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

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.