Non-Gaussian transverse momentum fluctuations from impact parameter fluctuations

The transverse momentum per particle, [pt], fluctuates event by event in ultrarelativistic nucleus-nucleus collisions, for a given multiplicity. These fluctuations are small and approximately Gaussian, but a nonzero skewness has been predicted on the basis of hydrodynamic calculations, and seen experimentally. We argue that the mechanism driving the skewness is that, if the system thermalizes, the mean transverse momentum increases with impact parameter for a fixed collision multiplicity. We postulate that fluctuations are Gaussian at fixed impact parameter, and that non-Gaussianities solely result from impact parameter fluctuations. Using recent data on the variance of [pt] fluctuations, we make quantitative predictions for their skewness and kurtosis as a function of the collision multiplicity. We predict, in particular, a spectacular increase of the skewness below the knee of the multiplicity distribution, followed by a fast decrease.

Automated summary

In ultrarelativistic nucleus-nucleus collisions, the transverse momentum per particle fluctuates event by event for a given multiplicity. These fluctuations have been predicted and observed to have nonzero skewness, in addition to being small and approximately Gaussian. We propose that the skewness is driven by the increase of the mean transverse momentum with impact parameter, assuming that fluctuations are Gaussian at a fixed impact parameter and non-Gaussianities result solely from impact parameter fluctuations. Based on recent data, we make quantitative predictions for the skewness and kurtosis of the transverse momentum fluctuations as a function of collision multiplicity, particularly predicting a remarkable increase of the skewness below the knee of the multiplicity distribution followed by a rapid decrease.