Why Simple Stellar Population models do not reproduce the colours of
  Galactic open clusters
  (...) We search for an explanation of the disagreement between the observed
integrated colours of 650 local Galactic clusters and the theoretical colours
of present-day SSP models. We check the hypothesis that the systematic offsets
between observed and theoretical colours, which are $(B$$-$$V)\approx 0.3$ and
$(J$$-$$K_s)\approx 0.8$, are caused by neglecting the discrete nature of the
underlying mass function. Using Monte Carlo simulations, we construct
artificial clusters of coeval stars taken from a mass distribution defined by
an Salpeter initial mass function (IMF) and compare them with corresponding
"continuous-IMF" SSP models. If the discreteness of the IMF is taken into
account, the model fits the observations perfectly and is able to explain
naturally a number of red "outliers" observed in the empirical colour-age
relation. We find that the \textit{systematic} offset between the continuous-
and discrete-IMF colours reaches its maximum of about 0.5 in $(B$$-$$V)$ for a
cluster mass $M_c=10^2 m_\odot$ at ages $\log t\approx 7$, and diminishes
substantially but not completely to about one hundredth of a magnitude at $\log
t >7.9$ at cluster masses $M_c> 10^5 m_\odot$. At younger ages, it is still
present even in massive clusters, and for $M_c \leqslant 10^4 m_\odot$ it is
larger than 0.1 mag in $(B$$-$$V)$. Only for very massive clusters ($M_c>10^6
m_\odot$) with ages $\log t< 7.5$ is the offset small (of the order of 0.04
mag) and smaller than the typical observational error of colours of
extragalactic clusters.
