Scattering of mesons in quantum simulators

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 extreme conditions prohibitive for direct experiments. In this work, we demonstrate that present-day quantum simulators can give access to S-matrix measurements of elastic and inelastic meson collisions in Abelian gauge theories, mimicking experiments with linear particle accelerators. Considering for definiteness a $(1 + 1)$-dimensional $\mathbb{Z}_2$-lattice gauge theory realizable with Rydberg-atom arrays, we solve the meson scattering problem exactly for large fermion mass and arbitrary coupling strength. This allows us to compute the amplitudes of scattering channels, in which new mesons with different internal structures may be produced. Our numerical simulations of realistic wavepackets collisions reproduce the predicted cross section peaks. We discuss experimental protocols to observe and measure these phenomena.