Discretization effects in finite-volume $2\to2$ scattering

We incorporate non-zero lattice-spacing effects into L\"uscher's finite-volume scattering formalism. The new quantization condition takes lattice energies as input and returns a version of the discretized scattering amplitude whose definition is transparent in the context of Symanzik Effective Theory. In contrast to the standard formalism, this approach uses single-hadron discretization effects to define modified versions of the finite-volume zeta functions. The new formalism requires two sets of angular-momentum indices, which encode the ultraviolet mixing of angular momentum states (due to the lattice spacing), in addition to the well-known infrared mixing (due to the finite volume).