  Kinetic facilitated models and the Mode Coupling Theory (MCT) model B are
within those systems known to exhibit a discontinuous dynamical transition with
a two step relaxation. We consider a general scaling approach, within mean
field theory, for such systems by considering the behavior of the density
correlator <q(t)> and the dynamical susceptibility <q^2(t)> -<q(t)>^2. Focusing
on the Fredrickson and Andersen (FA) facilitated spin model on the Bethe
lattice, we extend a cluster approach that was previously developed for
continuous glass transitions by Arenzon et al (Phys. Rev. E 90, 020301(R)
(2014)) to describe the decay to the plateau, and consider a damage spreading
mechanism to describe the departure from the plateau. We predict scaling laws,
which relate dynamical exponents to the static exponents of mean field
bootstrap percolation. The dynamical behavior and the scaling laws for both
density correlator and dynamical susceptibility coincide with those predicted
by MCT. These results explain the origin of scaling laws and the universal
behavior associated with the glass transition in mean field, which is
characterized by the divergence of the static length of the bootstrap
percolation model with an upper critical dimension d_c=8.
