Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Efficiency correction of particle-averaged quantities

Masakiyo Kitazawa, ShinIchi Esumi, Takafumi Niida, Toshihiro Nonaka

TL;DR

The paper develops analytic formulas to reconstruct particle-averaged observables and their higher-order correlators from data affected by detector efficiency, assuming independent observation probabilities. It presents uniform- and multi-bin efficiency corrections, as well as per-particle corrections, expressed through generating-function-based integrals and sums. The key finding is that these analytic corrections do not, in general, match conventional intuitive formulas, with validation provided in simple models. The work offers a transparent alternative to unfolding methods and lays groundwork for practical, numerically tractable corrections in event-by-event analyses of heavy-ion and related experiments.

Abstract

We derive analytic formulas to reconstruct particle-averaged quantities from experimental results that suffer from the efficiency loss of particle measurements. These formulas are derived under the assumption that the probabilities of observing individual particles are independent. The formulas do not agree with the conventionally used intuitive formulas.

Efficiency correction of particle-averaged quantities

TL;DR

The paper develops analytic formulas to reconstruct particle-averaged observables and their higher-order correlators from data affected by detector efficiency, assuming independent observation probabilities. It presents uniform- and multi-bin efficiency corrections, as well as per-particle corrections, expressed through generating-function-based integrals and sums. The key finding is that these analytic corrections do not, in general, match conventional intuitive formulas, with validation provided in simple models. The work offers a transparent alternative to unfolding methods and lays groundwork for practical, numerically tractable corrections in event-by-event analyses of heavy-ion and related experiments.

Abstract

We derive analytic formulas to reconstruct particle-averaged quantities from experimental results that suffer from the efficiency loss of particle measurements. These formulas are derived under the assumption that the probabilities of observing individual particles are independent. The formulas do not agree with the conventionally used intuitive formulas.
Paper Structure (15 sections, 77 equations, 1 figure)

This paper contains 15 sections, 77 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Definition of the problem and summary of the results
  3. Quantities to be investigated
  4. Assumptions and results
  5. Correction for averages
  6. Uniform efficiency
  7. Multiple efficiencies
  8. Comments
  9. Higher order correlations
  10. Uniform efficiency
  11. Multiple efficiencies
  12. Discussions
  13. Reconstruction of $\langle 1/N\rangle$
  14. Check of Eq. \ref{['eq:1/N=K']}
  15. Efficiency correction in a simple model

Figures (1)

  • Figure B1: Reconstructed value with the conventional formula \ref{['eq:<<pm>>']} for $N_+=N_-=N/2$ and $r_+=1$ as a function of $r_-$ for three values of $N$.