Event mixing does not reproduce single particle acceptance convolutions for nonuniform pseudorapidity distributions

TL;DR

This paper demonstrates that the commonly used event mixing method for acceptance correction is invalid when the pseudorapidity distribution is nonuniform, impacting the interpretation of long-range correlations in high-energy collisions.

Contribution

It clarifies the correct form of acceptance correction as a convolution of single-particle efficiencies, highlighting the limitations of the mixed-event method in certain conditions.

Findings

Mixed-event method is inaccurate for nonuniform pseudorapidity distributions.

Correct acceptance correction is the convolution of single-particle efficiencies.

Proper correction can reveal long-range correlations in collision data.

Abstract

We point out that the mixed-event method for two-particle acceptance correction, widely used in particle correlation measurements at RHIC and LHC, is wrong in cases where the single particle pseudorapidity distribution is significantly nonuniform. The correct acceptance should be the convolution of two single-particle efficiency$\times$acceptance functions. The error of the mixed-event method, which guarantees a uniform $\Delta\eta$ two-particle combinatorial density, is, however, small in correlation analyses where the two particles are integrated over an extended pseudorapidity $\eta$ range. With one particle fixed in $\eta$ and the right acceptance correction, the background-subtracted correlated pair density may reveal not only a short-range but also a long-range $\Delta\eta$ dependence. This has important physics implication, and may provide crucial information to disentangle physics mechanisms for the recently observed long-range ridge correlation in asymmetric proton-lead collisions at the LHC.