Intermittency, the empty bin effect and uncertainty in factorial moments

Abstract

The measurement of factorial moments depends strongly on the high-multiplicity tail of the underlying multiplicity distribution. When the number of events is finite, the multiplicity distribution is truncated, leading in some cases to a significant decrease of measured factorial moments compared to their true values and thus complicating the interpretation of experimental data. We calculate the conditions for the occurrence of this so called “empty bin effect”, and, using the negative binomial distribution, give an example how to estimate its size. For present NA22 parameters, we find little distortion except possibly in the fifth order moment. Theoretical analyses and experimental estimates of error should take the empty bin effect into account explicitly before attempting some conclusion, especially in the case of ongoing and future two- and three-dimensional analyses where the average multiplicity per bin decreases much faster.