Multiparticle integral and differential correlation functions

This paper formalizes the use of integral and differential cumulants for measurements of multiparticle event-by-event transverse momentum fluctuations, rapidity fluctuations, as well as net-charge fluctuations. This enables the introduction of multiparticle balance functions, defined based on differential correlation functions (factorial cumulants), that suppress two- and three-prong resonance decays effects and enable measurements of underlying long-range correlations obeying quantum number conservation constraints. These multiparticle balance functions satisfy simple sum rules determined by quantum number conservation. It is additionally shown that these multiparticle balance functions arise as an intrinsic component of high-order net-charge cumulants. This implies that the magnitude of these cumulants, measured in a specific experimental acceptance, is strictly constrained by charge conservation and primarily determined by the rapidity and momentum width of these balance functions. The paper also presents techniques to reduce the computation time of differential correlation functions up to order $n=10$ based on the methods of moments.

Figure 1

Schematic illustrations of four-particle correlation analyses involving a finite rapidity gap to suppress resonance decays and other short-range correlations. The horizontal and vertical axes $\eta$ and $\phi$, respectively, denote the pseudorapidity and azimuthal coordinates of measured particles. Gray areas schematically indicate the azimuthal ($\phi$) and pseudorapidity ($\eta$) acceptance of measurements. Panels (a, b) illustrate measurement involving negatively and positively charged particles in valid unlike sign combinations into two distinct ranges of pseudorapidity (full azimuthal coverage) separated by a rapidity gap $\mathrm{\Delta }\eta$. Panels (c, d) illustrate four-particle inclusive correlation measurements involving a finite rapidity gap and a specific coverage in azimuth, which enable acceptance configurations sensitive to (c) back-to-back particle production or (d) out-of-back-to-back emission.

Figure 2

Examples of measurements involving a $\overline{\mathrm{\Lambda }}$ antibaryon and a proton in rapidity partition A with (a) a ${\mathrm{\Xi }}^{-}$ baryon and a neutral $\overline{\mathrm{\Lambda }}$ antibaryon or (b) an ${\mathrm{\Omega }}^{-}$ baryon and a ${\overline{\mathrm{\Xi }}}^{+}$ antibaryon in partition B. The horizontal and vertical axes $\eta$ and $\varphi$, respectively, denote the pseudorapidity and azimuthal coordinates of measured particles. Gray areas schematically indicate the azimuthal ($\phi$) and pseudorapidity ($\eta$) acceptance of measurements.