  The luminosity functions (LFs) of star cluster systems (i.e. the number of
clusters per luminosity interval) are vital diagnostics to probe the conditions
of star cluster formation. Early studies have revealed a clear dichotomy
between old globular clusters and young clusters, with the former characterised
by Gaussian-shaped LFs, and the latter following a power law. Recently, this
view was challenged by studies of galaxy merger remnants and post-starburst
galaxies. In this paper we re-evaluate the young ($\lta$ few hundreds of Myrs,
with the majority $\lta$ few tens of Myrs) star cluster system in the ongoing
spiral-spiral major merger system NGC 4038/39, the "Antennae" galaxies. The
Antennae galaxies represent a very active and complex star-forming environment,
which hampers cluster selection and photometry as well as the determination of
observational completeness fractions. A main issue of concern is the large
number of bright young stars contained in most earlier studies, which we
carefully exclude from our cluster sample by accurately determining the source
sizes. The resulting LFs are fitted both with Gaussian and with power-law
distributions, taking into account both the observational completeness
fractions and photometric errors, and compared using a likelihood ratio test.
The likelihood ratio results are rigidly evaluated using Monte Carlo
simulations. We perform a number of additional tests, e.g. with subsets of the
total sample, all confirming our main result: that a Gaussian distribution fits
the observed LFs of clusters in this preferentially very young cluster system
significantly better than a power-law distribution, at a (statistical) error
probability of less than 0.5 per cent.
