Systematic procedure for analyzing cumulants at any order

Abstract

We present a systematic procedure for analyzing cumulants to arbitrary order in the context of heavy-ion collisions. It generalizes and improves existing procedures in many respects. In particular, particles which are correlated are allowed to belong to different phase-space windows, which may overlap. It also allows for the analysis of cumulants at any order, using a simple algorithm rather than complicated expressions to be derived and coded by hand. In the case of azimuthal correlations, it automatically corrects to leading order for detector non-uniformity, and it is useful for numerous other applications as well. We discuss several of these applications: anisotropic flow, event-plane correlations, symmetric cumulants, net baryon and net charge fluctuations.

Kurtosis of elliptic flow fluctuations

“…The bottom line is that with great precision comes great discriminating power, although at the cost of increasing the statistics of hydrodynamic calculations. With the advent of LHC3 data, we expect future dedicated analyses using robust methods [50] to characterize the details of flow fluctuations, such as the kurtosis studied in this paper, with unprecedented accuracy. This will lead to novel insightful tests of the hydrodynamic picture, in the nontrivial regime where the hydrodynamic response driving anisotropic flow is strongly nonlinear.…”

Isolating dynamical net-charge fluctuations

“…Thus the dynamical cumulant of order n differs from the ordinary cumulant κ n only by terms which involve lowerorder cumulants. These subtracted terms correspond to self-correlations [34,35] and to non-dynamical correlations induced by the global conservation law. Note that the expression of d 2 in Eq.…”

“…Expressing the left-hand side as a function of N and Q using Eq. (12) and expanding to order z 4 , one obtains the explicit expressions [34][35][36]:…”

“…Selfcorrelations are not true correlations [22] and subtracting them does not change the physics one wishes to probe with cumulants. They are routinely subtracted in analyses of anisotropic flow [34,37]. Our point in this paper is that they should also be subtracted in analyses of netcharge fluctuations.…”

“…On the technical side, note that the subtracted terms in Eq. (6) are themselves cumulants [34] of the distribution of Q or N (such as N 2 − N 2 ) or mixed cumulants involving both Q and N . Note also that…”