetries
  6. Unbinned Log-Likelihood when a Background must be Subtracted
  7. Generating Events to Test the Method
  8. Results of Test of the Method
  9. Binned Analysis
  10. Unbinned Log-likelihood Analysis
  11. Unfolding: Binned and Unbinned
  12. Likelihood Ratio Estimation Using Event Classification
  13. Unbinned Unfolding with OmniFold
  14. Conclusions
  15. Acknowledgments

Figures (5)

  • Figure 1: Reweighted distributions using the likelihood ratio method. The blue line represents the source distribution, the filled area indicates the target distribution, and the dashed green line shows the reweighted source distribution with weights calculated using equation \ref{['likelihood']}.
  • Figure 2: Statistical and model uncertainties.
  • Figure 3: Diagram illustrating the OmniFold technique. Taken from Andreassen:2019cjw.
  • Figure 4: Rates of convergence of the unbinned log-likelihood TSSA extraction. The case of weak smearing is illustrated on the top, strong smearing on the bottom. Each color (black, red, blue, etc.) represents a statistically independent set of data used to test the unfolding, and in all cases the embedded value of the asymmetry was $A_N=0.2$.
  • Figure 5: Examples of histograms of results of 50 tests of the unfolding and analysis methods. Left to right are the cases of binned unfolding of binned data (analysis method 1), unbinned unfolding followed by binned analysis (method 2), and unbinned unfolding followed by log-likelihood analysis (method 3). The test sample in these cases was "pol/lumi imbalance" and strong smearing was used.