  A major objective of the strong ongoing drive to realize quantum simulators
of gauge theories is achieving the capability to probe collider-relevant
physics on them. In this regard, a highly pertinent and sought-after
application is the controlled collisions of elementary and composite particles,
as well as the scattering processes in their wake. Here, we propose
particle-collision experiments in a cold-atom quantum simulator for a $1+1$D
$\mathrm{U}(1)$ lattice gauge theory with a tunable topological $\theta$-term,
where we demonstrate an experimentally feasible protocol to impart momenta to
elementary (anti)particles and their meson composites. We numerically benchmark
the collisions of moving wave packets for both elementary and composite
particles, uncovering a plethora of rich phenomena, such as oscillatory string
dynamics in the wake of elementary (anti)particle collisions due to
confinement. We also probe string inversion and entropy production processes
across Coleman's phase transition through far-from-equilibrium quenches. We
further demonstrate how collisions of composite particles unveil their internal
structure. Our work paves the way towards the experimental investigation of
collision dynamics in state-of-the-art quantum simulators of gauge theories,
and sets the stage for microscopic understanding of collider-relevant physics
in these platforms.
