Efficient formulas for efficiency correction of cumulants

TL;DR

This paper introduces efficient formulas to correct cumulants for particle detection efficiency losses, accommodating multiple efficiencies and realistic pT-dependent efficiencies, significantly reducing computational costs.

Contribution

It provides a new set of formulas based on the binomial model that simplifies and accelerates efficiency corrections for cumulants in particle physics experiments.

Findings

Formulas connect observed and original cumulants under efficiency losses.

Reduction in numerical cost for high-order cumulant corrections.

Applicability to realistic pT-dependent efficiency scenarios.

Abstract

We derive formulas which connect cumulants of particle numbers observed with efficiency losses with the original ones based on the binomial model. These formulas can describe the case with multiple efficiencies in a compact form. Compared with the presently suggested ones based on factorial moments, these formulas would drastically reduce the numerical cost for efficiency corrections when the order of the cumulant and the number of different efficiencies are large. The efficiency correction with realistic $p_T$-dependent efficiency would be carried out with the aid of these formulas.