  Sticky hard spheres, i.e., hard particles decorated with a short-ranged
attractive interaction potential, constitute a relatively simple model with
highly non-trivial glassy dynamics. The mode-coupling theory of the glass
transition (MCT) offers a qualitative account of the complex reentrant dynamics
of sticky hard spheres, but the predicted glass transition point is notoriously
underestimated. Here we apply an improved first-principles-based theory,
referred to as generalized mode-coupling theory (GMCT), to sticky hard spheres.
This theoretical framework seeks to go beyond MCT by hierarchically expanding
the dynamics in higher-order density correlation functions -- an approach that
may become exact if sufficiently many correlations are taken into account. We
predict the phase diagrams from the first few levels of the GMCT hierarchy and
the dynamics-related critical exponents, all of which are much closer to the
empirical observations than MCT. Notably, the prominent reentrant glassy
dynamics, the glass-glass transition, and the higher-order bifurcation
singularity classes ($A_3$ and $A_4$) of sticky hard spheres are found to be
preserved within GMCT at arbitrary order. Moreover, we demonstrate that when
the hierarchical order of GMCT increases, the effect of the short-ranged
attractive interactions becomes more evident in the dynamics. This implies that
GMCT is more sensitive to subtle microstructural differences than MCT, and that
the framework provides a promising first-principles approach to systematically
go beyond the MCT regime.
