Correction methods for finite-acceptance effects in two-particle correlation analyses

Two-particle angular correlations have been widely used as a tool to explore particle production mechanisms in heavy-ion collisions. The mixed-event technique is generally used as a standard method to correct for finite-acceptance effects. We demonstrate that event mixing only provides an approximate acceptance correction, and propose new methods for finite-acceptance corrections. Starting from discussions about 2-dimensional correction procedures, new methods are derived for specific assumptions on the properties of the signal, such as uniform signal distribution or $\delta$-function-like trigger particle distribution, and suitable for two-particle correlation analyses from particles at mid-rapidity and jet-hadron or high $p_{\text{T}}$-triggered hadron-hadron correlations. Per-trigger associated particle yields from the mixed-event method and the new methods are compared through Monte Carlo simulations containing well-defined correlation signals. Significant differences are observed at large pseudorapidity differences in general and especially for asymmetric particle distribution like that produced in proton--nucleus collisions. The applicability and validity of the new methods are discussed in detail.