  Observations of young star clusters reveal that the high-mass end of the
cluster initial mass function (CIMF) deviates from a pure power-law and instead
truncates exponentially. We investigate the effects of this truncation on the
formation of globular cluster (GC) systems by updating our analytic model for
cluster formation and evolution, which is based on dark matter halo merger
trees coupled to empirical galactic scaling relations, and has been shown in
previous work to match a wide array of observational data. The cutoff masses of
$M_c=10^{6.5} M_{\odot}$ or $10^{7}M_{\odot}$ match many scaling relations:
between the GC system mass and host halo mass, between the average metallicity
of the GC system and host halo mass, and the distribution of cluster masses.
This range of $M_c$ agrees with indirect measurements from extragalactic GC
systems. Models with $M_c<10^{6.5}M_{\odot}$ cannot reproduce the observed GC
metallicity and mass distributions in massive galaxies. The slope of the
mass-metallicity relation for metal-poor clusters (blue tilt) for all $M_c$
models is consistent with observations within their errors, when measured using
the same method. We introduce an alternative, more robust fitting method, which
reveals a trend of increasing tilt slope for lower $M_c$. In our model the blue
tilt arises because the metal-poor clusters form in relatively low-mass
galaxies which lack sufficient cold gas to sample the CIMF at highest masses.
Massive blue clusters form in progressively more massive galaxies and inherit
their higher metallicity. The metal-rich clusters do not exhibit such a tilt
because they form in significantly more massive galaxies, which have enough
cold gas to fully sample the CIMF.
