  Simulating real-time evolution in theories of fundamental interactions
represents one of the central challenges in contemporary theoretical physics.
Cold-atom platforms stand as promising candidates to realize quantum
simulations of non-perturbative phenomena in gauge theories, such as vacuum
decay and hadron collisions, in prohibitive conditions for direct experiments.
In this work, we demonstrate that present-day quantum simulators can imitate
linear particle accelerators, giving access to S-matrix measurements of elastic
and inelastic meson collisions in low-dimensional Abelian gauge theories.
Considering for definiteness a $(1+1)$-dimensional $\mathbb{Z}_2$-lattice gauge
theory realizable with Rydberg-atom arrays, we present protocols to observe and
measure selected meson-meson scattering processes. We provide a benchmark
theoretical study of scattering amplitudes in the regime of large fermion mass,
including an exact solution valid for arbitrary coupling strength. This allows
us to discuss the occurrence of inelastic scattering channels, featuring the
production of new mesons with different internal structures. We present
numerical simulations of realistic wavepacket collisions, which reproduce the
predicted cross section peaks. This work highlights the potential of quantum
simulations to give unprecedented access to real-time scattering dynamics.
