  Large amplitude Alfv\'en waves tend to be unstable to parametric
instabilities which result in a decay process of the initial wave into
different daughter waves depending upon the amplitude of the fluctuations and
the plasma beta. The propagation angle with respect to the mean magnetic field
of the daughter waves plays an important role in determining the type of decay.
In this paper, we revisit this problem by means of multi-dimensional hybrid
simulations. In particular, we study the decay and the subsequent nonlinear
evolution of large-amplitude Alfv\'en waves by investigating the saturation
mechanism of the instability and its final nonlinear state reached for
different wave amplitudes and plasma beta conditions. As opposed to
one-dimensional simulations where the Decay instability is suppressed for
increasing plasma beta values, we find that the decay process in
multi-dimensions persists at large values of the plasma beta via the
filamentation/magnetosonic decay instabilities. In general, the decay process
acts as a trigger both to develop a perpendicular turbulent cascade and to
enhance mean field-aligned wave-particle interactions. We find indeed that the
saturated state is characterized by a turbulent plasma displaying a
field-aligned beam at the Alfv\'en speed and increased temperatures that we
ascribe to the Landau resonance and pitch angle scattering in phase space.
