Hadronic scattering in (1+1)D SU(2) lattice gauge theory from tensor networks

We present a first real-time study of hadronic scattering in a (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques. Working in the gaugeless Hamiltonian formulation -- where the gauge field is exactly integrated out and no truncation of the electric flux is required -- we investigate scattering processes across sectors of fixed global baryon number $B = 0, 1, 2$. These correspond respectively to meson-meson, meson-baryon, and baryon-baryon collisions. At strong coupling, the $B = 0$ and $B = 2$ channels exhibit predominantly elastic dynamics closely resembling those of the U(1) Schwinger model. In contrast, the mixed $B = 1$ sector shows qualitatively new behavior: meson and baryon wave packets become entangled during the collision, and depending on their initial kinematics, the slower state becomes spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information-lattice, which together reveal how correlations build up and relax during the interaction. Our results establish a first benchmark for non-Abelian real-time scattering from first principles and open the path toward quantum-simulation studies of baryon-number dynamics and inelastic processes in gauge theories.