Lattice QCD computations of two-hadron scattering amplitudes typically employ the volume dependence of individual two-hadron states.
While this has worked well below inelastic thresholds, the extension to higher center-of-mass energies has proved difficult.
A recently-proposed alternative approach does not employ the finite volume at all but instead relies on spectral densities of temporal
correlation functions to bridge the gap between Euclidean and Minkowski time.
After outlining the general framework, a simple test case is presented, in which a real-time inclusive scattering processes is determined from
the spectral function of a Euclidean two-point correlation function in the two-dimensional O(3) model. The difficult inverse problem is
overcome by computing the desired spectral function smeared with a variety of finite-width kernels. Systematic errors due to the finite volume,
continuum limit, and spectral reconstruction are demonstrably controlled, enabling a determination of the inclusive rate at energies exceeding
the four-particle production threshold by extrapolation to the zero-smearing-width limit. Everything discussed here is (in principle) applicable
in QCD to determine similar inclusive rates such as the R-ratio.
